%!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: phd.dvi %%Pages: 91 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: LucidaBright LucidaBright-Demi LucidaNewMath-AltItalic %%+ LucidaNewMath-Symbol LucidaBright-Oblique LucidaSans-Typewriter %%+ LucidaNewMath-Extension LucidaNewMath-Arrows LucidaBright-Italic %%+ LucidaSans %%DocumentPaperSizes: a4 %%EndComments %DVIPSCommandLine: dvips phd -o phd.ps %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 1996.12.13:0932 %%BeginProcSet: texc.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{ /nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{ /sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0] N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{ 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 sub]/id ch-image N /rw ch-width 7 add 8 idiv string N /rc 0 N /gp 0 N /cp 0 N{rc 0 ne{rc 1 sub /rc X rw}{G}ifelse}imagemask restore}B /G{{id gp get /gp gp 1 add N dup 18 mod S 18 idiv pl S get exec}loop}B /adv{cp add /cp X}B /chg{rw cp id gp 4 index getinterval putinterval dup gp add /gp X adv}B /nd{/cp 0 N rw exit}B /lsh{rw cp 2 copy get dup 0 eq{pop 1}{ dup 255 eq{pop 254}{dup dup add 255 and S 1 and or}ifelse}ifelse put 1 adv}B /rsh{rw cp 2 copy get dup 0 eq{pop 128}{dup 255 eq{pop 127}{dup 2 idiv S 128 and or}ifelse}ifelse put 1 adv}B /clr{rw cp 2 index string putinterval adv}B /set{rw cp fillstr 0 4 index getinterval putinterval adv}B /fillstr 18 string 0 1 17{2 copy 255 put pop}for N /pl[{adv 1 chg} {adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{ adv rsh nd}{1 add adv}{/rc X nd}{1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]dup{bind pop}forall N /D{/cc X dup type /stringtype ne{] }if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{ cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict /eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false} ifelse}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail {dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M} B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{ 4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{ p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end %%EndProcSet %%BeginFont: LucidaBright % Lucida is a registered trademark of Bigelow & Holmes Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.008) readonly def /Notice ((c) 1991, 1992 Bigelow & Holmes Inc. Pat. Des. 289,421. All Rights Reserved.) readonly def /Notice ((c) 1991, 1992 Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida Bright) readonly def /FamilyName (LucidaBright) readonly def /Weight (Normal) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaBright def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding StandardEncoding def /FontBBox{-286 -211 1014 967}readonly def /UniqueID 5029001 def currentdict end currentfile eexec 8053514D28EC28DA1630165FAB262882D3FCA78881823C5537FE6C3DDA8EE5B897E17CB027F5C7 3FDBB56B0A7C25FC3512B55FE8F3ACFBFFCC7F4A382D8299CC8FD37D3CEA49DABDCA92847AF056 0B404EF71134B0F3D99934FC9D0B4E602011B9CFB856C23F958F3C5A2FBE0EF8587D1F5774879C 324E51FCB22888B74F241550D7401EB990D4F3A7AF635198422283CAC1B6CD446DDBCBD915DB9B FF88844E784C6BF7389803D9450B0C21756A0173064625F1E0957F287025663FF0BF93EC8CECBC 40B196AD90237A1F1675C6BF97A5A9B9097D7CC374C1F4410B68AF93D9DBB0A73311883AE45CD3 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cleartomark %%EndFont %%BeginFont: LucidaBright-Demi % Lucida is a registered trademark of Bigelow & Holmes Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.008) readonly def /Notice ((c) 1991, 1992 Bigelow & Holmes Inc. Pat. Des. 289,422. All Rights Reserved.) readonly def /Notice ((c) 1991, 1992 Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida Bright Demibold) readonly def /FamilyName (LucidaBright) readonly def /Weight (DemiBold) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaBright-Demi def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding StandardEncoding def /FontBBox{-287 -205 1122 967}readonly def /UniqueID 5029002 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D7190FA2D133A583138F76695558E7AE9348D37CAC665 1806D08527C1BB4A062A4835AC37784CC39AD8841404E438B4D52D3901E47A1DE4F7924E0FB3DA F442499175BAB1226EDF692A4956739F8828E80592F450C5D5C22AC88BCFBE9748F61D18243A16 F4A4467F084E8E2BE46EF47FC51C3A8199E3CDA62FF9C4FB73956DAB8B6683D2156377808CB350 26073E80523F59A30D195FCF9B9FCE4FFAFFF195AA1C31AE164F9B6A929E4FF5745A1B209465B8 F86647C0AB8C6B230BB1560953F886AE1E4FFF2A23E837051E49434391FA09CAE11DD5E0FE812D 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cleartomark %%EndFont %%BeginFont: LucidaNewMath-AltItalic % Lucida is a registered trademark of Bigelow & Holmes Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.007) readonly def /Notice ((c) 1992, 1993 Bigelow & Holmes Inc. All Rights Reserved.) readonly def /Notice ((c) 1992, 1993 Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida New Math Alternate Italic) readonly def /FamilyName (LucidaNewMath) readonly def /Weight (Normal) readonly def /ItalicAngle -11.25 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaNewMath-AltItalic def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 128 /psi put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 129 /omicron put dup 130 /openbracketleft put dup 131 /openbracketright put dup 132 /parenleft put dup 133 /parenright put dup 134 /bracketleft put dup 135 /bracketright put dup 136 /integraldbl put dup 137 /integraltrpl put dup 138 /contintegral put dup 139 /surfintegral put dup 140 /volintegral put dup 141 /clwintegral put dup 142 /cclwcontintegral put dup 143 /clwcontintegral put dup 144 /Finv put dup 145 /Gmir put dup 146 /Omegainv put dup 147 /Euler put dup 148 /complement put dup 149 /beth put dup 150 /gimel put dup 151 /daleth put dup 152 /gscript put dup 153 /hscript put dup 154 /zscript put dup 155 /kappa1 put dup 156 /zeroslash put dup 157 /planckover2pi put dup 158 /lambdabar put dup 159 /lscriptbar put dup 160 /space put dup 171 /primereverse1 put dup 172 /forcesextra put dup 197 /original put dup 198 /image put dup 199 /multimap put dup 200 /primereverse put dup 201 /circleR put dup 202 /circleS put dup 203 /maltesecross put dup 204 /circleminus1 put dup 205 /shortsolidus put dup 206 /multicloseleft put dup 207 /multicloseright put dup 208 /multiopenleft put dup 209 /multiopenright put dup 210 /xor put dup 211 /tacktrpl put dup 212 /assertion put dup 213 /notassertion put dup 214 /truestate put dup 215 /falsestate put dup 216 /shortsolidusback put dup 217 /intercal put dup 218 /lessdblequivlnt put dup 219 /greaterdblequivlnt put dup 220 /lessdot put dup 221 /greaterdot put dup 222 /verymuchless put dup 223 /verymuchgreater put dup 224 /lessequal1 put dup 225 /greaterequal1 put dup 226 /equalless put dup 227 /equalgreater put dup 228 /precedesequal1 put dup 229 /followsequal1 put dup 230 /equalprecedes1 put dup 231 /equalfollows1 put dup 232 /lessequalgreater put dup 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: LucidaNewMath-Symbol % Lucida is a registered trademark of Bigelow & Holmes Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.003) readonly def /Notice ((c) 1992 Bigelow & Holmes Inc. All Rights Reserved.) readonly def /Notice ((c) 1992 Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida New Math Symbol) readonly def /FamilyName (LucidaNewMath) readonly def /Weight (Normal) readonly def /ItalicAngle -11.25 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaNewMath-Symbol def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 129 /radicalext put dup 130 /plus put dup 131 /equal put dup 132 /curland put dup 133 /curlor put dup 134 /increment put dup 135 /product put dup 136 /summation put dup 137 /dotplus put dup 138 /rightangle put dup 139 /angle put dup 140 /measuredangle put dup 141 /sphericalangle put dup 142 /rightanglearc put dup 143 /righttriangle put dup 144 /therefore put dup 145 /because put dup 146 /colon put dup 147 /proportion put dup 148 /dotminus put dup 149 /excess put dup 150 /geomproportion put dup 151 /homothetic put dup 152 /sine put dup 153 /minustilde put dup 154 /lessmuch1 put dup 155 /approxorequal put dup 156 /greatermuch1 put dup 157 /almostorequal put dup 158 /tildetrpl put dup 159 /allequal put dup 160 /space put dup 171 /prime1 put dup 172 /radical1 put dup 197 /lazys put dup 198 /lazysinv put dup 199 /geomequivalent put dup 200 /difference put dup 201 /approachlimit put dup 202 /geomequal put dup 203 /approxequalorimage put dup 204 /imageorapproxequal put dup 205 /colonequal put dup 206 /equalcolon put dup 207 /ringinequal put dup 208 /ringequal put dup 209 /corresponds put dup 210 /estimates put dup 211 /equiangular put dup 212 /perspcorrespond put dup 213 /deltaequal put dup 214 /definequal put dup 215 /measurequal put dup 216 /questionequal put dup 217 /strictequivalence put dup 218 /lessdblequal put dup 219 /greaterdblequal put dup 220 /lessequivlnt put dup 221 /greaterequivlnt put dup 222 /lessorgreater put dup 223 /greaterorless put dup 224 /precedequivlnt put dup 225 /followsequivlnt put dup 226 /multiset put dup 227 /multiplymultiset put dup 228 /squareimage put dup 229 /squareoriginal put dup 230 /circlering put dup 231 /circleasterisk put dup 232 /circleequal put dup 233 /circlebar put dup 234 /squareplus put dup 235 /squareminus put dup 236 /squaremultiply put dup 237 /squaredot put dup 238 /satisfy put dup 239 /satisfiedby put dup 240 /force put dup 241 /hermitconjmatrix put dup 242 /lowerrank put dup 243 /higherrank put dup 244 /triangleftequal put dup 245 /triangrightequal put dup 246 /nand put dup 247 /nor put dup 248 /subsetdbl put dup 249 /supersetdbl put dup 250 /uniondbl put dup 251 /intersectiondbl put dup 252 /negeighteenthem put dup 253 /eighteenthem put dup 254 /eighthem put dup 255 /tenthem put dup 128 /arrowleft put readonly def /FontBBox{0 -954 1260 898}readonly def /UniqueID 5029018 def currentdict end currentfile eexec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Pat. Des. 289,421. All Rights Reserved.) readonly def /Notice ((c) 1991, 1992 Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida Bright Oblique) readonly def /FamilyName (LucidaBright) readonly def /Weight (Normal) readonly def /ItalicAngle -11.3 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaBright-Oblique def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0.0002 0.001 0 0] readonly def /Encoding StandardEncoding def /FontBBox{-286 -211 1014 967}readonly def /UniqueID 5029015 def currentdict end currentfile eexec 8053514D28EC28DA1630165FAB262882D3FCA78881823C5537FE6C3DDA8EE5B897E17CB027F5C7 3FDBB56B0A7C25FC3512B55FE8F3ACFBFFCC7F4A382D8299CC8FD37D3CEA49DABDCA92847AF056 0B404EF71134B0F3D99934FC9D0B4E602011B9CFB856C23F958F3C5A2FBE0EF8587D1F5774879C 324E51FCB22888B74F241550D7401EB990D4F3A7AF635198422283CAC1B6CD446DDBCBD915DB9B FF88844E784C6BF7389803D9450B0C21756A0173064625F1E0957F287025663FF0BF93EC8CECBC 40B196AD90237A1F1675C6BF97A5A9B9097D7CC374C1F4410B68AF93D9DBB0A73311883AE45CD3 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: LucidaSans-Typewriter % Lucida is a registered trademark of Bigelow & Holmes Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.003) readonly def /Notice ((c) 1991 Bigelow & Holmes Inc. Pat. Des. 289,422. All Rights Reserved.) readonly def /Notice ((c) 1991, 1992 by Y&Y, Inc. All Rights Reserved.) readonly def /FullName (Lucida Sans Typewriter) readonly def /FamilyName (LucidaSansTypewriter) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaSans-Typewriter def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding StandardEncoding def /FontBBox{-12 -205 618 928}readonly def /UniqueID 5029009 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D7190FA2D133A583138F76695558E7AE9348D37CAC665 1806D08527C1BB4A062A4835AC37784CC39AD8841404E438B4D52D3901E47A1DE4F7924E0FB3DA F442499175BAB1226EDF692A4956739F8828E80592F450C5D5C22AC88BCFBE9748F61D18243A16 F4A4467F084E8E2BE46EF47FC51C3A8199E3CDA62FF9C4FB73956DAB8B6683D2156377808CB350 26073E80523F59A30D195FCF9B9FCE4FFAFFF195AA1C31AE164F9B6A929E4FF572FD5D100F7E72 C3258853BB8A8928B38669590B921E9AB5CD4D604AE6C1E4E917CFFB9D25B5FDEC06E29EBCCA01 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All Rights Reserved.) readonly def /Notice ((c) 1991, 1992 Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida New Math Extension) readonly def /FamilyName (LucidaNewMath) readonly def /Weight (Normal) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaNewMath-Extension def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /parenleftbig put dup 162 /parenrightbig put dup 163 /bracketleftbig put dup 164 /bracketrightbig put dup 165 /floorleftbig put dup 166 /floorrightbig put dup 167 /ceilingleftbig put dup 168 /ceilingrightbig put dup 169 /braceleftbig put dup 170 /bracerightbig put dup 173 /angbracketleftbig put dup 174 /angbracketrightbig put dup 175 /vextendsingle put dup 176 /vextenddouble put dup 177 /slashbig put dup 178 /backslashbig put dup 179 /parenleftBig put dup 180 /parenrightBig put dup 181 /parenleftbigg put dup 182 /parenrightbigg put dup 183 /bracketleftbigg put dup 184 /bracketrightbigg put dup 185 /floorleftbigg put dup 186 /floorrightbigg put dup 187 /ceilingleftbigg put dup 188 /ceilingrightbigg put dup 189 /braceleftbigg put dup 190 /bracerightbigg put dup 191 /angbracketleftbigg put dup 192 /angbracktrightbigg put dup 193 /slashbigg put dup 194 /backslashbigg put dup 195 /parenleftBigg put dup 196 /arrowdblbt put dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 4 /floorleftbig put dup 5 /floorrightbig put dup 6 /ceilingleftbig put dup 7 /ceilingrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 14 /slashbig put dup 15 /backslashbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 22 /floorleftbigg put dup 23 /floorrightbigg put dup 24 /ceilingleftbigg put dup 25 /ceilingrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 28 /angbracketleftbigg put dup 29 /angbracktrightbigg put dup 30 /slashbigg put dup 31 /backslashbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 36 /floorleftBigg put dup 37 /floorrightBigg put dup 38 /ceilingleftBigg put dup 39 /ceilingrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 42 /angbracketleftBigg put dup 43 /angbracketrightBigg put dup 44 /slashBigg put dup 45 /backslashBigg put dup 46 /slashBig put dup 47 /backslashBig put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 54 /bracketleftex put dup 55 /bracketrightex put dup 56 /bracelefttp put dup 57 /bracerighttp put dup 58 /braceleftbt put dup 59 /bracerightbt put dup 60 /braceleftmid put dup 61 /bracerightmid put dup 62 /braceex put dup 63 /arrowvertex put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 68 /angbracketleftBig put dup 69 /angbracketrightBig put dup 70 /unionsqtext put dup 71 /unionsqdisplay put dup 72 /contintegraltext put dup 73 /contintegraldisplay put dup 74 /circledottext put dup 75 /circledotdisplay put dup 76 /circleplustext put dup 77 /circleplusdisplay put dup 78 /circlemultiplytext put dup 79 /circlemultdisplay put dup 80 /summationtext put dup 81 /producttext put dup 82 /integraltext put dup 83 /uniontext put dup 84 /intersectiontext put dup 85 /unionmultitext put dup 86 /logicalandtext put dup 87 /logicalortext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 91 /uniondisplay put dup 92 /intersectiondisplay put dup 93 /unionmultidisplay put dup 94 /logicalanddisplay put dup 95 /logicalordisplay put dup 96 /coproducttext put dup 97 /coproductdisplay put dup 98 /hatwide put dup 99 /hatwider put dup 100 /hatwidest put dup 101 /tildewide put dup 102 /tildewider put dup 103 /tildewidest put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 106 /floorleftBig put dup 107 /floorrightBig put dup 108 /ceilingleftBig put dup 109 /ceilingrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put dup 113 /radicalBig put dup 114 /radicalbigg put dup 115 /radicalBigg put dup 116 /radicalbt put dup 117 /radicalvertex put dup 118 /radicaltp put dup 119 /arrowvertexdbl put dup 120 /arrowtp put dup 121 /arrowbt put dup 122 /bracehtipdownleft put dup 123 /bracehtipdownright put dup 124 /bracehtipupleft put dup 125 /bracehtipupright put dup 126 /arrowdbltp put dup 127 /arrowdblbt put dup 130 /openbracketleftbig put dup 131 /openbracketrightbig put dup 132 /openbracketleftBig put dup 133 /openbracketrightBig put dup 134 /openbracketleftbigg put dup 135 /openbracketrightbigg put dup 136 /openbracketleftBigg put dup 137 /openbracketrightBigg put dup 138 /openbracketlefttp put dup 139 /openbracketrighttp put dup 140 /openbracketleftbt put dup 141 /openbracketrightbt put dup 142 /openbracketleftex put dup 143 /openbracketrightex put dup 144 /surfintegraltext put dup 145 /surfintegraldisplay put dup 146 /integralmid put dup 147 /contintegralmid put dup 148 /surfintegralmid put dup 149 /integraltp put dup 150 /integralbt put dup 151 /integralex put dup 159 /radical put dup 160 /space put dup 197 /hatwide1 put dup 198 /hatwider1 put dup 199 /tildewide1 put dup 200 /tildewider1 put dup 208 /Gamma put dup 209 /Delta put dup 210 /Theta put dup 211 /Lambda put dup 212 /Xi put dup 213 /Pi put dup 214 /Sigma put dup 215 /Upsilon put dup 216 /Phi put dup 217 /Psi put dup 218 /Omega put dup 252 /negeighteenthem put dup 253 /eighteenthem put dup 254 /eighthem put dup 255 /tenthem put dup 128 /parenleftBigg put readonly def /FontBBox{-20 -2707 2329 843}readonly def /UniqueID 5029019 def currentdict end 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: LucidaNewMath-Arrows % Lucida is a registered trademark of Bigelow & Holmes Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.004) readonly def /Notice ((c) 1992-1994 Bigelow & Holmes Inc. All Rights Reserved.) readonly def /Notice ((c) 1992-1994 Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida New Math Arrows) readonly def /FamilyName (LucidaNewMath) readonly def /Weight (Normal) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaNewMath-Arrows def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /circle put dup 162 /circlesolid put dup 163 /square put dup 164 /squaresolid put dup 165 /triangle put dup 166 /trianglesolid put dup 167 /triangleinv put dup 168 /triangleinvsolid put dup 169 /diamond put dup 170 /diamondsolid put dup 173 /diamondmathsolid put dup 174 /upslope put dup 175 /downslope put dup 176 /sqimageornotequal put dup 177 /sqoriginornotequal put dup 178 /unionsqdbl put dup 179 /intersectionsqdbl put dup 180 /domsubtract put dup 181 /rngsubtract put dup 182 /vertellipsis put dup 183 /midhorizellipsis put dup 184 /upslopeellipsis put dup 185 /downslopeellipsis put dup 186 /equalparallel put dup 187 /approxnotequal put dup 188 /pibond put dup 189 /starequal put dup 190 /planckover2pi1 put dup 191 /elementmacron put dup 192 /notelement put dup 193 /ownermacron put dup 194 /notowner put dup 195 /notexistential put dup 196 /notlessgreater put dup 128 /notexistential put dup 0 /circle put dup 1 /circlesolid put dup 2 /square put dup 3 /squaresolid put dup 4 /triangle put dup 5 /trianglesolid put dup 6 /triangleinv put dup 7 /triangleinvsolid put dup 8 /diamond put dup 9 /diamondsolid put dup 10 /diamondmathsolid put dup 11 /upslope put dup 12 /downslope put dup 13 /sqimageornotequal put dup 14 /sqoriginornotequal put dup 15 /unionsqdbl put dup 16 /intersectionsqdbl put dup 17 /domsubtract put dup 18 /rngsubtract put dup 19 /vertellipsis put dup 20 /midhorizellipsis put dup 21 /upslopeellipsis put dup 22 /downslopeellipsis put dup 23 /equalparallel put dup 24 /approxnotequal put dup 25 /pibond put dup 26 /starequal put dup 27 /planckover2pi1 put dup 28 /elementmacron put dup 29 /notelement put dup 30 /ownermacron put dup 31 /notowner put dup 32 /notexistential put dup 33 /arrowlongboth put dup 34 /arrowlongbothv put dup 35 /dblarrowheadleft put dup 36 /dblarrowheadup put dup 37 /dblarrowheadright put dup 38 /ampersand put dup 39 /dblarrowheaddown put dup 40 /arrowtailleft put dup 41 /arrowtailright put dup 42 /arrowbarleft put dup 43 /arrowbarup put dup 44 /arrowbarright put dup 45 /arrowext put dup 46 /arrowbardown put dup 47 /arrowtableft put dup 48 /arrowtabright put dup 49 /arrowbothvbase put dup 50 /arrowleftnot put dup 51 /arrowrightnot put dup 52 /arrowbothnot put dup 53 /arrowlongbothnot put dup 54 /headleft put dup 55 /headright put dup 56 /arrowdashleft put dup 57 /arrowdashup put dup 58 /arrowdashright put dup 59 /arrowdashdown put dup 60 /arrowhookleft put dup 61 /arrowdblext put dup 62 /arrowhookright put dup 63 /arrowloopleft put dup 64 /arrowloopright put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /brackettopnw put dup 92 /brackettopne put dup 93 /bracketbotsw put dup 94 /bracketbotse put dup 95 /arrowdblvext put dup 96 /arrowdbllongbothv put dup 97 /arrowdbllongboth put dup 98 /arrowdblnw put dup 99 /arrowdblne put dup 100 /arrowdblsw put dup 101 /arrowdblse put dup 102 /arrowdblleftnot put dup 103 /arrowdblbothnot put dup 104 /arrowdblrightnot put dup 105 /arrowdbllongbothnot put dup 106 /arrowtripleleft put dup 107 /k put dup 108 /arrowtripleright put dup 109 /arrowparrrightleft put dup 110 /arrowparrleftright put dup 111 /dblarrowupdown put dup 112 /dblarrowdownup put dup 113 /dblarrowleft put dup 114 /dblarrowup put dup 115 /dblarrowright put dup 116 /dblarrowdown put dup 117 /harpoonupright put dup 118 /harpoonupleft put dup 119 /harpoondownright put dup 120 /harpoondownleft put dup 121 /harpoonleftright put dup 122 /harpoonrightleft put dup 123 /arrowupleft put dup 124 /arrowvext put dup 125 /arrowupright put dup 126 /vectorleft put dup 127 /notlessgreater put dup 129 /arrowdownleft put dup 130 /arrowdownright put dup 131 /arrowrightdown put dup 132 /arrowleftdown put dup 133 /arrowrightup put dup 134 /arrowleftup put dup 135 /arrowsemanticlockw put dup 136 /arrowsemclockw put dup 137 /arrowsemanticlockwplus put dup 138 /arrowsemclockwminus put dup 139 /arrowanticlockw put dup 140 /arrowclockw put dup 141 /arrowsquiggleleft put dup 142 /arrowsquiggleright put dup 143 /arrowwaveleft put dup 144 /arrowwaveright put dup 145 /arrowwaveboth put dup 146 /arrowmidbarright put dup 147 /arrowzigzag put dup 148 /notequal put dup 149 /notequivalence put dup 150 /notsimilar put dup 151 /notasymptequal put dup 152 /notalmostequal put dup 153 /notapproxequal put dup 154 /notless put dup 155 /notgreater put dup 156 /notlessequal put dup 157 /notgreaterequal put dup 158 /notlessequivlnt put dup 159 /notgreaterequivlnt put dup 160 /space put dup 171 /star1 put dup 172 /checkmark put dup 197 /notgreaterless put dup 198 /notpropersubset put dup 199 /notpropersuperset put dup 200 /notreflexsubset put dup 201 /notreflexsuperset put dup 202 /notsubsetdblequal put dup 203 /notsupersetdblequal put dup 204 /subsetnotequal put dup 205 /supersetnotequal put dup 206 /subsetornotequal1 put dup 207 /supersetornotequal1 put dup 208 /notsubsetorequal put dup 209 /notsupersetorequal put dup 210 /subsetornotequal put dup 211 /supersetornotequal put dup 212 /notsubsetsqequal put dup 213 /notsupersetsqequal put dup 214 /notlessequal1 put dup 215 /notgreaterequal1 put dup 216 /notlessdblequal put dup 217 /notgreaterdblequal put dup 218 /lessnotequal put dup 219 /greaternotequal put dup 220 /lessnotdblequal put dup 221 /greaternotdblequal put dup 222 /lessnotdblequal1 put dup 223 /greaternotdblequal1 put dup 224 /lessnotequivlnt put dup 225 /periodcenteredbold put dup 226 /greaternotequivlnt put dup 227 /lessnotdblequivlnt put dup 228 /greaternotdblequivlnt put dup 229 /notpreceeds put dup 230 /notfollows put dup 231 /notpreceedsequal put dup 232 /notfollowsequal put dup 233 /preceedsnotequal put dup 234 /followsnotequal put dup 235 /preceedsnotsimilar put dup 236 /followsnotsimilar put dup 237 /preceedsnotequivlnt put dup 238 /followsnotequivlnt put dup 239 /nottriangleleft put dup 240 /nottriangleright put dup 241 /nottriangleleftequal put dup 242 /nottrianglerightequal put dup 243 /notequivasymptotic put dup 244 /notbarshort put dup 245 /notparallelshort put dup 246 /notbar put dup 247 /notbardbl put dup 248 /notturnstileleft put dup 249 /notsatisfies put dup 250 /notforces put dup 251 /notforcesextra put dup 252 /negeighteenthem put dup 253 /eighteenthem put dup 254 /eighthem put dup 255 /tenthem put readonly def /FontBBox{-114 -205 1108 964}readonly def /UniqueID 5029020 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: LucidaBright-Italic % Lucida is a registered trademark of Bigelow & Holmes Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.008) readonly def /Notice ((c) 1991, 1992 Bigelow & Holmes Inc. Pat. Des. 289,773. All Rights Reserved.) readonly def /Notice ((c) 1991, 1992 by Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida Bright Italic) readonly def /FamilyName (LucidaBright) readonly def /Weight (Normal) readonly def /ItalicAngle -15.5 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaBright-Italic def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding StandardEncoding def /FontBBox{-290 -211 1124 967}readonly def /UniqueID 5029003 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D7190FA2D133A583138F76695558E7AE9348D37CAC665 1806D08527C1BB4A062A4835AC37784CC39AD8841404E438B4D52D3901E47A1DE4F7924E0FB3DA F442499175BAB1226EDF692A4956739F8828E80592F450C5D5C22AC88BCFBE9748F61D18243A16 F4A4467F084E8E2BE46EF47FC51C3A8199E3CDA62FF9C4FB73956DAB8B6683D2156377808CB350 26073E80523F59A30D195FCF9B9FCE4FFAFFF195AA1C31AE164F9B6A929E4FF572FD5D100F7E72 C3258853BB8A8928B38669590B921E9AB5CD4D604AE6C1E4E917CFFB9D25B5FDEC06E29EBCCA01 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((c) 1992 Bigelow & Holmes Inc. Pat. Des. 289,420. All rights reserved.) readonly def /Notice ((c) 1992 by Y&Y Inc. All Rights Reserved.) readonly def /FullName (Lucida Sans Regular) readonly def /FamilyName (LucidaSans) readonly def /Weight (Normal) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /LucidaSans def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding StandardEncoding def /FontBBox{-301 -211 1006 967}readonly def /UniqueID 5029005 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D7190FA2D133A583138F76695558E7AE9348D37CAC665 1806D08527C1BB4A062A4835AC37784CC39AD8841404E438B4D52D3901E47A1DE4F7924E0FB3DA F442499175BAB1226EDF692A4956739F8828E80592F450C5D5C22AC88BCFBE9748F61D18243A16 F4A4467F084E8E2BE46EF47FC51C3A8199E3CDA62FF9C4FB73956DAB8B6683D2156377808CB350 26073E80523F59A30D195FCF9B9FCE4FFAFFF195AA1C31AE164F9B6A929E4FF572FD5D100F7E72 C3258853BB8A8928B38669590B921E9AB5CD4D604AE6C1E4E917CFFB9D25B5FDEC06E29EBCCA01 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b(since)g(the)h(pioneering)e(work)h(by)g(Slater)i(and)f(G)2209 1418 y(\302)2212 1419 y(asp)2366 1418 y(\302)2369 1419 y(ar)2460 1384 y Fz(8)2504 1419 y FE(.)106 1575 y(The)35 b(Thomas-Fermi)h(method)g(and)h(the)f(X)p FC(\013)h FE(scheme)f(were)h (at)g(the)f(time)h(of)-41 1695 y(their)e(inceptions)g(considered)f(as)i (useful)e(models)h(based)h(on)e(the)i(notion)f(that)-41 1816 y(the)28 b(energy)g(of)g(an)f(electronic)i(system)f(can)g(be)g (expressed)f(in)g(terms)h(of)f(its)g(den-)-41 1936 y(sity.)41 b(A)29 b(formal)g(proof)f(of)g(this)h(notion)f(came)i(in)f(1964,)e (when)i(it)f(was)i(shown)e(by)-41 2056 y(Hohenberg)20 b(and)f(Kohn)902 2022 y Fz(9)965 2056 y FE(that)i(the)f(ground-state)g (energy)h(of)e(an)h(electron)g(system)-41 2177 y(is)30 b(uniquely)h(de\256ned)f(by)h(its)f(density,)h(although)g(the)h(exact)f (functional)g(depen-)-41 2297 y(dence)36 b(of)f(the)h(energy)g(on)f (density)h(remains)f(unknown.)58 b(The)36 b(important)f(the-)-41 2418 y(orem)d(has)f(later)i(been)f(extended)f(to)h(degenerate)h(and)f (spin-polarised)e(ground)-41 2538 y(states)g(by)f(Levy)594 2504 y Fz(10)677 2538 y FE(.)38 b(Of)29 b(further)f(importance)h(was)g (the)g(introduction)f(of)g(a)h(set)g(of)-41 2658 y(one-electron)g (equations)g(from)e(which)g(one)h(in)f(principle)f(could)i(obtain)g (the)g(ex-)-41 2779 y(act)g(electron)f(density)f(and)g(thus)g(the)h (total)h(energy.)38 b(These)26 b(equations)g(by)h(Kohn)-41 2899 y(and)39 b(Sham)414 2865 y Fz(11)536 2899 y FE(have)f(served)g(as) h(a)g(starting)g(point)e(for)h(new)h(approximate)f(DFT)-41 3019 y(methods.)106 3176 y(The)25 b(self-consistent)h(Kohn-Sham)h (\(KS\))f(equations)h(are)f(obtained)g(by)g(a)g(vari-)-41 3296 y(ational)h(principle.)37 b(The)26 b(total)h(energy)g(of)f(the)h (system)g(is)e(written)i(as)f(a)h(sum)f(of)g(a)-41 3417 y(few)h(terms,)h(that)g(are)g(known)f(classically,)h(i.e.)e(the)i (kinetic)f(energy)h(of)f(an)g(equiv-)-41 3537 y(alent)40 b(noninteracting)e(system)h(with)f(density)g FC(\032)t(\204)p Fx(r)p FC(\205)p FE(,)i(the)f(potential)g(energy)g(in)-41 3657 y(the)27 b(external)g(potential,)g(and)e(the)i(classical)g (Coulomb)e(energy.)38 b(The)26 b(remaining)-41 3778 y(part)32 b(is)e(packed)h(into)g(a)g(common)g(term)h(called)g (exchange-correlation)h(energy,)-41 3898 y FC(E)18 3912 y FB(x)s(c)109 3898 y FE(,)25 b(which)e(incorporates)h(all)h(many-body) f(effects.)37 b(This)23 b(is)g(the)h(only)g(unknown)-41 4018 y(quantity)29 b(and)e(is)f(a)h(subject)h(of)f(approximation.)37 b(The)27 b(expression)f(for)g(the)i(total)-41 4139 y(energy)c(is)e (then)i(varied)f(with)f(respect)i(to)g(the)f(density)g(and)g(a)h(set)f (of)g(one-particle)-41 4259 y(Schr)156 4258 y(\310)156 4259 y(odinger-like)28 b(KS)h(equations)g(with)f(effective)g(potential) h(is)f(obtained.)106 4415 y(Until)33 b(mid-80s)f(the)i(exact)h (exchange-correlation)h(term)e FC(E)2490 4429 y FB(x)s(c)2615 4415 y FE(was)g(approxi-)-41 4536 y(mated)e(by)f(the)h(expression)e (for)g(the)h(exchange-correlation)i(energy)f(of)e(an)i(uni-)-41 4656 y(form)38 b(homogeneous)g(electron)h(gas.)68 b(The)37 b(exchange)i(energy)g(per)f(particle)h(in)-41 4789 y(the)j(uniform)e (gas)i FC(")797 4737 y FB(unif)795 4800 y(x)1020 4789 y FE(can)g(in)f(fact)h(be)g(calculated)h(exactly)2521 4755 y Fz(5)p FB(;)p Fz(7)2666 4789 y FE(and)f(for)f(the)-41 4910 y(correlation)32 b(energy)g(analytic)g(parametrisations)1969 4875 y Fz(12)p FE(\261)r Fz(15)2209 4910 y FE(of)f(an)g(accurate)i (Monte-)-41 5030 y(Carlo)42 b(result)503 4996 y Fz(16)629 5030 y FE(are)g(used.)79 b(These)42 b(approximations)f(are)i(commonly)f (named)-41 5150 y(Local)f(Density)f(Approximations)f(\(LDA\),)h(due)g (to)g(the)g(fact)h(that)g(only)f(a)g(local)-41 5271 y(information)35 b(about)i(the)g(electron)g(gas)f(at)h(each)g(point)f(in)f(the)i(real)g (space)g(\(i.e.)-41 5391 y FC(\032)t(\204)p Fx(r)p FC(\205)p FE(,)d(or)f(more)g(commonly)g FC(r)1165 5405 y FB(s)1204 5391 y FC(\204)p Fx(r)p FC(\205)p FE(,)g(the)h(Seitz)g(radius)e(of)h (the)g(electron\))i(is)d(used)1550 5640 y(2)p eop %%Page: 3 11 3 10 bop 555 315 3238 4 v 555 576 a FE(to)23 b(obtain)g(the)g (approximate)g(exchange-correlation)h(energy.)37 b(Even)22 b(though)h(the)555 696 y(density)k(in)f(real)i(systems)f(is)f(far)h (from)f(being)g(homogeneous)h(the)g(LDA)h(approx-)555 817 y(imation)i(works)f(quite)h(well,)g(it)f(very)h(often)g(gives)f (correct)h(qualitative)h(answers)555 937 y(about)i(the)f(studied)f (system.)49 b(The)31 b(reason)h(for)f(it)h(is)f(that)i(LDA)f(obeys)g (many)g(of)555 1057 y(the)j(exact)g(conditions)d(the)i(exact)h (exchange-correlation)h(energy)e(in)f(any)h(elec-)555 1178 y(tron)j(system)f(obeys.)62 b(Nevertheless,)38 b(this)e (approximation)g(is)f(well)i(known)e(to)555 1298 y(have)j(several)g (de\256ciencies.)65 b(It)38 b(usually)g(incorrectly)g(overbinds)e(and)h (favours)555 1419 y(too)26 b(short)f(lengths)g(of)g(the)h(chemical)g (bonds.)36 b(It)25 b(also)h(severely)g(underestimates)555 1539 y(energy)h(barrier)e(at)h(transition)f(states)i(\(or)f(even)f (gives)g(no)g(barrier\))h(and)g(predicts)555 1659 y(wrong)i(ground)g (state)i(of)e(molecules)h(and)f(crystals.)702 1780 y(Another)41 b(small)h(improvement)f(is)f(the)i(inclusion)e(of)g(spin)g(dependence) 3710 1745 y Fz(12)555 1900 y FE(\(i.e.)f(relative)29 b(spin)e(polarisation)h FC(\020)7 b(\204)p Fx(r)p FC(\205)p FE(\))29 b(into)f(the)h(approximate)f(expression)g(for)555 2021 y(the)35 b(exchange-correlation)i(energy.)57 b(The)34 b(Local)h(Spin)f(Density)h(\(LSD\))h(approx-)555 2141 y(imation)43 b(allows)f(us)h(to)f(calculate)j(the)e(properties)f(of)g (molecules)h(near)g(or)f(at)555 2261 y(dissociation)28 b(point,)f(ferromagnetic)i(materials,)g(etc.)702 2382 y(One)39 b(of)g(the)g(possible)f(ways)i(to)f(improve)f(the)i(accuracy)h (of)d(LSD)i(approxi-)555 2502 y(mation)27 b(is)e(to)i(include)e(the)i (nonlocal)g(information)e(about)i(the)f(electron)i(system)555 2622 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b(LSD)f(approximation)f(should)g(perform)555 4789 y(well)28 b(in)e(systems)h(where)g FC(s)32 b FA(\034)25 b FE(1)i(and)g(on)f(the)i(other)f(hand,)g(by)f(construction)i(the)555 4910 y(GGAs)h(should)f(work)g(well)g(in)g(systems)h(where)g(the)g (magnitude)f(of)g(the)h(reduced)555 5030 y(density)g(gradient)f FC(s)34 b FE(is)27 b(of)h(order)g(1.)702 5150 y(The)c(GGAs)h(typically) g(yield)g(total)g(energies)g(and)f(atomisation)i(energies)e(that)555 5271 y(are)j(more)e(accurate)j(than)e(those)g(of)f(the)h(HF)f(or)h(LSD) g(approximation,)f(as)h(well)g(as)555 5391 y(improved)e(barriers)g(to)h (chemical)g(reactions)g(and)f(improved)g(lengths)g(of)g(hydro-)2146 5640 y(3)p eop %%Page: 4 12 4 11 bop -41 275 a Fw(Chapter)29 b(1.)e(Introduction)p -41 315 3238 4 v -41 576 a FE(gen)g(and)f(metal-ligand)i(bonds.)37 b(GGAs)27 b(can)g(also)f(correct)i(the)f(more)g(subtle)g(LSD)-41 696 y(errors)19 b(in)f(the)i(lattice)g(constants)g(and)f(bulk)f(moduli) g(of)h(metals.)36 b(One)19 b(of)f(the)i(most)-41 817 y(prominent)25 b(results)g(of)f(GGA)h(was)h(a)f(correct)h(ground)e (state)j(and)e(elastic)g(proper-)-41 937 y(ties)h(of)f(iron)450 903 y Fz(28)532 937 y FE(.)37 b(This)25 b(result)h(attracted)i(a)e (wide)f(interest)h(of)f(scienti\256c)h(as)g(well)g(as)-41 1057 y(of)21 b(general)i(public,)f(the)g(results)f(were)h(described)f (in)g(the)h(scienti\256c)g(enclosure)g(of)-41 1178 y(New)33 b(York)g(Times)709 1143 y Fz(29)791 1178 y FE(.)52 b(Nevertheless,)35 b(there)e(remain)g(certain)h(problems)f(where)-41 1298 y(GGA)h(results)g(differ)d(signi\256cantly)j(from)f(experimental)h (values.)53 b(Good)33 b(exam-)-41 1419 y(ples)f(are)g(bond)e(lengths)i (in)f(Werner)h(complexes)1927 1384 y Fz(30)2041 1419 y FE(\(molecules)h(with)e(ionic-like)-41 1539 y(bindings\),)c (semiconductors)h(and)g(alkali)h(halides)1974 1505 y Fz(31)2057 1539 y FE(.)106 1659 y(To)19 b(understand)i(better)g(why)f (different)g(approximations)f(for)h(the)h(exchange-)-41 1780 y(correlation)g(energy)h(perform)d(as)i(they)g(do)f(and)h(to)f (pave)h(a)g(new)f(way)h(for)f(their)g(im-)-41 1900 y(provement)26 b(one)g(needs)g(a)h(more)f(profound)e(understanding)i(of)f(the)i (qualitative)-41 2021 y(and)j(quantitative)h(behaviour)e(of)g(the)i (electronic)f(density)g(and)g(its)f(derivatives.)-41 2141 y(Since)22 b(the)g(approximations)f(for)g(exchange-correlation)j (energy)e FC(E)2619 2155 y FB(x)s(c)2732 2141 y FE(are)g(known)-41 2261 y(to)j(be)f(valid)g(only)g(in)g(a)g(limited)g(range)h(of)f (density)g(parameters)h FC(r)2533 2275 y FB(s)2572 2261 y FE(,)f FC(\020)7 b FE(,)25 b(and)g FC(s)6 b FE(,)24 b(it)g(is)-41 2382 y(crucial)31 b(to)g(understand)g(what)g(the)g (physical)g(ranges)g(of)f(these)i(parameters)g(for)-41 2502 y(typical)h(electronic)g(systems)f(are.)49 b(So)33 b(I)e(propose)h(a)g(method)g(of)f(an)h(analysis)h(of)-41 2622 y(the)f(electronic)h(density)e(which)g(would)f(tell)j(how)e(the)h (density)f(parameters)h(are)-41 2743 y(distributed)23 b(in)g(atoms,)i(molecules,)f(and)g(crystals.)38 b(Such)24 b(an)f(analysis)h(would)f(al-)-41 2863 y(low)28 b(us)f(to)g(estimate)i (the)f(physical)f(ranges)h(of)f(the)h(density)f(parameters,)i(where)-41 2984 y(their)g(corresponding)e(distribution)g(functions)h(change)h (signi\256cantly)g(in)f(phys-)-41 3104 y(ical)h(processes.)39 b(To)28 b(summarise)g(the)h(information)f(in)f(the)i(distributions)e (func-)-41 3224 y(tions)c(I)h(propose)f(to)h(calculate)h(the)f(true)g (energy-weighted)h(averages)f(of)f(density)-41 3345 y(parameters.)55 b(The)33 b(average)h(value)g(of)e FC(s)39 b FE(de\256nes)33 b(the)h(average)g(inhomogeneity)-41 3465 y(of)c(the)g(system,)h(and)f (will)f(help)h(to)g(compare)h(GGA)f(results)g(to)g(LSD)h(results)f(and) -41 3586 y(explain)e(why)f(GGA)h(typically)h(gives)d(longer)i(bond)f (lengths,)h(lower)g(atomisation)-41 3706 y(energies,)39 b(and)d(higher)g(energy)i(barriers)e(at)i(transition)e(states.)65 b(I)36 b(also)h(expect)-41 3826 y(that)26 b(this)e(analysis)h(would)f 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FC(r)2622 4924 y FB(s)2685 4910 y FE(and)g FC(s)6 b FE(.)36 b(Next)-41 5030 y(comes)22 b(the)g(description)f(of)g(the)h(method)f(I)h(use)f(to)h(calculate)i (the)e(average)h(values)-41 5150 y(of)30 b FC(r)132 5164 y FB(s)200 5150 y FE(and)h FC(s)6 b FE(,)29 b(which)h(allow)h(me)f(to)g (explain)g(why)h(the)f(GGA)h(functionals)f(behave)-41 5271 y(as)g(they)h(do.)43 b(Chapter)30 b(5)f(summarises)g(results)i (and)f(states)h(conclusions.)42 b(I)30 b(put)-41 5391 y(the)i(technical)g(details)f(about)g(the)g(computer)g(code)g Fv(Crystal)g FE(and)g(integration)1550 5640 y(4)p eop %%Page: 5 13 5 12 bop 555 315 3238 4 v 555 576 a FE(techniques)31 b(used)f(to)h(calculate)i(the)e(exchange-correlation)h(energies)f(and)f (dis-)555 696 y(tribution)35 b(functions)e(for)i(atoms,)h(molecules)g (and)e(solids)g(into)g(the)i(appendix.)555 817 y(The)29 b(complete)g(list)f(of)g(literature)h(is)f(listed)g(at)i(the)e(end.) 2146 5640 y(5)p eop %%Page: 6 14 6 13 bop -41 275 a Fw(Chapter)29 b(1.)e(Introduction)p 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3544 y FB(i)1196 3517 y FA(\202)1291 3426 y Fu(X)1330 3626 y FB(i)1413 3517 y FC(v)8 b(\204)p Fx(r)1571 3531 y FB(i)1601 3517 y FC(\205)21 b FA(\202)1769 3452 y FE(1)p 1769 3490 V 1769 3584 a(2)1851 3426 y Fu(X)1863 3626 y FB(i;j)2126 3452 y FE(1)p 1983 3490 343 4 v 1983 3584 a FA(j)p Fx(r)2061 3598 y FB(i)2114 3584 y FA(\000)f Fx(r)2251 3598 y FB(j)2291 3584 y FA(j)2357 3517 y(\000)g FC(E)2515 3415 y Fu(o)2571 3517 y(\331)10 b FC(\204)p Fx(r)2729 3531 y Fz(1)2772 3517 y FC(;)15 b(:)g(:)g(:)i(;)e Fx(r)3027 3531 y FB(N)3089 3517 y FC(\205)26 b FA(\203)f FE(0)h FC(:)149 b FE(\(2.1.1\))555 3838 y(Terms)35 b FC(v)8 b(\204)p Fx(r)1035 3852 y FB(i)1065 3838 y FC(\205)35 b FE(represent)g(the)h(one-particle)g(external)g(potentials)f(and)g (the)g(last)555 3958 y(term)23 b(is)f(the)h(interelectron)h(Coulomb)d (interaction.)37 b(Spin)22 b(and)g(spin-orbital)g(cou-)555 4078 y(pling)28 b(are)h(neglected.)39 b(Atomic)29 b(units)f(are)h(used) f(throughout)h(the)f(text)3389 4044 y Ft(\003)3446 4078 y 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y(proximation.)106 937 y(Historically)g(two)g(simple)f(physical)h(approaches)g(have)g (been)g(used)g(which)-41 1057 y(will)28 b(help)g(us)g(to)h(understand)f (the)h(basic)g(idea)f(of)g(the)g(DFT.)106 1178 y(The)c(\256rst)h (approach)h(was)f(proposed)e(by)i(Thomas)g(and)g(Fermi)2579 1143 y Fz(3)p FB(;)p Fz(4)2680 1178 y FE(.)37 b(They)25 b(have)-41 1298 y(started)35 b(from)e(the)h(assumption)g(that)g(a)h (many-body)f(electron)g(system)h(can)f(be)-41 1419 y(broken)k(up)f (into)h(cells)h(of)e(suitable)i(size)f(in)f(which)g(the)i(electrons)g (can)g(be)f(re-)-41 1539 y(garded)22 b(as)g(a)g(homogeneous)g(electron) h(gas)f(with)f(constant)i(density)f FC(\032)t(\204)p Fx(r)p FC(\205)p FE(,)g(where)-41 1659 y Fx(r)29 b FE(speci\256es)f (the)h(position)e(of)h(the)h(centre)g(of)f(the)h(cell.)106 1780 y(The)f(equations)h(that)g(de\256ne)g(the)f(Thomas-Fermi)g(model)h (are:)504 2034 y FC(\032)t(\204)p Fx(r)p FC(\205)83 b FA(\203)1011 1969 y FE(1)p 948 2007 183 4 v 948 2101 a(3)p FC(\031)1088 2074 y Fz(2)1155 2035 y FC(\204)1198 2034 y(k)1257 2048 y FB(F)1305 2034 y FC(\204)p Fx(r)p FC(\205)1434 2035 y(\205)1476 1987 y Fz(3)1546 2034 y FA(\203)1718 1969 y FE(1)p 1655 2007 V 1655 2101 a(3)p FC(\031)1795 2074 y Fz(2)1848 1932 y Fu(\020)1900 2034 y FE(2)1957 2035 y FC(\204)1999 2034 y(\026)25 b FA(\000)c FC(v)2243 2048 y FB(e)q(f)10 b(f)2378 2034 y FC(\204)p Fx(r)p FC(\205)2507 2035 y(\205)2549 1932 y Fu(\021)2601 1949 y Fz(3)p FB(=)p Fz(2)2744 2034 y FC(;)98 b FE(\(2.1.2a\))370 2274 y FC(v)434 2288 y FB(e)q(f)10 b(f)569 2274 y FC(\204)p Fx(r)p FC(\205)83 b FA(\203)g FC(v)8 b(\204)p Fx(r)p FC(\205)19 b FA(\202)1253 2143 y Fu(Z)1338 2274 y FC(d)p Fx(r)1447 2235 y Ft(0)1542 2209 y FC(\032)t(\204)p Fx(r)1693 2175 y Ft(0)1723 2209 y FC(\205)p 1503 2247 302 4 v 1503 2341 a FA(j)p Fx(r)i FA(\000)f Fx(r)1739 2314 y Ft(0)1770 2341 y FA(j)1840 2274 y FC(:)996 b FE(\(2.1.2b\))-41 2530 y(The)36 b(effective)g(potential)i FC(v)1093 2544 y FB(e)q(f)10 b(f)1264 2530 y FE(consists)36 b(of)g(the)g(external)i (potential)f(plus)f(the)-41 2650 y(mean)41 b(electrostatic)i(potential) f(at)f(the)g(point)f Fx(r)h FE(due)f(to)h(the)g(electron)h(charge)-41 2771 y(distribution)35 b(at)i(the)f(point)g Fx(r)1154 2736 y Ft(0)1184 2771 y FE(.)62 b(It)36 b(is)f(clearly)j(seen)e(the)h (two)f(equations)g(\(2.1.2\))-41 2891 y(depend)e(nonlinearly)f(on)h (the)g(electron)h(density)f(and)g(have)g(to)g(be)g(solved)f(self-)-41 3011 y(consistently)c(for)f FC(\032)t(\204)p Fx(r)p FC(\205)g FE(and)g FC(v)1179 3025 y FB(e)q(f)10 b(f)1314 3011 y FC(\204)p Fx(r)p FC(\205)p FE(.)106 3132 y(The)35 b(second)g(approach)h (was)g(proposed)e(by)i(Hartree)2275 3097 y Fz(32)2359 3132 y FE(.)59 b(In)36 b(this)f(approach)-41 3252 y(the)f(basic)f (variables)g(are)h(one-particle)g(orbitals)f(in)f(a)i(space-varying)f (effective)-41 3373 y(potential,)28 b(rather)g(than)g(the)g(electronic) h(density,)e FC(\032)t(\204)p Fx(r)p FC(\205)p FE(.)37 b(This)27 b(model)g(is)g(consid-)-41 3493 y(erably)i(more)g(precise)f (than)h(the)g(Thomas-Fermi)f(model.)106 3613 y(For)k(the)i(effective)e (potential)i FC(v)1384 3627 y FB(e)q(f)10 b(f)1519 3613 y FC(\204)p Fx(r)p FC(\205)33 b FE(one)g(uses)f(the)i(same)f (mean-\256eld)h(ex-)-41 3734 y(pression)24 b(as)i(in)f(Thomas-Fermi)f (model.)38 b(The)25 b(one-particle)h(Schr)2579 3733 y(\310)2579 3734 y(odinger)f(equa-)-41 3854 y(tion:)786 3896 y Fu(n)842 3998 y FA(\000)926 3932 y FE(1)p 926 3970 57 4 v 926 4065 a(2)993 3998 y FA(r)1076 3959 y Fz(2)1140 3998 y FA(\202)20 b FC(v)1298 4012 y FB(e)q(f)10 b(f)1434 3998 y FC(\204)p Fx(r)p FC(\205)1563 3896 y Fu(o)1618 3998 y FC(')1704 4012 y FB(i)1737 3998 y FC(\204)p Fx(r)p FC(\205)25 b FA(\203)h FC(")2039 4012 y FB(i)2071 3998 y FC(')2157 4012 y FB(i)2189 3998 y FC(\204)p Fx(r)p FC(\205)f(;)549 b FE(\(2.1.3\))-41 4198 y(is)34 b(solved)g(for)g FC(N)42 b FE(lowest)35 b(eigenvalues)g(and)f(the)h(electron)h(density)e FC(\032)t(\204)p Fx(r)p FC(\205)g FE(is)g(ob-)-41 4318 y(tained)29 b(from)f(the)g(expression:)1145 4615 y FC(\032)t(\204)p Fx(r)p FC(\205)e FA(\203)1495 4496 y FB(N)1471 4524 y Fu(X)1465 4724 y FB(i)p Ft(\203)p Fz(1)1599 4615 y FA(j)p FC(')1720 4629 y FB(i)1751 4615 y FC(\204)p Fx(r)p FC(\205)p FA(j)1915 4576 y Fz(2)1984 4615 y FC(:)908 b FE(\(2.1.4\))106 4910 y(The)24 b(Hartree)i(equations)f(can)h(be)e(re\256ned)h(by)g (adding)f(the)h(exchange)h(effects,)-41 5030 y(which)i(lead)h(to)g (Hartree-Fock)g(equations)1642 4996 y Fz(33)1726 5030 y FE(.)106 5150 y(In)35 b(both)g(models)g(the)h(electronic)g(density)f FC(\032)t(\204)p Fx(r)p FC(\205)g FE(plays)g(an)h(important)f(role.)-41 5271 y(We)25 b(may)g(then)f(ask)h(a)f(question)h(whether)g(there)g (exists)f(a)g(formally)h(exact)g(theory)-41 5391 y(for)32 b(the)g(ground)g(state)h(of)f(electronic)h(systems)f(expressed)g (solely)h(in)e(terms)i(of)1550 5640 y(8)p eop %%Page: 9 17 9 16 bop 1990 275 a Fw(2.2.)27 b(The)h(lemma)h(of)e(Hohenberg)h(and)h (Kohn)p 555 315 3238 4 v 555 576 a FE(electronic)d(density)f 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y(terms)i(of)f(the)h(electron)g(density.)702 2124 y(Originally)d(the)g(lemma)h(of)e(Hohenberg)h(and)g(Kohn)f(was)h (derived)f(for)h(a)g(spin-)555 2244 y(independent)37 b(case.)66 b(Later)39 b(an)e(extended)h(proof)e(for)h(a)h (spin-dependent)e(case)555 2365 y(was)20 b(made)g(by)f(von)g(Barth)g (and)h(Hedin)2045 2330 y Fz(12)2127 2365 y FE(.)35 b(To)19 b(simplify)e(the)j(text)h(only)e(the)h(original)555 2485 y(lemma)42 b(will)f(be)g(stated.)78 b(Again,)44 b(the)d(nondegenerate)i (ground)d(state)j(will)d(be)555 2605 y(assumed,)i(even)d(though)g(the)g (lemma)h(holds)e(also)i(for)e(a)h(degenerate)i(ground)555 2726 y(state)773 2691 y Fz(34)858 2726 y FE(.)d(Another)29 b(approach)f(to)h(proof)e(this)h(theorem)h(was)f(devised)g(by)g(Levy) 3686 2691 y Fz(10)3769 2726 y FE(,)555 2846 y(using)g(constrained)g (search)h(formalism.)702 2966 y(We)h(shall)g(be)g(considering)f(a)i (collection)g(of)e(electrons,)i(enclosed)g(in)e(a)h(large)555 3087 y(box,)37 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FA(\202)2254 5373 y Fu(b)2240 5391 y FC(V)2303 5405 y FB(e)q(e)2399 5391 y FA(\202)2508 5373 y Fu(b)2493 5391 y FC(V)38 b(;)844 b FE(\(2.2.6a\))2146 5640 y(9)p eop %%Page: 10 18 10 17 bop -41 275 a Fw(Chapter)29 b(2.)e(Fundamentals)i(of)f(DFT)p -41 315 3238 4 v 1126 558 a Fu(b)1101 576 y FC(H)1187 537 y Ft(0)1300 576 y FA(\203)1474 558 y Fu(b)1457 576 y FC(T)33 b FA(\202)1658 558 y Fu(b)1644 576 y FC(V)1707 590 y FB(e)q(e)1802 576 y FA(\202)1911 558 y Fu(b)1897 576 y FC(V)1972 537 y Ft(0)2028 576 y FC(;)808 b FE(\(2.2.6b\))-41 794 y(respectively.)60 b(The)801 776 y Fu(b)787 794 y FC(V)47 b FE(and)1116 776 y Fu(b)1101 794 y FC(V)1176 760 y Ft(0)1242 794 y FE(are)36 b(two)g(different)e(external)i (potential)g(energy)-41 915 y(operators.)81 b(Now,)44 b(clearly,)j Fu(\331)53 b FE(can)43 b(not)f(be)g(equal)h(to)g Fu(\331)2287 880 y Ft(0)2318 915 y FE(,)i(since)d(they)h(satisfy)-41 1035 y(different)24 b(Hamiltonian)g(operators)g(\(unless)h FC(v)8 b(\204)p Fx(r)p FC(\205)24 b FA(\203)i FC(v)2164 1000 y Ft(0)2193 1035 y FC(\204)p Fx(r)p FC(\205)12 b FA(\202)g FC(c)5 b(o)r(ns)h(t)t(:)p FE(\).)37 b(By)24 b(using)-41 1155 y(Rayleigh-Ritz)30 b(variation)e(principle)f(we)i (have:)700 1373 y FC(E)h FA(\203)c(h)p Fu(\331)10 b FA(j)1065 1355 y Fu(b)1040 1373 y FC(H)c FA(j)p Fu(\331)k FA(i)82 b FC(<)h FA(h)p Fu(\331)1631 1334 y Ft(0)1662 1373 y FA(j)1721 1355 y Fu(b)1697 1373 y FC(H)6 b FA(j)p Fu(\331)1889 1334 y Ft(0)1919 1373 y FA(i)1358 1519 y(\203)83 b(h)p Fu(\331)1631 1480 y Ft(0)1662 1519 y FA(j)1721 1501 y Fu(b)1697 1519 y FC(H)1783 1480 y Ft(0)1833 1519 y FA(\202)1941 1501 y Fu(b)1927 1519 y FC(V)33 b FA(\000)2132 1501 y Fu(b)2117 1519 y FC(V)2192 1480 y Ft(0)2223 1519 y FA(j)p Fu(\331)2330 1480 y Ft(0)2360 1519 y FA(i)25 b FC(;)463 b FE(\(2.2.7\))-41 1737 y(or)826 1878 y FC(E)30 b(<)c(E)1079 1839 y Ft(0)1129 1878 y FA(\202)1224 1746 y Fu(Z)1309 1878 y FC(d)p Fx(r)16 b FC(\032)t(\204)p Fx(r)p FC(\205)1628 1776 y Fu(\020)1680 1878 y FC(v)8 b(\204)p Fx(r)p FC(\205)19 b 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y(ated)j(with)e(two)h(different)e(Hamiltonian)i(operators)g (is)f(wrong)g(and)g(thus)h(proves)-41 3228 y(the)j(lemma)g(of)f (Hohenberg)g(and)g(Kohn)p 1563 3228 60 71 v -41 3322 3238 4 v 106 3559 a(The)h(lemma)h(shows)e(there)i(is)f(a)h(unique)f (correspondence)g(between)h(the)g(ex-)-41 3679 y(ternal)g(potential)f FC(v)8 b(\204)p Fx(r)p FC(\205)27 b FE(and)i(the)g(electron)h(density)e FC(\032)t(\204)p Fx(r)p FC(\205)p FE(,)g(if)g(we)g(regard)h(two)g(po-) -41 3799 y(tentials,)g(differing)e(only)h(by)g(a)h(constant,)g(to)g(be) f(equivalent.)106 3920 y(The)20 b(lemma)h(of)f(Hohenberg)g(and)h(Kohn)f (has)g(very)h(broad)f(consequences.)37 b(Let)-41 4040 y(us)28 b(\256rst)g(notice)g(that)i(the)e(density)g FC(\032)t(\204)p Fx(r)p FC(\205)g FE(determines)g(the)g(number)g(of)f(electrons)-41 4161 y FC(N)36 b FE(in)27 b(the)i(system)g(through)f(the)h(condition:) 1066 4417 y FC(N)7 b(\206\032)t(\207)25 b FA(\021)1425 4286 y Fu(Z)1510 4417 y FC(d)p Fx(r)16 b FC(\032)t(\204)p Fx(r)p FC(\205)26 b FA(\203)f FC(N)33 b(:)773 b FE(\(2.2.11\))-41 4669 y(For)27 b(the)g(system)g(with)f(a)h(known)e(number)i(of)f (electrons)h(the)g(kinetic)f(energy)h(op-)-41 4789 y(erator)35 b(and)f(the)h(interelectron)g(repulsion)f(operator)g(can)h(be)f(easily) h(speci\256ed.)-41 4910 y(Since)30 b(the)g(lemma)h(tells)f(us)g(that)h FC(\032)t(\204)p Fx(r)p FC(\205)e FE(uniquely)h(determines)f(the)h (external)h(po-)-41 5030 y(tential)26 b FC(v)8 b(\204)p Fx(r)p FC(\205)p FE(,)24 b(the)h(full)g(Hamiltonian)1478 5012 y Fu(b)1453 5030 y FC(H)31 b FE(is)24 b(known.)37 b(Thus,)24 b(the)h(electron)h(density)-41 5150 y FC(\032)t(\204)p Fx(r)p FC(\205)39 b FE(implicitly)f(determines)h(the)g(physical)g (system)g(and)f(its)h(properties,)h(e.g.)-41 5271 y(the)c(ground)f (state)i(and)f(the)g(excited)g(states)h(many-electron)g(wave)f (functions,)-41 5391 y(correlation)29 b(functions,)f(etc.)1522 5640 y(10)p eop %%Page: 11 19 11 18 bop 1990 275 a Fw(2.2.)27 b(The)h(lemma)h(of)e(Hohenberg)h(and)h (Kohn)p 555 315 3238 4 v 555 576 a Fi(2.2.1)107 b(The)35 b(energy)f(functional)555 770 y FE(Let)23 b(us)e(consider)h(the)g (density)g FC(\032)t(\204)p Fx(r)p FC(\205)p FE(,)g(which)g(is)f(the)h (density)g(of)f(the)i(ground)e(state,)555 891 y(corresponding)30 b(to)g(some)h(external)g(potential)h FC(v)8 b(\204)p Fx(r)p FC(\205)p FE(.)42 b(From)31 b(the)f(lemma)i(of)d(Ho-)555 1011 y(henberg)g(and)f(Kohn)g(it)g(is)g(obvious,)f(that)i(the)g (quantity:)1787 1258 y(\304)1776 1259 y FC(v)7 b(\204)p Fx(r)p FC(\205)26 b FA(\021)g FC(v)8 b(\204)p Fx(r)p FC(\205)19 b FA(\000)2437 1194 y FC(E)p 2427 1232 84 4 v 2427 1326 a(N)2546 1259 y(;)886 b FE(\(2.2.12\))555 1496 y(is)28 b(a)h(uniquely)f(determined)h(by)f(electron)h(density)f FC(\032)t(\204)p Fx(r)p FC(\205)p FE(.)38 b(Now)28 b(we)h(write:)762 1742 y FA(h)p Fu(\331)10 b FA(j)p FC(\204)973 1724 y Fu(b)956 1742 y FC(T)33 b FA(\202)1157 1724 y Fu(b)1143 1742 y FC(V)1206 1756 y FB(e)q(e)1281 1742 y FC(\205)p FA(j)p Fu(\331)10 b FA(i)25 b(\203)h FC(E)e FA(\000)1778 1611 y Fu(Z)1863 1742 y FC(d)p Fx(r)16 b FC(\032)t(\204)p Fx(r)p FC(\205v)8 b(\204)p Fx(r)p FC(\205)24 b FA(\203)i(\000)2596 1611 y Fu(Z)2682 1742 y FC(d)p Fx(r)15 b FC(\032)t(\204)p Fx(r)p FC(\205)3010 1741 y FE(\304)3000 1742 y FC(v)7 b(\204)p Fx(r)p FC(\205)25 b(:)207 b FE(\(2.2.13\))555 1985 y(Since)837 1984 y(\304)826 1985 y FC(v)7 b(\204)p Fx(r)p FC(\205)36 b FE(is)g(a)h(unique)f(functional)g(of)g FC(\032)t(\204)p Fx(r)p FC(\205)p FE(,)i(so)e(is)f(the)i(entire)g (right)f(side)g(of)555 2105 y(equation)30 b(\(2.2.13\))c(and)i (therefore)h(also)g(the)g(left)f(side.)38 b(Thus)27 b(we)i(de\256ne:) 1558 2314 y FC(F)10 b(\206\032)t(\204)p Fx(r)p FC(\205\207)25 b FA(\021)g(h)p Fu(\331)10 b FA(j)p FC(\204)2237 2295 y Fu(b)2220 2314 y FC(T)33 b FA(\202)2421 2295 y Fu(b)2406 2314 y FC(V)2469 2328 y FB(e)q(e)2545 2314 y FC(\205)p FA(j)p Fu(\331)10 b FA(i)25 b FC(;)668 b FE(\(2.2.14\))555 2522 y(which)33 b(is)f(again)i(a)f(unique)g(functional)g(of)f FC(\032)t(\204)p Fx(r)p FC(\205)p FE(.)52 b(With)33 b(the)g(aid)g(of)f (\(2.2.14\),)g(we)555 2642 y(de\256ne,)d(for)e(a)i(given)f(potential)h FC(v)8 b(\204)p Fx(r)p FC(\205)p FE(,)27 b(the)h(energy)h(functional:) 1314 2889 y FC(E)1373 2903 y FB(v)1426 2889 y FC(\206\032)1534 2850 y Ft(0)1564 2889 y FC(\204)p Fx(r)p FC(\205\207)c FA(\021)1861 2758 y Fu(Z)1946 2889 y FC(d)p Fx(r)15 b FC(\032)2135 2850 y Ft(0)2166 2889 y FC(\204)p Fx(r)p FC(\205v)8 b(\204)p Fx(r)p FC(\205)19 b FA(\202)i FC(F)10 b(\206\032)2782 2850 y Ft(0)2811 2889 y FC(\204)p Fx(r)p FC(\205\207)25 b(:)424 b FE(\(2.2.15\))555 3132 y(Clearly,)32 b(for)e(the)h(ground)f(state)i(density)e FC(\032)t(\204)p Fx(r)p FC(\205)p FE(,)g(the)h(value)g(of)f(the)h(energy)g(func-)555 3252 y(tional)e FC(E)902 3266 y FB(v)955 3252 y FC(\206\032)t(\207)f FE(equals)h(to)g(the)g(ground)e(state)j(energy)f FC(E)5 b FE(.)702 3373 y(We)35 b(shall)h(now)f(show)g(that)i FC(E)1894 3387 y FB(v)1947 3373 y FC(\206\032)t(\207)e FE(attains)h(its)g(minimum)e(value)h(if)g(the)h(ad-)555 3493 y(missible)23 b(functions)f FC(\032)1470 3459 y Ft(0)1501 3493 y FC(\204)p Fx(r)p FC(\205)g FE(are)i(restricted)g(by)g (the)f(condition)g(\(2.2.11\).)34 b(It)24 b(is)f(well)555 3613 y(known)28 b(that)i(for)d(a)i(system)g(of)f FC(N)35 b FE(particles,)29 b(the)g(energy)g(functional)f(of)g Fu(\331)3549 3579 y Ft(0)3580 3613 y FE(:)1267 3822 y FA(E)1337 3836 y FB(v)1391 3822 y FC(\206)p Fu(\331)1506 3783 y Ft(0)1536 3822 y FC(\207)e FA(\021)f(h)p Fu(\331)1820 3783 y Ft(0)1851 3822 y FA(j)1900 3804 y Fu(b)1886 3822 y FC(V)11 b FA(j)p Fu(\331)2067 3783 y Ft(0)2098 3822 y FA(i)20 b(\202)h(h)p Fu(\331)2373 3783 y Ft(0)2403 3822 y FA(j)p FC(\204)2498 3804 y Fu(b)2481 3822 y FC(T)33 b FA(\202)2681 3804 y Fu(b)2667 3822 y FC(V)2730 3836 y FB(e)q(e)2805 3822 y FC(\205)p FA(j)p Fu(\331)2955 3783 y Ft(0)2985 3822 y FA(i)26 b FC(;)377 b FE(\(2.2.16\))555 4030 y(has)34 b(its)g(minimum)e(at)i(the)g(exact)h(ground)e(state)i Fu(\331)10 b FE(,)35 b(with)e(respect)i(to)f(arbitrary)555 4151 y(variations)d(of)f Fu(\331)1230 4116 y Ft(0)1261 4151 y FE(,)h(as)h(long)e(as)h(the)h(number)e(of)h(particles)g(is)f (kept)h(constant.)47 b(In)555 4271 y(particular,)26 b(let)g Fu(\331)1260 4236 y Ft(0)1315 4271 y FE(be)f(the)g(ground)f(state)i (associated)f(with)f(a)h(different)f(external)555 4391 y(potential)30 b FC(v)1061 4357 y Ft(0)1090 4391 y FC(\204)p Fx(r)p FC(\205)p FE(.)38 b(Then,)27 b(by)i(\(2.2.14\))d(and)i (\(2.2.16\):)700 4637 y FA(E)770 4651 y FB(v)824 4637 y FC(\206)p Fu(\331)939 4598 y Ft(0)969 4637 y FC(\207)e FA(\203)1138 4506 y Fu(Z)1223 4637 y FC(d)p Fx(r)15 b FC(v)8 b(\204)p Fx(r)p FC(\205\032)1613 4598 y Ft(0)1643 4637 y FC(\204)p Fx(r)p FC(\205)20 b FA(\202)g FC(F)10 b(\206\032)2058 4598 y Ft(0)2088 4637 y FC(\207)26 b(>)f FA(E)2326 4651 y FB(v)2380 4637 y FC(\206)p Fu(\331)10 b FC(\207)25 b FA(\203)2663 4506 y Fu(Z)2748 4637 y FC(d)p Fx(r)16 b FC(v)8 b(\204)p Fx(r)p FC(\205\032)t(\204)p Fx(r)p FC(\205)19 b FA(\202)i FC(F)10 b(\206\032)t(\207)24 b(:)3459 4790 y FE(\(2.2.17\))555 4910 y(The)40 b(many-electron)h(wave) f(function)g Fu(\331)50 b FE(determines)39 b(the)i(electronic)f (density)555 5031 y FC(\032)t(\204)p Fx(r)p FC(\205)28 b FE(via)g(equation:)640 5321 y FC(\032)t(\204)p Fx(r)p FC(\205)e FA(\203)959 5190 y Fu(Z)1045 5321 y FC(d)p Fx(r)1154 5335 y Fz(1)1212 5321 y FC(:)15 b(:)g(:)h(d)p Fx(r)1448 5335 y FB(N)1525 5321 y Fu(\331)1597 5282 y Ft(\003)1654 5321 y FC(\204)p Fx(r)1740 5335 y Fz(1)1783 5321 y FC(;)f(:)g(:)g(:)h(;)f Fx(r)2037 5335 y FB(N)2100 5321 y FC(\205)2143 5219 y Fu(\020)2225 5202 y FB(N)2201 5230 y Fu(X)2195 5430 y FB(i)p Ft(\203)p Fz(1)2329 5321 y FC(\016\204)p Fx(r)20 b FA(\000)h Fx(r)2634 5335 y FB(i)2666 5321 y FC(\205)2709 5219 y Fu(\021)2761 5321 y(\331)10 b FC(\204)p Fx(r)2919 5335 y Fz(1)2962 5321 y FC(;)15 b(:)g(:)g(:)i(;)e Fx(r)3217 5335 y FB(N)3279 5321 y FC(\205)26 b(:)84 b FE(\(2.2.18\))2118 5640 y(11)p eop %%Page: 12 20 12 19 bop -41 275 a Fw(Chapter)29 b(2.)e(Fundamentals)i(of)f(DFT)p -41 315 3238 4 v -41 576 a FE(Thus,)i(for)f(a)i(given)e FC(v)8 b FE(,)30 b FC(E)942 590 y FB(v)995 576 y FC(\206\032)1103 542 y Ft(0)1133 576 y FC(\204)p Fx(r)p FC(\205\207)f FE(is)h(minimised)e(by)i(the)h(ground-state)g(density)-41 696 y FC(\032)t(\204)p Fx(r)p FC(\205)i FE(corresponding)g(to)h FC(v)8 b(\204)p Fx(r)p FC(\205)32 b FE(and)h(the)h(minimum)e(value)i (of)f FC(E)38 b FE(is)33 b(the)h(ground)-41 817 y(state)c(energy.)106 940 y(With)39 b(this)g(we)h(have)f(stated)i(the)f(variation)g (principle)e(of)h(Hohenberg)g(and)-41 1061 y(Kohn.)c(For)18 b(each)i(given)e(potential)h FC(v)8 b(\204)p Fx(r)p FC(\205)17 b FE(one)i(can)g(in)f(principle)g(de\256ne)g(the)h(energy)-41 1181 y(functional)30 b(\(2.2.15\),)d(where)i FC(F)10 b(\206\032)1312 1147 y Ft(0)1342 1181 y FC(\204)p Fx(r)p FC(\205\207)28 b FE(is)h(given)g(in)f(\(2.2.14\).)39 b(The)29 b(energy)h(func-)-41 1301 y(tional)c(\(2.2.15\))e(gets)j(into) e(its)h(minimum)e(for)h FC(\032)1848 1267 y Ft(0)1879 1301 y FC(\204)p Fx(r)p FC(\205)p 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BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr } def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1587 1814 454 227 bl 1587 1814 454 227 C NC 454 227 m 1814 Y s 488 227 m -34 X s 471 318 m -17 X s 471 408 m -17 X s 471 499 m -17 X s 488 590 m -34 X s 471 680 m -17 X s 471 771 m -17 X s 471 862 m -17 X s 488 953 m -34 X s 471 1043 m -17 X s 471 1134 m -17 X s 471 1225 m -17 X s 488 1315 m -34 X s 471 1406 m -17 X s 471 1497 m -17 X s 471 1588 m -17 X s 488 1678 m -34 X s 471 1769 m -17 X s 471 1860 m -17 X s 471 1950 m -17 X s 488 2041 m -34 X s /xs 0 def (1) /Times-Roman 68 stwn gsave 408 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (1.2) /Times-Roman 68 stwn gsave 408 567 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.2) show gr /xs 0 def (1.4) /Times-Roman 68 stwn gsave 408 930 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.4) show gr /xs 0 def (1.6) /Times-Roman 68 stwn gsave 408 1293 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.6) show gr /xs 0 def (1.8) /Times-Roman 68 stwn gsave 408 1656 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.8) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr 454 227 m 1587 X s 454 261 m -34 Y s 559 244 m -17 Y s 665 244 m -17 Y s 771 244 m -17 Y s 877 244 m -17 Y s 983 261 m -34 Y s 1089 244 m -17 Y s 1194 244 m -17 Y s 1300 244 m -17 Y s 1406 244 m -17 Y s 1512 261 m -34 Y s 1618 244 m -17 Y s 1724 244 m -17 Y s 1830 244 m -17 Y s 1935 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 983 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1512 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 96 1860 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (F) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (xc) show gr 1587 1814 454 227 C 3 lw 454 227 m 1587 X s 454 581 m 1587 X s 454 831 m 1587 X s 454 1114 m 1587 X s 454 1926 m 1587 X s 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 299 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=0) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 635 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=2) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 889 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=6) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 1170 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=18) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 1842 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=) show currentpoint pop 0 t /Special findfont 86 sf 0 0 m (\245) show gr 1587 1814 454 227 C gr gr showpage end %%EndDocument @endspecial 1178 3751 a FE(Figure)g(2.6.1:)36 b FC(F)1824 3765 y FB(x)s(c)1944 3751 y FE(for)27 b(the)i(LSD)g(approximation.)702 4147 y(One)e(way)h(to)g(visualise)e(the)i(nonlocality)g(of)e(the)i(new) f(exchange-correlation)555 4267 y(GGA)38 b(functional)f(is)f(to)i (de\256ne)f(the)g(enhancement)i(factor)e FC(F)3037 4281 y FB(x)s(c)3166 4267 y FE(over)g(the)g(local)555 4387 y(exchange:)990 4650 y FC(E)1054 4611 y FB(G)q(G)q(A)1049 4674 y(x)s(c)1213 4650 y FC(\206\032)1317 4664 y Ft(")1355 4650 y FC(;)15 b(\032)1458 4664 y Ft(#)1498 4650 y FC(\207)25 b FA(\203)1666 4519 y Fu(Z)1751 4650 y FC(d)p Fx(r)16 b FC(\032)t(\204)p Fx(r)p FC(\205")2120 4598 y FB(unif)2118 4661 y(x)2301 4650 y FC(\204\032)t(\205F)2506 4664 y FB(x)s(c)2597 4650 y FC(\204r)2689 4664 y FB(s)2727 4650 y FC(;)f(\020)7 b(;)15 b(s)6 b(\205)25 b(;)434 b FE(\(2.6.64\))555 4908 y(where)29 b(the)g(reduced-density)g(gradient)g FC(s)34 b FE(\(2.6.60\),)26 b(a)j(dimensionless)f(measure)555 5028 y(of)g(the)g(gradient,)g(is)f(the)h(variable)g(that)h(represents)f (the)h(inhomogeneity)e(of)h(the)555 5149 y(electron)i(system.)702 5271 y(For)36 b(the)g(sake)g(of)g(simplicity)f(we)h(plot)g(the)h (enhancement)g(factor)g FC(F)3471 5285 y FB(x)s(c)3598 5271 y FE(only)555 5391 y(for)i(the)h(spin-unpolarised)d(case,)42 b(i.e.)70 b FC(\020)52 b FA(\203)45 b FE(0.)70 b(In)39 b(Fig.)f(2.6.1)f(we)i(plot)g FC(F)3575 5405 y FB(x)s(c)3706 5391 y FE(in)2118 5640 y(25)p eop %%Page: 26 34 26 33 bop -41 275 a Fw(Chapter)29 b(2.)e(Fundamentals)i(of)f(DFT)p -41 315 3238 4 v 43 3547 a @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 3685 @rwi @setspecial %%BeginDocument: fig/fxcpbe.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr } def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1587 1814 454 227 bl 1587 1814 454 227 C NC 454 227 m 1814 Y s 488 227 m -34 X s 471 318 m -17 X s 471 408 m -17 X s 471 499 m -17 X s 488 590 m -34 X s 471 680 m -17 X s 471 771 m -17 X s 471 862 m -17 X s 488 953 m -34 X s 471 1043 m -17 X s 471 1134 m -17 X s 471 1225 m -17 X s 488 1315 m -34 X s 471 1406 m -17 X s 471 1497 m -17 X s 471 1588 m -17 X s 488 1678 m -34 X s 471 1769 m -17 X s 471 1860 m -17 X s 471 1950 m -17 X s 488 2041 m -34 X s /xs 0 def (1) /Times-Roman 68 stwn gsave 408 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (1.2) /Times-Roman 68 stwn gsave 408 567 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.2) show gr /xs 0 def (1.4) /Times-Roman 68 stwn gsave 408 930 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.4) show gr /xs 0 def (1.6) /Times-Roman 68 stwn gsave 408 1293 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.6) show gr /xs 0 def (1.8) /Times-Roman 68 stwn gsave 408 1656 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.8) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr 454 227 m 1587 X s 454 261 m -34 Y s 559 244 m -17 Y s 665 244 m -17 Y s 771 244 m -17 Y s 877 244 m -17 Y s 983 261 m -34 Y s 1089 244 m -17 Y s 1194 244 m -17 Y s 1300 244 m -17 Y s 1406 244 m -17 Y s 1512 261 m -34 Y s 1618 244 m -17 Y s 1724 244 m -17 Y s 1830 244 m -17 Y s 1935 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 983 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1512 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 96 1860 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (F) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (xc) show gr 1587 1814 454 227 C 3 lw 454 227 m 26 1 d 27 3 d 26 5 d 26 7 d 27 8 d 26 11 d 27 12 d 26 14 d 27 15 d 26 17 d 27 18 d 26 19 d 27 21 d 26 21 d 27 22 d 26 23 d 26 23 d 27 24 d 26 24 d 27 25 d 26 24 d 27 25 d 26 25 d 27 24 d 26 25 d 27 24 d 26 24 d 26 24 d 27 24 d 26 23 d 27 23 d 26 22 d 27 22 d 26 21 d 27 21 d 26 21 d 27 19 d 26 20 d 27 19 d 26 18 d 26 18 d 27 18 d 26 17 d 27 16 d 26 16 d 27 16 d 26 15 d 27 15 d 26 14 d 27 14 d 26 13 d 27 13 d 26 13 d 26 12 d 27 12 d 26 11 d 27 11 d 26 11 d 27 10 d 26 11 d s 454 581 m 79 X 26 1 d 27 X 26 1 d 27 1 d 26 2 d 27 3 d 26 3 d 27 4 d 26 5 d 27 7 d 26 7 d 27 8 d 26 10 d 26 10 d 27 11 d 26 13 d 27 13 d 26 14 d 27 15 d 26 16 d 27 16 d 26 16 d 27 17 d 26 17 d 26 18 d 27 18 d 26 17 d 27 18 d 26 18 d 27 18 d 26 17 d 27 18 d 26 17 d 27 17 d 26 17 d 27 16 d 26 17 d 26 15 d 27 16 d 26 15 d 27 15 d 26 15 d 27 14 d 26 14 d 27 13 d 26 14 d 27 12 d 26 13 d 27 12 d 26 12 d 26 11 d 27 12 d 26 10 d 27 11 d 26 10 d 27 10 d 26 10 d s 454 831 m 238 X 26 1 d 27 X 26 1 d 27 1 d 26 1 d 27 2 d 26 3 d 26 2 d 27 4 d 26 4 d 27 5 d 26 6 d 27 6 d 26 7 d 27 8 d 26 8 d 27 9 d 26 10 d 26 10 d 27 11 d 26 11 d 27 12 d 26 12 d 27 12 d 26 12 d 27 13 d 26 13 d 27 12 d 26 13 d 27 13 d 26 13 d 26 13 d 27 12 d 26 13 d 27 12 d 26 12 d 27 12 d 26 12 d 27 11 d 26 12 d 27 11 d 26 11 d 27 11 d 26 10 d 26 10 d 27 10 d 26 10 d 27 10 d 26 9 d 27 9 d 26 9 d s 454 1114 m 79 X 26 -1 d 80 X 26 -1 d 27 -1 d 26 -1 d 27 -1 d 26 -2 d 27 -2 d 26 -2 d 27 -2 d 26 -2 d 26 -2 d 27 -3 d 26 -2 d 27 -2 d 26 -1 d 27 -2 d 26 X 27 -1 d 26 X 27 1 d 26 1 d 26 2 d 27 3 d 26 3 d 27 3 d 26 5 d 27 4 d 26 6 d 27 5 d 26 6 d 27 7 d 26 7 d 27 7 d 26 7 d 26 8 d 27 8 d 26 8 d 27 8 d 26 8 d 27 8 d 26 8 d 27 9 d 26 8 d 27 8 d 26 9 d 27 8 d 26 8 d 26 8 d 27 8 d 26 7 d 27 8 d 26 8 d 27 7 d 26 8 d s 454 1926 m 105 X 27 -1 d 26 X 27 -1 d 26 -1 d 27 -1 d 26 -2 d 27 -3 d 26 -3 d 27 -4 d 26 -5 d 27 -6 d 26 -6 d 26 -8 d 27 -8 d 26 -10 d 27 -10 d 26 -11 d 27 -12 d 26 -12 d 27 -13 d 26 -14 d 27 -14 d 26 -14 d 26 -15 d 27 -14 d 26 -15 d 27 -15 d 26 -14 d 27 -15 d 26 -14 d 27 -13 d 26 -13 d 27 -13 d 26 -12 d 27 -12 d 26 -11 d 26 -10 d 27 -10 d 26 -9 d 27 -8 d 26 -8 d 27 -8 d 26 -6 d 27 -6 d 26 -6 d 27 -5 d 26 -5 d 27 -4 d 26 -3 d 26 -3 d 27 -3 d 26 -3 d 27 -2 d 26 -1 d 27 -2 d 26 -1 d s 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 354 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=0) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 635 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=2) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 889 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=6) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 1170 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=18) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 533 1823 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=) show currentpoint pop 0 t /Special findfont 86 sf 0 0 m (\245) show gr 1587 1814 454 227 C gr gr showpage end %%EndDocument @endspecial 587 3751 a FE(Figure)g(2.6.2:)36 b FC(F)1233 3765 y FB(x)s(c)1353 3751 y FE(for)28 b(the)g(PBE)g(approximation.)-41 4173 y(the)35 b(LSD)g(approximation.)56 b(The)35 b(curves)f(are)h (horizontal)g(lines,)g(since)g(the)g(LSD)-41 4293 y(approximation)30 b(is)f(independent)g(of)h(the)g(local)h(gradient.)43 b(In)30 b(the)h(high)e(density)-41 4413 y(limit)37 b(\()p FC(r)285 4427 y FB(s)365 4413 y FA(!)k FE(0\))c(is)g FC(F)783 4427 y FB(x)s(c)915 4413 y FA(\203)k 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gr /xs 0 def (1) /Times-Roman 68 stwn gsave 408 658 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 408 1111 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 408 1565 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr 454 227 m 1587 X s 454 261 m -34 Y s 533 244 m -17 Y s 612 244 m -17 Y s 692 244 m -17 Y s 771 244 m -17 Y s 851 261 m -34 Y s 930 244 m -17 Y s 1009 244 m -17 Y s 1089 244 m -17 Y s 1168 244 m -17 Y s 1247 261 m -34 Y s 1327 244 m -17 Y s 1406 244 m -17 Y s 1486 244 m -17 Y s 1565 244 m -17 Y s 1644 261 m -34 Y s 1724 244 m -17 Y s 1803 244 m -17 Y s 1882 244 m -17 Y s 1962 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 851 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1247 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1644 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 96 1860 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (g) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (3) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(s\)) show gr 1587 1814 454 227 C 3 lw 454 227 m 161 X s 615 227 m 1 1 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241 m 9 X s 1987 241 m 3 X s 2001 241 m 11 -1 d s 2024 240 m 3 X s 2027 240 m 8 X s 2041 240 m cl s 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C [] 0 sd 1605 1724 m 119 X s 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 1763 1724 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (T=0) show gr 1587 1814 454 227 C 2268 2268 0 0 C [] 0 sd 1605 1588 m 22 X s 1650 1588 m 23 X s 1695 1588 m 23 X s 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 1763 1588 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (T=0.03) show gr 1587 1814 454 227 C gr gr showpage end %%EndDocument @endspecial -41 3859 a FE(Figure)j(3.2.1:)45 b(The)32 b(in\257uence)g(of)g(the)h(Fermi-Dirac-type)h(smoothing)e(function)-41 3979 y(on)k(the)g(integration)h(for)e(the)h(Li)g(atom.)61 b(The)36 b(solid)f(line)h(represents)g(the)g(zero-)-41 4099 y(temperature)42 b(result)f(and)f(the)h(dashed)f(line)g (represents)g(the)h(result)g(for)e FC(T)59 b FA(\203)-41 4220 y FE(0)p FC(:)p 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-34 X s 471 1300 m -17 X s 471 1353 m -17 X s 471 1406 m -17 X s 471 1459 m -17 X s 488 1512 m -34 X s 471 1565 m -17 X s 471 1618 m -17 X s 471 1671 m -17 X s 471 1724 m -17 X s 488 1777 m -34 X s 471 1830 m -17 X s 471 1882 m -17 X s 471 1935 m -17 X s 471 1988 m -17 X s 488 2041 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 408 1225 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 408 1489 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 408 1754 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 454 1247 m 680 X s 454 1281 m -34 Y s 499 1264 m -17 Y s 544 1264 m -17 Y s 590 1264 m -17 Y s 635 1264 m -17 Y s 680 1281 m -34 Y s 726 1264 m -17 Y s 771 1264 m -17 Y s 816 1264 m -17 Y s 862 1264 m -17 Y s 907 1281 m -34 Y s 953 1264 m -17 Y s 998 1264 m -17 Y s 1043 1264 m -17 Y s 1089 1264 m -17 Y s 1134 1281 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 680 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 907 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1134 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 680 794 454 1247 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn gsave 1134 1102 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show gr 680 794 454 1247 C 3 lw 454 1258 m 2 2 d 3 1 d 3 3 d 3 2 d 2 3 d 3 3 d 3 3 d 2 3 d 3 4 d 3 3 d 3 3 d 2 2 d 3 3 d 3 1 d 3 2 d 2 1 d 3 1 d 3 1 d 2 2 d 3 1 d 3 1 d 3 2 d 2 1 d 3 2 d 3 1 d 3 2 d 2 2 d 3 2 d 3 2 d 2 2 d 3 3 d 3 2 d 3 3 d 2 3 d 3 3 d 3 3 d 3 3 d 2 3 d 3 3 d 3 4 d 2 4 d 3 3 d 3 4 d 3 4 d 2 5 d 3 4 d 3 4 d 2 5 d 3 4 d 3 5 d 3 4 d 2 5 d 3 4 d 3 5 d 3 4 d 2 4 d 3 4 d 3 4 d 2 3 d 3 4 d 3 3 d 3 3 d 2 3 d 3 2 d 3 3 d 3 2 d 2 2 d 3 2 d 3 1 d 2 2 d 3 1 d 3 1 d 3 2 d 2 1 d 3 1 d 3 1 d 3 1 d 2 1 d 3 1 d 3 1 d 2 1 d 3 X 3 1 d 3 1 d 2 1 d 3 1 d 3 1 d 3 1 d 2 1 d 3 1 d 3 2 d 2 1 d 3 1 d 3 1 d 3 1 d 2 2 d 3 1 d 3 1 d 3 2 d 2 1 d 3 2 d 3 1 d 2 2 d 3 1 d 3 2 d 3 2 d 2 2 d 3 1 d 3 2 d 3 2 d 2 2 d 3 2 d 3 2 d 2 2 d 3 2 d 3 2 d 3 2 d 2 2 d 3 2 d 3 2 d 3 2 d 2 3 d 3 2 d 3 2 d 2 3 d 3 2 d 3 3 d 3 2 d 2 3 d 3 2 d 3 3 d 3 2 d 2 3 d 3 3 d 3 3 d 2 2 d 3 3 d 3 3 d 3 3 d 2 3 d 3 3 d 3 3 d 3 3 d 2 3 d 3 3 d 3 3 d 2 3 d 3 4 d 3 3 d 3 3 d 2 4 d 3 3 d 3 3 d 3 4 d 2 3 d 3 4 d 3 4 d 2 3 d 3 4 d 3 4 d 3 3 d 2 4 d 3 4 d 3 4 d 3 4 d 2 4 d 3 4 d 3 4 d 2 4 d 3 4 d 3 4 d 3 4 d 2 5 d 3 4 d 3 4 d 3 5 d 2 4 d 3 5 d 3 4 d 2 5 d 3 4 d 3 5 d 3 5 d 2 5 d 3 4 d 3 5 d 3 5 d 2 5 d 3 5 d 3 5 d 2 5 d 3 5 d 3 6 d 3 5 d 2 5 d 3 5 d 3 6 d 3 5 d 2 6 d 3 5 d 3 6 d 2 6 d 3 5 d s 1007 1845 m 3 6 d 3 6 d 2 6 d 3 6 d 3 6 d 3 6 d 2 6 d 3 6 d 3 6 d 2 7 d 3 6 d 3 6 d 3 7 d 2 6 d 3 7 d 3 6 d 3 7 d 2 7 d 3 7 d 3 7 d 2 7 d 3 7 d 3 7 d 3 7 d 2 7 d 3 7 d 3 8 d 3 7 d 2 8 d 3 7 d s 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 301 1962 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 476 1922 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (core) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 601 1922 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (CV) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 703 1922 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (valence) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 964 1922 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (tail) show gr 680 794 454 1247 C 2268 2268 0 0 C 1 lw 590 1247 m 23 Y s 590 1293 m 22 Y s 590 1338 m 23 Y s 590 1383 m 23 Y s 590 1429 m 23 Y s 590 1474 m 23 Y s 590 1520 m 22 Y s 590 1565 m 23 Y s 590 1610 m 23 Y s 590 1656 m 22 Y s 590 1701 m 23 Y s 590 1746 m 23 Y s 590 1792 m 22 Y s 590 1837 m 23 Y s 590 1882 m 23 Y s 590 1928 m 22 Y s 590 1973 m 23 Y s 590 2019 m 22 Y s 680 794 454 1247 C 2268 2268 0 0 C 672 1247 m 23 Y s 672 1293 m 22 Y s 672 1338 m 23 Y s 672 1383 m 23 Y s 672 1429 m 23 Y s 672 1474 m 23 Y s 672 1520 m 22 Y s 672 1565 m 23 Y s 672 1610 m 23 Y s 672 1656 m 22 Y s 672 1701 m 23 Y s 672 1746 m 23 Y s 672 1792 m 22 Y s 672 1837 m 23 Y s 672 1882 m 23 Y s 672 1928 m 22 Y s 672 1973 m 23 Y s 672 2019 m 22 Y s 680 794 454 1247 C 2268 2268 0 0 C 939 1247 m 23 Y s 939 1293 m 22 Y s 939 1338 m 23 Y s 939 1383 m 23 Y s 939 1429 m 23 Y s 939 1474 m 23 Y s 939 1520 m 22 Y s 939 1565 m 23 Y s 939 1610 m 23 Y s 939 1656 m 22 Y s 939 1701 m 23 Y s 939 1746 m 23 Y s 939 1792 m 22 Y s 939 1837 m 23 Y s 939 1882 m 23 Y s 939 1928 m 22 Y s 939 1973 m 23 Y s 939 2019 m 22 Y s 680 794 454 1247 C 2268 2268 0 0 C 454 1391 m 11 X s 476 1391 m 12 X s 499 1391 m 11 X s 522 1391 m 11 X s 544 1391 m 12 X s 567 1391 m 11 X s 590 1391 m 11 X s 612 1391 m 12 X s 635 1391 m 11 X s 658 1391 m 11 X s 680 1391 m 12 X s 703 1391 m 11 X s 726 1391 m 11 X s 748 1391 m 12 X s 771 1391 m 11 X s 794 1391 m 11 X s 816 1391 m 12 X s 839 1391 m 11 X s 862 1391 m 11 X s 885 1391 m 11 X s 907 1391 m 12 X s 930 1391 m 11 X s 953 1391 m 11 X s 975 1391 m 12 X s 998 1391 m 11 X s 1021 1391 m 11 X s 1043 1391 m 12 X s 1066 1391 m 11 X s 1089 1391 m 11 X s 1111 1391 m 12 X s 680 794 454 1247 C 2268 2268 0 0 C 454 1466 m 11 X s 476 1466 m 12 X s 499 1466 m 11 X s 522 1466 m 11 X s 544 1466 m 12 X s 567 1466 m 11 X s 590 1466 m 11 X s 612 1466 m 12 X s 635 1466 m 11 X s 658 1466 m 11 X s 680 1466 m 12 X s 703 1466 m 11 X s 726 1466 m 11 X s 748 1466 m 12 X s 771 1466 m 11 X s 794 1466 m 11 X s 816 1466 m 12 X s 839 1466 m 11 X s 862 1466 m 11 X s 885 1466 m 11 X s 907 1466 m 12 X s 930 1466 m 11 X s 953 1466 m 11 X s 975 1466 m 12 X s 998 1466 m 11 X s 1021 1466 m 11 X s 1043 1466 m 12 X s 1066 1466 m 11 X s 1089 1466 m 11 X s 1111 1466 m 12 X s 680 794 454 1247 C 2268 2268 0 0 C 454 1718 m 11 X s 476 1718 m 12 X s 499 1718 m 11 X s 522 1718 m 11 X s 544 1718 m 12 X s 567 1718 m 11 X s 590 1718 m 11 X s 612 1718 m 12 X s 635 1718 m 11 X s 658 1718 m 11 X s 680 1718 m 12 X s 703 1718 m 11 X s 726 1718 m 11 X s 748 1718 m 12 X s 771 1718 m 11 X s 794 1718 m 11 X s 816 1718 m 12 X s 839 1718 m 11 X s 862 1718 m 11 X s 885 1718 m 11 X s 907 1718 m 12 X s 930 1718 m 11 X s 953 1718 m 11 X s 975 1718 m 12 X s 998 1718 m 11 X s 1021 1718 m 11 X s 1043 1718 m 12 X s 1066 1718 m 11 X s 1089 1718 m 11 X s 1111 1718 m 12 X s 680 794 454 1247 C NC 680 794 1361 1247 bl 680 794 1361 1247 C NC 1361 1247 m 794 Y s 1395 1247 m -34 X s 1378 1300 m -17 X s 1378 1353 m -17 X s 1378 1406 m -17 X s 1378 1459 m -17 X s 1395 1512 m -34 X s 1378 1565 m -17 X s 1378 1618 m -17 X s 1378 1671 m -17 X s 1378 1724 m -17 X s 1395 1777 m -34 X s 1378 1830 m -17 X s 1378 1882 m -17 X s 1378 1935 m -17 X s 1378 1988 m -17 X s 1395 2041 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 1315 1225 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 1315 1489 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1315 1754 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1315 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 1361 1247 m 680 X s 1361 1281 m -34 Y s 1406 1264 m -17 Y s 1452 1264 m -17 Y s 1497 1264 m -17 Y s 1542 1264 m -17 Y s 1588 1281 m -34 Y s 1633 1264 m -17 Y s 1678 1264 m -17 Y s 1724 1264 m -17 Y s 1769 1264 m -17 Y s 1814 1281 m -34 Y s 1860 1264 m -17 Y s 1905 1264 m -17 Y s 1950 1264 m -17 Y s 1996 1264 m -17 Y s 2041 1281 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 1361 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (15) /Times-Roman 68 stwn gsave 1588 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (15) show gr /xs 0 def (30) /Times-Roman 68 stwn gsave 1814 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (30) show gr /xs 0 def (45) /Times-Roman 68 stwn gsave 2041 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (45) show gr 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (g) /Times-Roman 86 stwn (1) /Times-Roman 60 stwn (\(r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn (\)) /Times-Roman 86 stwn gsave 2041 1102 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (g) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (1) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\)) show gr 680 794 1361 1247 C 3 lw 1365 1248 m 6 2 d 10 2 d 19 2 d 34 2 d 50 2 d 61 2 d 60 2 d 45 2 d 24 2 d 6 2 d -7 2 d -13 2 d -16 2 d -15 2 d -11 2 d -6 2 d -1 2 d 8 2 d 18 2 d 30 2 d 44 2 d 60 2 d 70 2 d 72 2 d 63 2 d 41 2 d 15 2 d -7 2 d -23 2 d -33 2 d -36 2 d -38 2 d -36 2 d -35 2 d -32 2 d -29 2 d -27 2 d -25 2 d -23 2 d -21 2 d -19 2 d -18 2 d -16 2 d -15 2 d -14 2 d -13 2 d -11 2 d -11 2 d -10 2 d -10 2 d -8 2 d -8 2 d -8 2 d -6 2 d -7 2 d -6 2 d -5 2 d -5 2 d -5 2 d -5 2 d -4 2 d -4 2 d -3 2 d -3 2 d -4 2 d -2 2 d -3 2 d -3 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -1 2 d -1 2 d -2 2 d -1 2 d -1 2 d -1 2 d 2 Y -1 2 d 2 Y -1 2 d 5 Y 1 2 d 2 Y 1 2 d 1 2 d 2 2 d 1 2 d 2 2 d 3 2 d 3 2 d 4 2 d 4 2 d 6 2 d 7 2 d 9 2 d 10 2 d 12 2 d 15 2 d 17 2 d 18 2 d 19 2 d 18 2 d 15 2 d 12 2 d 7 2 d 2 2 d -2 2 d -5 2 d -6 2 d -8 2 d -7 2 d -8 2 d -8 2 d -7 2 d -6 2 d -6 2 d -6 2 d -6 2 d -5 2 d -5 2 d -4 2 d -5 2 d -4 2 d -3 2 d -4 2 d -4 2 d -3 2 d -3 2 d -3 2 d -3 2 d -3 2 d -3 2 d -3 2 d -2 2 d -3 2 d -2 2 d -3 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -1 2 d -2 2 d -2 2 d -1 2 d -2 2 d -1 2 d -2 2 d -1 2 d -2 2 d -1 2 d -1 2 d -2 2 d -1 2 d -1 2 d -1 2 d -2 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 1 d -1 2 d 2 Y -1 2 d -1 2 d -1 2 d -1 2 d 2 Y -1 2 d -1 2 d -1 2 d 2 Y -1 2 d -1 2 d 2 Y -1 2 d -1 2 d 2 Y -1 2 d 2 Y -1 2 d -1 2 d 2 Y s 1401 1652 m -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 4 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 4 Y -1 2 d 4 Y -1 2 d 4 Y -1 2 d 4 Y -1 2 d 4 Y -1 2 d 4 Y -1 2 d 6 Y -1 2 d 4 Y -1 2 d 6 Y -1 2 d 6 Y -1 2 d 8 Y -1 2 d 6 Y -1 2 d 8 Y -1 2 d 10 Y -1 1 d 10 Y -1 2 d 10 Y -1 2 d 12 Y -1 2 d 14 Y -1 2 d 14 Y -1 2 d 18 Y -1 2 d 20 Y -1 2 d 20 Y -1 2 d 28 Y -1 2 d 33 Y -1 2 d 32 Y -1 2 d 1 2 d 2 Y -1 2 d 4 Y s 2268 2268 0 0 C 1361 1248 m 2 Y s 1361 1250 m 2 Y s 1361 1252 m 2 Y s 1361 1254 m 2 Y s 1361 1256 m 2 Y s 1361 1258 m 2 Y s 1361 1260 m 2 Y s 1361 1262 m 2 Y s 1361 1264 m 2 Y s 1361 1266 m 2 Y s 1361 1268 m 2 Y s 1361 1270 m 1 Y s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 1361 1282 m20 1361 1282 m20 1361 1294 m s 1361 1294 m 2 Y s 1361 1296 m 2 Y s 1361 1298 m 2 Y s 1361 1300 m 2 Y s 1361 1302 m 2 Y s 1361 1304 m 2 Y s 1361 1306 m 2 Y s 1361 1308 m 2 Y s 1361 1310 m 2 Y s 1361 1312 m 2 Y s 1361 1314 m 2 Y s 1361 1316 m s 1361 1328 m20 1361 1328 m20 1361 1339 m 1 Y s 1361 1340 m 2 Y s 1361 1342 m 2 Y s 1361 1344 m 2 Y s 1361 1346 m 2 Y s 1361 1348 m 2 Y s 1361 1350 m 2 Y s 1361 1352 m 2 Y s 1361 1354 m 2 Y s 1361 1356 m 2 Y s 1361 1358 m 2 Y s 1361 1360 m 2 Y s 1361 1373 m20 1361 1373 m20 1361 1384 m 2 Y s 1361 1386 m 2 Y s 1361 1388 m 2 Y s 1361 1390 m 2 Y s 1361 1392 m 2 Y s 1361 1394 m 2 Y s 1361 1396 m 2 Y s 1361 1398 m 2 Y s 1361 1400 m 2 Y s 1361 1402 m 2 Y s 1361 1404 m 2 Y s 1361 1406 m 1 Y s 1361 1418 m20 1361 1418 m20 1369 1426 m 5 1 d s 1374 1427 m 9 2 d s 1383 1429 m 8 2 d s 1402 1432 m20 1402 1432 m20 1414 1434 m 7 1 d s 1421 1435 m 9 2 d s 1430 1437 m 6 2 d s 1446 1442 m20 1446 1442 m20 1457 1446 m 8 1 d s 1465 1447 m 11 2 d s 1476 1449 m 4 1 d s 1491 1452 m20 1491 1452 m20 1502 1453 m 1 X s 1503 1453 m 17 2 d s 1520 1455 m 5 1 d s 1536 1457 m20 1536 1457 m20 1547 1458 m 10 1 d s 1557 1459 m 13 2 d s 1581 1462 m20 1581 1462 m20 1592 1464 m 10 1 d s 1602 1465 m 6 2 d s 1608 1467 m 1 X s 1609 1467 m 2 2 d s 1611 1469 m s 1611 1469 m -1 1 d s 1610 1470 m -1 1 d s 1609 1471 m s 1598 1475 m20 1598 1475 m20 1587 1478 m -4 1 d s 1583 1479 m -8 2 d s 1575 1481 m -8 2 d s 1567 1483 m -2 1 d s 1554 1487 m20 1554 1487 m20 1543 1491 m -1 X s 1542 1491 m -6 2 d s 1536 1493 m -5 2 d s 1531 1495 m -5 2 d s 1526 1497 m -4 2 d s 1512 1504 m20 1512 1504 m20 1502 1509 m -3 2 d s 1499 1511 m -3 2 d s 1496 1513 m -3 2 d s 1493 1515 m -3 2 d s 1490 1517 m -3 2 d s 1487 1519 m -3 2 d s 1484 1521 m -1 X s 1474 1528 m20 1474 1528 m20 1466 1536 m -1 1 d s 1465 1537 m -2 2 d s 1463 1539 m -2 2 d s 1461 1541 m -2 2 d s 1459 1543 m -2 2 d s 1457 1545 m -2 2 d s 1455 1547 m -2 2 d s 1453 1549 m -1 2 d s 1452 1551 m -2 1 d s 1443 1561 m20 1443 1561 m20 1437 1571 m s 1437 1571 m -2 2 d s 1435 1573 m -1 2 d s 1434 1575 m -1 2 d s 1433 1577 m -1 2 d s 1432 1579 m -2 2 d s 1430 1581 m -1 2 d s 1429 1583 m -1 2 d s 1428 1585 m -1 2 d s 1427 1587 m -1 2 d s 1426 1589 m -1 1 d s 1420 1600 m20 1420 1600 m20 1415 1611 m 1 Y s 1415 1612 m -1 2 d s 1414 1614 m -1 2 d s 1413 1616 m -1 2 d s 1412 1618 m -1 2 d s 1411 1620 m 2 Y s 1411 1622 m -1 2 d s 1410 1624 m -1 2 d s 1409 1626 m -1 2 d s 1408 1628 m 2 Y s 1408 1630 m -1 2 d s 1404 1643 m20 1404 1643 m20 680 794 1361 1247 C 2268 2268 0 0 C 1401 1652 m -1 2 d s 1400 1654 m 2 Y s 1400 1656 m -1 2 d s 1399 1658 m 2 Y s 1399 1660 m -1 2 d s 1398 1662 m 2 Y s 1398 1664 m -1 2 d s 1397 1666 m 2 Y s 1397 1668 m -1 2 d s 1396 1670 m 2 Y s 1396 1672 m -1 2 d s 1395 1674 m s 1393 1685 m20 1393 1685 m20 1391 1696 m -1 2 d s 1390 1698 m 2 Y s 1390 1700 m 2 Y s 1390 1702 m -1 2 d s 1389 1704 m 2 Y s 1389 1706 m 2 Y s 1389 1708 m -1 2 d s 1388 1710 m 2 Y s 1388 1712 m 2 Y s 1388 1714 m -1 2 d s 1387 1716 m 2 Y s 1387 1718 m 1 Y s 1385 1730 m20 1385 1730 m20 1384 1741 m -1 1 d s 1383 1742 m 2 Y s 1383 1744 m 2 Y s 1383 1746 m 2 Y s 1383 1748 m -1 2 d s 1382 1750 m 2 Y s 1382 1752 m 2 Y s 1382 1754 m 2 Y s 1382 1756 m -1 2 d s 1381 1758 m 2 Y s 1381 1760 m 2 Y s 1381 1762 m 2 Y s 1381 1764 m s 1380 1775 m20 1380 1775 m20 1378 1786 m 2 Y s 1378 1788 m 2 Y s 1378 1790 m 2 Y s 1378 1792 m 2 Y s 1378 1794 m 2 Y s 1378 1796 m -1 1 d s 1377 1797 m 2 Y s 1377 1799 m 2 Y s 1377 1801 m 2 Y s 1377 1803 m 2 Y s 1377 1805 m 2 Y s 1377 1807 m -1 2 d s 1376 1820 m20 1376 1820 m20 1375 1831 m 2 Y s 1375 1833 m -1 2 d s 1374 1835 m 2 Y s 1374 1837 m 2 Y s 1374 1839 m 2 Y s 1374 1841 m 2 Y s 1374 1843 m 2 Y s 1374 1845 m 2 Y s 1374 1847 m 2 Y s 1374 1849 m -1 2 d s 1373 1851 m 2 Y s 1373 1853 m 1 Y s 1373 1865 m20 1373 1865 m20 1372 1877 m s 1372 1877 m 2 Y s 1372 1879 m 2 Y s 1372 1881 m 2 Y s 1372 1883 m 2 Y s 1372 1885 m -1 2 d s 1371 1887 m 2 Y s 1371 1889 m 2 Y s 1371 1891 m 2 Y s 1371 1893 m 2 Y s 1371 1895 m 2 Y s 1371 1897 m 2 Y s 1371 1899 m s 1370 1911 m20 1370 1911 m20 1370 1922 m 1 Y s 1370 1923 m 2 Y s 1370 1925 m 2 Y s 1370 1927 m 2 Y s 1370 1929 m -1 2 d s 1369 1931 m 2 Y s 1369 1933 m 2 Y s 1369 1935 m 2 Y s 1369 1937 m 2 Y s 1369 1939 m 2 Y s 1369 1941 m 2 Y s 1369 1943 m 2 Y s 1369 1945 m s 1369 1956 m20 1369 1956 m20 1368 1967 m 2 Y s 1368 1969 m 2 Y s 1368 1971 m 2 Y s 1368 1973 m 2 Y s 1368 1975 m 2 Y s 1368 1977 m 2 Y s 1368 1979 m 2 Y s 1368 1981 m 2 Y s 1368 1983 m 2 Y s 1368 1985 m 1 Y s 1368 1986 m 2 Y s 1368 1988 m 2 Y s 1367 2001 m20 1367 2001 m20 1367 2013 m 1 Y s 1367 2014 m 2 Y s 1367 2016 m 2 Y s 1367 2018 m 2 Y s 1367 2020 m 2 Y s 1367 2022 m 2 Y s 1367 2024 m 2 Y s 1367 2026 m 2 Y s 1367 2028 m -1 2 d s 1366 2030 m 1 2 d s 1367 2032 m 2 Y s 1367 2034 m -1 1 d s 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C gsave 1208 1962 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show gr 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (core) /Times-Roman 48 stwn gsave 1996 1340 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (core) show gr 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (CV) /Times-Roman 48 stwn gsave 1996 1406 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (CV) show gr 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (valence) /Times-Roman 48 stwn gsave 1996 1644 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (valence) show gr 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (tail) /Times-Roman 48 stwn gsave 1996 1922 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (tail) show gr 680 794 1361 1247 C 2268 2268 0 0 C 1 lw 1361 1391 m 11 X s 1383 1391 m 12 X s 1406 1391 m 12 X s 1429 1391 m 11 X s 1452 1391 m 11 X s 1474 1391 m 12 X s 1497 1391 m 11 X s 1520 1391 m 11 X s 1542 1391 m 12 X s 1565 1391 m 11 X s 1588 1391 m 11 X s 1610 1391 m 12 X s 1633 1391 m 11 X s 1656 1391 m 11 X s 1678 1391 m 12 X s 1701 1391 m 11 X s 1724 1391 m 11 X s 1746 1391 m 12 X s 1769 1391 m 11 X s 1792 1391 m 11 X s 1814 1391 m 12 X s 1837 1391 m 11 X s 1860 1391 m 11 X s 1882 1391 m 12 X s 1905 1391 m 11 X s 1928 1391 m 11 X s 1950 1391 m 12 X s 1973 1391 m 11 X s 1996 1391 m 11 X s 2019 1391 m 11 X s 680 794 1361 1247 C 2268 2268 0 0 C 1361 1466 m 11 X s 1383 1466 m 12 X s 1406 1466 m 12 X s 1429 1466 m 11 X s 1452 1466 m 11 X s 1474 1466 m 12 X s 1497 1466 m 11 X s 1520 1466 m 11 X s 1542 1466 m 12 X s 1565 1466 m 11 X s 1588 1466 m 11 X s 1610 1466 m 12 X s 1633 1466 m 11 X s 1656 1466 m 11 X s 1678 1466 m 12 X s 1701 1466 m 11 X s 1724 1466 m 11 X s 1746 1466 m 12 X s 1769 1466 m 11 X s 1792 1466 m 11 X s 1814 1466 m 12 X s 1837 1466 m 11 X s 1860 1466 m 11 X s 1882 1466 m 12 X s 1905 1466 m 11 X s 1928 1466 m 11 X s 1950 1466 m 12 X s 1973 1466 m 11 X s 1996 1466 m 11 X s 2019 1466 m 11 X s 680 794 1361 1247 C 2268 2268 0 0 C 1361 1718 m 11 X s 1383 1718 m 12 X s 1406 1718 m 12 X s 1429 1718 m 11 X s 1452 1718 m 11 X s 1474 1718 m 12 X s 1497 1718 m 11 X s 1520 1718 m 11 X s 1542 1718 m 12 X s 1565 1718 m 11 X s 1588 1718 m 11 X s 1610 1718 m 12 X s 1633 1718 m 11 X s 1656 1718 m 11 X s 1678 1718 m 12 X s 1701 1718 m 11 X s 1724 1718 m 11 X s 1746 1718 m 12 X s 1769 1718 m 11 X s 1792 1718 m 11 X s 1814 1718 m 12 X s 1837 1718 m 11 X s 1860 1718 m 11 X s 1882 1718 m 12 X s 1905 1718 m 11 X s 1928 1718 m 11 X s 1950 1718 m 12 X s 1973 1718 m 11 X s 1996 1718 m 11 X s 2019 1718 m 11 X s 680 794 1361 1247 C NC 680 794 454 227 bl 680 794 454 227 C NC 454 227 m 794 Y s 488 227 m -34 X s 471 280 m -17 X s 471 333 m -17 X s 471 386 m -17 X s 471 438 m -17 X s 488 491 m -34 X s 471 544 m -17 X s 471 597 m -17 X s 471 650 m -17 X s 471 703 m -17 X s 488 756 m -34 X s 471 809 m -17 X s 471 862 m -17 X s 471 915 m -17 X s 471 968 m -17 X s 488 1021 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 408 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 408 469 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 408 733 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 408 998 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 454 227 m 680 X s 454 261 m -34 Y s 499 244 m -17 Y s 544 244 m -17 Y s 590 244 m -17 Y s 635 244 m -17 Y s 680 261 m -34 Y s 726 244 m -17 Y s 771 244 m -17 Y s 816 244 m -17 Y s 862 244 m -17 Y s 907 261 m -34 Y s 953 244 m -17 Y s 998 244 m -17 Y s 1043 244 m -17 Y s 1089 244 m -17 Y s 1134 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 680 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 907 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1134 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 680 794 454 227 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn gsave 1134 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show gr 680 794 454 227 C 3 lw 454 325 m 2 11 d 4 Y 2 13 d 1 4 d 2 15 d 1 3 d 3 19 d 2 20 d 2 14 d 1 4 d 1 8 d 1 4 d 1 1 d 1 4 d 1 1 d 1 Y 1 -1 d 1 -1 d 1 -3 d -1 Y 1 -3 d 1 -5 d 1 -8 d 1 -8 d 2 -17 d 2 -28 d 2 -21 d 1 -4 d 2 -13 d 1 -8 d 1 -6 d 1 -6 d 1 -2 d 1 -4 d 1 -4 d 1 -3 d 2 -1 d 1 -1 d 2 1 d 2 1 d 1 Y 3 3 d 3 5 d 3 6 d 2 6 d 3 7 d 3 7 d 3 7 d 2 7 d 3 7 d 3 8 d 2 8 d 3 8 d 3 8 d 3 8 d 2 9 d 3 8 d 3 9 d 3 9 d 2 9 d 3 9 d 3 8 d 2 9 d 3 8 d 3 8 d 3 8 d 2 6 d 3 6 d 3 6 d 2 3 d 3 3 d 2 1 d 4 X 2 -1 d -1 Y 2 -3 d 1 -1 d 2 -4 d 1 -2 d 2 -5 d 1 -2 d 2 -7 d -2 Y 3 -9 d -2 Y 3 -12 d 2 -13 d 3 -13 d 3 -14 d 3 -15 d 2 -14 d 3 -14 d 3 -13 d 3 -13 d 2 -11 d 3 -11 d 3 -9 d 2 -9 d 3 -7 d 3 -6 d 3 -5 d 2 -5 d 3 -3 d 3 -3 d 3 -2 d 2 -1 d 3 -1 d 3 -1 d 2 X 3 1 d 3 1 d 3 1 d 2 1 d 3 2 d 3 1 d 3 2 d 2 2 d 3 2 d 3 2 d 2 2 d 3 3 d 3 2 d 3 2 d 2 3 d 3 2 d 3 2 d 3 3 d 2 2 d 3 3 d 3 2 d 2 3 d 3 2 d 3 3 d 3 2 d 2 2 d 3 3 d 3 2 d 3 3 d 2 2 d 3 3 d 3 2 d 2 2 d 3 3 d 3 2 d 3 3 d 2 2 d 3 2 d 3 3 d 3 2 d 2 3 d 3 2 d 3 2 d 2 3 d 3 2 d 3 2 d 3 3 d 2 2 d 3 3 d 3 2 d 3 2 d 2 3 d 3 2 d 3 3 d 2 2 d 3 2 d 3 3 d 3 2 d 2 3 d 3 2 d 3 3 d 3 2 d 2 3 d 3 2 d 3 3 d 2 2 d 3 3 d 3 2 d 3 3 d 2 2 d 3 3 d 3 2 d 3 3 d 2 2 d 3 3 d 3 3 d 2 2 d 3 3 d 3 3 d 3 2 d 2 3 d 3 3 d 3 2 d 3 3 d 2 3 d 3 2 d 3 3 d 2 3 d 3 3 d 3 3 d 3 2 d 2 3 d 3 3 d 3 3 d 3 3 d 2 3 d 3 3 d 3 3 d 2 3 d 3 3 d 3 3 d 3 3 d 2 3 d 3 3 d 3 3 d 3 3 d 2 3 d 3 3 d 3 4 d 2 3 d 3 3 d 3 3 d 3 4 d 2 3 d 3 3 d 3 4 d 3 3 d 2 3 d 3 4 d 3 3 d 2 4 d 3 3 d s 1007 600 m 3 4 d 3 3 d 2 4 d 3 3 d 3 4 d 3 4 d 2 4 d 3 3 d 3 4 d 2 4 d 3 4 d 3 4 d 3 3 d 2 4 d 3 4 d 3 4 d 3 4 d 2 4 d 3 5 d 3 4 d 2 4 d 3 4 d 3 4 d 3 5 d 2 4 d 3 4 d 3 5 d 3 4 d 2 5 d 3 4 d 3 5 d 2 5 d 3 4 d 3 5 d 3 5 d 2 4 d 3 5 d 3 5 d 3 5 d 2 5 d 3 5 d 3 5 d 2 5 d 3 6 d 3 5 d 3 5 d 2 5 d 3 6 d 3 5 d 3 6 d 2 5 d 3 6 d 3 6 d 2 5 d 3 6 d 3 6 d 3 6 d 2 6 d 3 6 d 3 6 d 3 6 d 2 6 d 3 6 d 3 7 d 2 6 d 3 6 d 3 7 d 3 6 d 2 7 d 3 7 d 3 6 d 3 7 d 2 7 d 3 7 d 3 7 d 2 7 d 3 7 d 3 8 d 3 7 d 2 7 d 3 8 d s 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 301 941 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 476 902 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (core) show gr 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 601 902 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (CV) show gr 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 703 902 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (valence) show gr 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 964 902 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (tail) show gr 680 794 454 227 C 2268 2268 0 0 C 1 lw 590 227 m 22 Y s 590 272 m 23 Y s 590 318 m 22 Y s 590 363 m 23 Y s 590 408 m 23 Y s 590 454 m 22 Y s 590 499 m 23 Y s 590 544 m 23 Y s 590 590 m 22 Y s 590 635 m 23 Y s 590 680 m 23 Y s 590 726 m 22 Y s 590 771 m 23 Y s 590 816 m 23 Y s 590 862 m 23 Y s 590 907 m 23 Y s 590 953 m 22 Y s 590 998 m 23 Y s 680 794 454 227 C 2268 2268 0 0 C 672 227 m 22 Y s 672 272 m 23 Y s 672 318 m 22 Y s 672 363 m 23 Y s 672 408 m 23 Y s 672 454 m 22 Y s 672 499 m 23 Y s 672 544 m 23 Y s 672 590 m 22 Y s 672 635 m 23 Y s 672 680 m 23 Y s 672 726 m 22 Y s 672 771 m 23 Y s 672 816 m 23 Y s 672 862 m 23 Y s 672 907 m 23 Y s 672 953 m 22 Y s 672 998 m 23 Y s 680 794 454 227 C 2268 2268 0 0 C 939 227 m 22 Y s 939 272 m 23 Y s 939 318 m 22 Y s 939 363 m 23 Y s 939 408 m 23 Y s 939 454 m 22 Y s 939 499 m 23 Y s 939 544 m 23 Y s 939 590 m 22 Y s 939 635 m 23 Y s 939 680 m 23 Y s 939 726 m 22 Y s 939 771 m 23 Y s 939 816 m 23 Y s 939 862 m 23 Y s 939 907 m 23 Y s 939 953 m 22 Y s 939 998 m 23 Y s 680 794 454 227 C 2268 2268 0 0 C 454 286 m 11 X s 476 286 m 12 X s 499 286 m 11 X s 522 286 m 11 X s 544 286 m 12 X s 567 286 m 11 X s 590 286 m 11 X s 612 286 m 12 X s 635 286 m 11 X s 658 286 m 11 X s 680 286 m 12 X s 703 286 m 11 X s 726 286 m 11 X s 748 286 m 12 X s 771 286 m 11 X s 794 286 m 11 X s 816 286 m 12 X s 839 286 m 11 X s 862 286 m 11 X s 885 286 m 11 X s 907 286 m 12 X s 930 286 m 11 X s 953 286 m 11 X s 975 286 m 12 X s 998 286 m 11 X s 1021 286 m 11 X s 1043 286 m 12 X s 1066 286 m 11 X s 1089 286 m 11 X s 1111 286 m 12 X s 680 794 454 227 C 2268 2268 0 0 C 454 520 m 11 X s 476 520 m 12 X s 499 520 m 11 X s 522 520 m 11 X s 544 520 m 12 X s 567 520 m 11 X s 590 520 m 11 X s 612 520 m 12 X s 635 520 m 11 X s 658 520 m 11 X s 680 520 m 12 X s 703 520 m 11 X s 726 520 m 11 X s 748 520 m 12 X s 771 520 m 11 X s 794 520 m 11 X s 816 520 m 12 X s 839 520 m 11 X s 862 520 m 11 X s 885 520 m 11 X s 907 520 m 12 X s 930 520 m 11 X s 953 520 m 11 X s 975 520 m 12 X s 998 520 m 11 X s 1021 520 m 11 X s 1043 520 m 12 X s 1066 520 m 11 X s 1089 520 m 11 X s 1111 520 m 12 X s 680 794 454 227 C /w 20 def /w2 {w 2 div} def /w3 {w 3 div} def 672 286 m20 590 520 m20 NC 680 794 1361 227 bl 680 794 1361 227 C NC 1361 227 m 794 Y s 1395 227 m -34 X s 1378 280 m -17 X s 1378 333 m -17 X s 1378 386 m -17 X s 1378 438 m -17 X s 1395 491 m -34 X s 1378 544 m -17 X s 1378 597 m -17 X s 1378 650 m -17 X s 1378 703 m -17 X s 1395 756 m -34 X s 1378 809 m -17 X s 1378 862 m -17 X s 1378 915 m -17 X s 1378 968 m -17 X s 1395 1021 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 1315 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 1315 469 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1315 733 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1315 998 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 1361 227 m 680 X s 1361 261 m -34 Y s 1406 244 m -17 Y s 1452 244 m -17 Y s 1497 244 m -17 Y s 1542 244 m -17 Y s 1588 261 m -34 Y s 1633 244 m -17 Y s 1678 244 m -17 Y s 1724 244 m -17 Y s 1769 244 m -17 Y s 1814 261 m -34 Y s 1860 244 m -17 Y s 1905 244 m -17 Y s 1950 244 m -17 Y s 1996 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 1361 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (15) /Times-Roman 68 stwn gsave 1588 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (15) show gr /xs 0 def (30) /Times-Roman 68 stwn gsave 1814 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (30) show gr /xs 0 def (45) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (45) show gr 680 794 1361 227 C 2268 2268 0 0 C /xs 0 def (g) /Times-Roman 86 stwn (3) /Times-Roman 60 stwn (\(s\)) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (g) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (3) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(s\)) show gr 680 794 1361 227 C 3 lw 1361 228 m 40 Y 1 2 d 1 2 d 2 2 d 6 2 d 10 2 d 20 2 d 37 2 d 55 2 d 67 1 d 52 2 d 21 2 d -4 2 d -11 2 d -1 2 d 21 2 d 50 2 d 78 2 d 79 2 d 42 2 d 3 X 2 Y -14 2 d -14 X -34 2 d -31 2 d -24 2 d -19 2 d -15 2 d -12 2 d -9 2 d -7 2 d -6 2 d -5 2 d -3 2 d -3 2 d -2 2 d -1 2 d -1 2 d -1 2 d -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -1 2 d -2 2 d -1 2 d -2 2 d -1 2 d -2 2 d -2 2 d -2 2 d -1 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -2 2 d -1 2 d -2 2 d -1 2 d -2 2 d -1 2 d -1 2 d -1 2 d 8 Y 2 2 d 2 2 d 3 2 d 5 2 d 7 2 d 10 2 d 12 2 d 14 2 d 10 2 d -4 2 d -21 1 d -6 1 d -43 2 d -43 2 d -31 2 d -19 2 d -11 2 d -6 2 d -3 2 d -3 2 d -1 2 d -1 2 d -2 2 d 1 Y -1 2 d -1 2 d 2 Y -1 2 d 8 Y 1 2 d 1 2 d 1 2 d 2 2 d 2 2 d 3 2 d 4 2 d 6 2 d 8 2 d 10 2 d 14 2 d 15 2 d 11 2 d -1 2 d -18 2 d -5 X -42 2 d -44 2 d -32 2 d -19 2 d -11 2 d -5 2 d -3 2 d -2 2 d -1 2 d -1 2 d -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 2 Y -1 2 d 4 Y -1 2 d 2 Y -1 2 d 4 Y -1 2 d 2 Y -1 2 d 4 Y -1 2 d 4 Y -1 2 d 4 Y -1 2 d 4 Y -1 2 d 6 Y -1 2 d 6 Y -1 2 d 6 Y s 1378 632 m -1 2 d 6 Y -1 2 d 8 Y -1 2 d 8 Y -1 2 d 7 Y -1 2 d 10 Y -1 2 d 12 Y -1 2 d 12 Y -1 2 d 16 Y -1 2 d 16 Y -1 2 d 22 Y -1 2 d 26 Y -1 2 d 32 Y -1 2 d 45 Y -1 2 d 60 Y -1 2 d 2 Y 1 2 d -1 2 d 72 Y s 2268 2268 0 0 C 1361 228 m 2 Y s 1361 230 m 2 Y s 1361 232 m 2 Y s 1361 234 m 2 Y s 1361 236 m 2 Y s 1361 238 m 2 Y s 1361 240 m 2 Y s 1361 242 m 2 Y s 1361 244 m 2 Y s 1361 246 m 2 Y s 1361 248 m 2 Y s 1361 250 m s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 1361 262 m20 1361 262 m20 1364 272 m 1 2 d s 1365 274 m 6 2 d s 1371 276 m 10 2 d s 1381 278 m 5 X s 1397 279 m20 1397 279 m20 1408 280 m 23 1 d s 1442 282 m20 1442 282 m20 1453 282 m 23 1 d s 1487 283 m20 1487 283 m20 1499 284 m 22 X s 1533 285 m20 1533 285 m20 1544 285 m 15 X s 1559 285 m 8 1 d s 1578 286 m20 1578 286 m20 1589 287 m 17 X s 1606 287 m 4 X s 1610 287 m 2 X s 1623 287 m20 1623 287 m20 1627 290 m -2 1 d s 1625 291 m -5 X s 1620 291 m -13 2 d s 1607 293 m -2 X s 1593 294 m20 1593 294 m20 1582 295 m -4 X s 1578 295 m -18 2 d s 1560 297 m s 1548 299 m20 1548 299 m20 1537 301 m -1 X s 1536 301 m -8 2 d s 1528 303 m -6 2 d s 1522 305 m -5 2 d s 1517 307 m -1 1 d s 1506 314 m20 1506 314 m20 1500 324 m -1 1 d s 1499 325 m -1 2 d s 1498 327 m 2 Y s 1498 329 m -1 2 d s 1497 331 m -1 2 d s 1496 333 m 2 Y s 1496 335 m -1 2 d s 1495 337 m 2 Y s 1495 339 m -1 2 d s 1494 341 m 2 Y s 1494 343 m -1 2 d s 1493 345 m s 1491 356 m20 1491 356 m20 1487 367 m 2 Y s 1487 369 m -1 2 d s 1486 371 m -1 2 d s 1485 373 m -1 2 d s 1484 375 m 2 Y s 1484 377 m -1 2 d s 1483 379 m -1 2 d s 1482 381 m -1 2 d s 1481 383 m -1 2 d s 1480 385 m -1 2 d s 1479 387 m 1 Y s 1473 398 m20 1473 398 m20 1468 408 m 1 Y s 1468 409 m -1 2 d s 1467 411 m -1 2 d s 1466 413 m -1 2 d s 1465 415 m -1 2 d s 1464 417 m -2 2 d s 1462 419 m -1 2 d s 1461 421 m -1 2 d s 1460 423 m -1 2 d s 1459 425 m -1 2 d s 1458 427 m -1 1 d s 1451 438 m20 1451 438 m20 1442 444 m -1 1 d s 1441 445 m -4 2 d s 1437 447 m -3 2 d s 1434 449 m -3 2 d s 1431 451 m -1 2 d s 1430 453 m -2 2 d s 1428 455 m -1 2 d s 1427 457 m -1 2 d s 1426 459 m s 1421 469 m20 1421 469 m20 1416 480 m s 1416 480 m -1 2 d s 1415 482 m -1 2 d s 1414 484 m -1 2 d s 1413 486 m -1 2 d s 1412 488 m 2 Y s 1412 490 m -1 2 d s 1411 492 m -1 2 d s 1410 494 m -1 2 d s 1409 496 m -1 2 d s 1408 498 m 2 Y s 1408 500 m 1 Y s 1404 511 m20 1404 511 m20 1400 522 m s 1400 522 m -1 2 d s 1399 524 m 2 Y s 1399 526 m -1 2 d s 1398 528 m 2 Y s 1398 530 m -1 2 d s 1397 532 m -1 2 d s 1396 534 m 2 Y s 1396 536 m -1 2 d s 1395 538 m 2 Y s 1395 540 m -1 2 d s 1394 542 m 2 Y s 1391 555 m20 1391 555 m20 1388 566 m s 1388 566 m 2 Y s 1388 568 m 2 Y s 1388 570 m -1 2 d s 1387 572 m 2 Y s 1387 574 m -1 2 d s 1386 576 m 2 Y s 1386 578 m 2 Y s 1386 580 m -1 2 d s 1385 582 m 2 Y s 1385 584 m -1 2 d s 1384 586 m 2 Y s 1384 588 m s 1382 599 m20 1382 599 m20 1380 610 m 2 Y s 1380 612 m 2 Y s 1380 614 m 2 Y s 1380 616 m -1 2 d s 1379 618 m 2 Y s 1379 620 m 2 Y s 1379 622 m 2 Y s 1379 624 m -1 2 d s 1378 626 m 2 Y s 1378 628 m 2 Y s 1378 630 m 2 Y s 680 794 1361 227 C 2268 2268 0 0 C 1378 632 m -1 2 d s 1377 634 m 2 Y s 1377 636 m 2 Y s 1377 638 m 2 Y s 1377 640 m -1 2 d s 1376 642 m 2 Y s 1376 644 m 2 Y s 1376 646 m 2 Y s 1376 648 m 2 Y s 1376 650 m -1 2 d s 1375 652 m 2 Y s 1375 654 m s 1374 665 m20 1374 665 m20 1373 677 m s 1373 677 m 2 Y s 1373 679 m 2 Y s 1373 681 m -1 2 d s 1372 683 m 2 Y s 1372 685 m 2 Y s 1372 687 m 2 Y s 1372 689 m 2 Y s 1372 691 m 2 Y s 1372 693 m 2 Y s 1372 695 m -1 2 d s 1371 697 m 2 Y s 1371 699 m s 1370 711 m20 1370 711 m20 1370 722 m 1 Y s 1370 723 m 2 Y s 1370 725 m 2 Y s 1370 727 m -1 2 d s 1369 729 m 2 Y s 1369 731 m 2 Y s 1369 733 m 2 Y s 1369 735 m 2 Y s 1369 737 m 2 Y s 1369 739 m 2 Y s 1369 741 m 2 Y s 1369 743 m 2 Y s 1368 756 m20 1368 756 m20 1368 767 m 2 Y s 1368 769 m -1 2 d s 1367 771 m 2 Y s 1367 773 m 2 Y s 1367 775 m 2 Y s 1367 777 m 2 Y s 1367 779 m 2 Y s 1367 781 m 2 Y s 1367 783 m 2 Y s 1367 785 m 2 Y s 1367 787 m 2 Y s 1367 789 m 1 Y s 1366 801 m20 1366 801 m20 1366 813 m s 1366 813 m 2 Y s 1366 815 m 2 Y s 1366 817 m 2 Y s 1366 819 m 2 Y s 1366 821 m 2 Y s 1366 823 m 2 Y s 1366 825 m 2 Y s 1366 827 m 2 Y s 1366 829 m 2 Y s 1366 831 m -1 2 d s 1365 833 m 2 Y s 1365 835 m s 1365 847 m20 1365 847 m20 1365 858 m s 1365 858 m 2 Y s 1365 860 m 2 Y s 1365 862 m 2 Y s 1365 864 m 2 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227 C 2268 2268 0 0 C 680 794 1361 227 C 2268 2268 0 0 C /xs 0 def (combined) /Times-Roman 48 stwn gsave 1996 386 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (combined) show gr 680 794 1361 227 C 2268 2268 0 0 C 680 794 1361 227 C 2268 2268 0 0 C /xs 0 def (tail) /Times-Roman 48 stwn gsave 1996 902 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (tail) show gr 680 794 1361 227 C 2268 2268 0 0 C 1 lw 1361 520 m 11 X s 1383 520 m 12 X s 1406 520 m 12 X s 1429 520 m 11 X s 1452 520 m 11 X s 1474 520 m 12 X s 1497 520 m 11 X s 1520 520 m 11 X s 1542 520 m 12 X s 1565 520 m 11 X s 1588 520 m 11 X s 1610 520 m 12 X s 1633 520 m 11 X s 1656 520 m 11 X s 1678 520 m 12 X s 1701 520 m 11 X s 1724 520 m 11 X s 1746 520 m 12 X s 1769 520 m 11 X s 1792 520 m 11 X s 1814 520 m 12 X s 1837 520 m 11 X s 1860 520 m 11 X s 1882 520 m 12 X s 1905 520 m 11 X s 1928 520 m 11 X s 1950 520 m 12 X s 1973 520 m 11 X s 1996 520 m 11 X s 2019 520 m 11 X s 680 794 1361 227 C gr gr showpage 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/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique 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/degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 680 794 454 1247 bl 680 794 454 1247 C NC 454 1247 m 794 Y s 488 1247 m -34 X s 471 1279 m -17 X s 471 1311 m -17 X s 471 1343 m -17 X s 471 1374 m -17 X s 488 1406 m -34 X s 471 1438 m -17 X s 471 1470 m -17 X s 471 1501 m -17 X s 471 1533 m -17 X s 488 1565 m -34 X s 471 1597 m -17 X s 471 1628 m -17 X s 471 1660 m -17 X s 471 1692 m -17 X s 488 1724 m -34 X s 471 1755 m -17 X s 471 1787 m -17 X s 471 1819 m -17 X s 471 1851 m -17 X s 488 1882 m -34 X s 471 1914 m -17 X s 471 1946 m -17 X s 471 1978 m -17 X s 471 2009 m -17 X s 488 2041 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 408 1225 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 408 1383 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 408 1542 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 408 1701 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 408 1860 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr /xs 0 def (5) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (5) show gr 454 1247 m 680 X s 454 1281 m -34 Y s 488 1264 m -17 Y s 522 1264 m -17 Y s 556 1264 m -17 Y s 590 1264 m -17 Y s 624 1281 m -34 Y s 658 1264 m -17 Y s 692 1264 m -17 Y s 726 1264 m -17 Y s 760 1264 m -17 Y s 794 1281 m -34 Y s 828 1264 m -17 Y s 862 1264 m -17 Y s 896 1264 m -17 Y s 930 1264 m -17 Y s 964 1281 m -34 Y s 998 1264 m -17 Y s 1032 1264 m -17 Y s 1066 1264 m -17 Y s 1100 1264 m -17 Y s 1134 1281 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 624 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 794 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 964 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 1134 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr 680 794 454 1247 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn gsave 1134 1102 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show gr 680 794 454 1247 C 3 lw 454 1264 m 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 2 d 2 2 d 2 2 d 2 1 d 2 2 d 2 2 d 2 3 d 2 2 d 2 2 d 3 3 d 2 2 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 4 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 2 d 2 3 d 2 2 d 2 2 d 2 2 d 3 2 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 1 d 2 1 d 2 1 d 2 X 2 1 d 2 1 d 2 1 d 2 1 d 2 X 2 1 d 2 1 d 2 1 d 2 X 2 1 d 2 1 d 2 1 d 3 1 d 2 X 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 1 d 2 2 d 2 1 d 2 1 d 2 1 d 2 1 d 3 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 2 d 2 1 d 2 2 d 2 2 d 2 1 d 2 2 d 2 2 d 3 1 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 1 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 3 d 2 2 d 2 2 d 2 2 d 2 2 d 2 3 d 3 2 d 2 2 d 2 2 d 2 3 d 2 2 d 2 3 d 2 2 d 2 3 d 2 2 d 2 3 d 2 2 d 2 3 d 2 2 d 2 3 d 2 3 d 2 2 d 2 3 d 2 3 d 2 3 d 2 2 d 2 3 d 2 3 d 3 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 4 d 2 3 d 2 3 d 2 4 d 2 3 d 2 3 d 2 4 d 2 3 d 2 4 d 2 3 d 2 4 d 2 3 d 3 4 d 2 3 d 2 4 d 2 4 d 2 4 d 2 3 d 2 4 d 2 4 d 2 4 d 2 4 d 2 4 d 2 4 d 2 3 d 2 5 d 2 4 d 2 4 d 2 4 d 2 4 d 2 4 d 2 4 d 2 5 d 2 4 d 3 4 d 2 4 d 2 5 d 2 4 d 2 5 d 2 4 d 2 5 d s 869 1724 m 2 4 d 2 5 d 2 4 d 2 5 d 2 5 d 2 4 d 2 5 d 2 5 d 2 4 d 2 5 d 2 5 d 2 5 d 2 5 d 2 5 d 2 5 d 3 5 d 2 5 d 2 5 d 2 5 d 2 5 d 2 6 d 2 5 d 2 5 d 2 6 d 2 5 d 2 5 d 2 6 d 2 5 d 2 6 d 2 5 d 2 6 d 2 6 d 2 5 d 2 6 d 2 6 d 2 6 d 2 6 d 3 6 d 2 6 d 2 6 d 2 6 d 2 6 d 2 6 d 2 6 d 2 7 d 2 6 d 2 6 d 2 7 d 2 7 d 2 6 d 2 7 d 2 7 d 2 6 d 2 7 d 2 7 d 2 7 d 2 7 d s 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 301 1962 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 471 1914 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (c.) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 513 1914 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (CV) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 590 1914 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (valence) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 811 1914 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (tail) show gr 680 794 454 1247 C 2268 2268 0 0 C 1 lw 513 1247 m 23 Y s 513 1293 m 22 Y s 513 1338 m 23 Y s 513 1383 m 23 Y s 513 1429 m 23 Y s 513 1474 m 23 Y s 513 1520 m 22 Y s 513 1565 m 23 Y s 513 1610 m 23 Y s 513 1656 m 22 Y s 513 1701 m 23 Y s 513 1746 m 23 Y s 513 1792 m 22 Y s 513 1837 m 23 Y s 513 1882 m 23 Y s 513 1928 m 22 Y s 513 1973 m 23 Y s 513 2019 m 22 Y s 680 794 454 1247 C 2268 2268 0 0 C 572 1247 m 23 Y s 572 1293 m 22 Y s 572 1338 m 23 Y s 572 1383 m 23 Y s 572 1429 m 23 Y s 572 1474 m 23 Y s 572 1520 m 22 Y s 572 1565 m 23 Y s 572 1610 m 23 Y s 572 1656 m 22 Y s 572 1701 m 23 Y s 572 1746 m 23 Y s 572 1792 m 22 Y s 572 1837 m 23 Y s 572 1882 m 23 Y s 572 1928 m 22 Y s 572 1973 m 23 Y s 572 2019 m 22 Y s 680 794 454 1247 C 2268 2268 0 0 C 786 1247 m 23 Y s 786 1293 m 22 Y s 786 1338 m 23 Y s 786 1383 m 23 Y s 786 1429 m 23 Y s 786 1474 m 23 Y s 786 1520 m 22 Y s 786 1565 m 23 Y s 786 1610 m 23 Y s 786 1656 m 22 Y s 786 1701 m 23 Y s 786 1746 m 23 Y s 786 1792 m 22 Y s 786 1837 m 23 Y s 786 1882 m 23 Y s 786 1928 m 22 Y s 786 1973 m 23 Y s 786 2019 m 22 Y s 680 794 454 1247 C 2268 2268 0 0 C 454 1323 m 11 X s 476 1323 m 12 X s 499 1323 m 11 X s 522 1323 m 11 X s 544 1323 m 12 X s 567 1323 m 11 X s 590 1323 m 11 X s 612 1323 m 12 X s 635 1323 m 11 X s 658 1323 m 11 X s 680 1323 m 12 X s 703 1323 m 11 X s 726 1323 m 11 X s 748 1323 m 12 X s 771 1323 m 11 X s 794 1323 m 11 X s 816 1323 m 12 X s 839 1323 m 11 X s 862 1323 m 11 X s 885 1323 m 11 X s 907 1323 m 12 X s 930 1323 m 11 X s 953 1323 m 11 X s 975 1323 m 12 X s 998 1323 m 11 X s 1021 1323 m 11 X s 1043 1323 m 12 X s 1066 1323 m 11 X s 1089 1323 m 11 X s 1111 1323 m 12 X s 680 794 454 1247 C 2268 2268 0 0 C 454 1374 m 11 X s 476 1374 m 12 X s 499 1374 m 11 X s 522 1374 m 11 X s 544 1374 m 12 X s 567 1374 m 11 X s 590 1374 m 11 X s 612 1374 m 12 X s 635 1374 m 11 X s 658 1374 m 11 X s 680 1374 m 12 X s 703 1374 m 11 X s 726 1374 m 11 X s 748 1374 m 12 X s 771 1374 m 11 X s 794 1374 m 11 X s 816 1374 m 12 X s 839 1374 m 11 X s 862 1374 m 11 X s 885 1374 m 11 X s 907 1374 m 12 X s 930 1374 m 11 X s 953 1374 m 11 X s 975 1374 m 12 X s 998 1374 m 11 X s 1021 1374 m 11 X s 1043 1374 m 12 X s 1066 1374 m 11 X s 1089 1374 m 11 X s 1111 1374 m 12 X s 680 794 454 1247 C 2268 2268 0 0 C 454 1567 m 11 X s 476 1567 m 12 X s 499 1567 m 11 X s 522 1567 m 11 X s 544 1567 m 12 X s 567 1567 m 11 X s 590 1567 m 11 X s 612 1567 m 12 X s 635 1567 m 11 X s 658 1567 m 11 X s 680 1567 m 12 X s 703 1567 m 11 X s 726 1567 m 11 X s 748 1567 m 12 X s 771 1567 m 11 X s 794 1567 m 11 X s 816 1567 m 12 X s 839 1567 m 11 X s 862 1567 m 11 X s 885 1567 m 11 X s 907 1567 m 12 X s 930 1567 m 11 X s 953 1567 m 11 X s 975 1567 m 12 X s 998 1567 m 11 X s 1021 1567 m 11 X s 1043 1567 m 12 X s 1066 1567 m 11 X s 1089 1567 m 11 X s 1111 1567 m 12 X s 680 794 454 1247 C NC 680 794 1361 1247 bl 680 794 1361 1247 C NC 1361 1247 m 794 Y s 1395 1247 m -34 X s 1378 1279 m -17 X s 1378 1311 m -17 X s 1378 1343 m -17 X s 1378 1374 m -17 X s 1395 1406 m -34 X s 1378 1438 m -17 X s 1378 1470 m -17 X s 1378 1501 m -17 X s 1378 1533 m -17 X s 1395 1565 m -34 X s 1378 1597 m -17 X s 1378 1628 m -17 X s 1378 1660 m -17 X s 1378 1692 m -17 X s 1395 1724 m -34 X s 1378 1755 m -17 X s 1378 1787 m -17 X s 1378 1819 m -17 X s 1378 1851 m -17 X s 1395 1882 m -34 X s 1378 1914 m -17 X s 1378 1946 m -17 X s 1378 1978 m -17 X s 1378 2009 m -17 X s 1395 2041 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 1315 1225 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 1315 1383 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1315 1542 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1315 1701 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 1315 1860 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr /xs 0 def (5) /Times-Roman 68 stwn gsave 1315 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (5) show gr 1361 1247 m 680 X s 1361 1281 m -34 Y s 1395 1264 m -17 Y s 1429 1264 m -17 Y s 1463 1264 m -17 Y s 1497 1264 m -17 Y s 1531 1281 m -34 Y s 1565 1264 m -17 Y s 1599 1264 m -17 Y s 1633 1264 m -17 Y s 1667 1264 m -17 Y s 1701 1281 m -34 Y s 1735 1264 m -17 Y s 1769 1264 m -17 Y s 1803 1264 m -17 Y s 1837 1264 m -17 Y s 1871 1281 m -34 Y s 1905 1264 m -17 Y s 1939 1264 m -17 Y s 1973 1264 m -17 Y s 2007 1264 m -17 Y s 2041 1281 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 1361 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1531 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 1701 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr /xs 0 def (6) /Times-Roman 68 stwn gsave 1871 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (6) show gr /xs 0 def (8) /Times-Roman 68 stwn gsave 2041 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (8) show gr 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (g) /Times-Roman 86 stwn (1) /Times-Roman 60 stwn (\(r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn (\)) /Times-Roman 86 stwn gsave 2041 1102 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (g) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (1) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\)) show gr 680 794 1361 1247 C 3 lw 1363 1248 m 1 2 d 2 1 d 3 2 d 5 2 d 8 1 d 13 2 d 20 1 d 29 2 d 42 2 d 56 1 d 69 2 d 78 1 d 79 2 d 74 1 d 63 2 d 47 2 d 32 1 d 16 2 d 4 1 d -8 2 d -15 2 d -21 1 d -25 2 d -27 1 d -28 2 d -28 2 d -27 1 d -26 2 d -25 1 d -23 2 d -22 1 d -21 2 d -19 2 d -18 1 d -16 2 d -16 1 d -14 2 d -13 2 d -12 1 d -11 2 d -10 1 d -10 2 d -8 2 d -8 1 d -7 2 d -6 1 d -6 2 d -5 2 d -4 1 d -4 2 d -4 1 d -2 2 d -3 1 d -1 2 d -1 2 d -1 1 d 2 Y 1 1 d 2 2 d 2 2 d 4 1 d 5 2 d 5 1 d 8 2 d 9 2 d 11 1 d 14 2 d 16 1 d 20 2 d 23 2 d 27 1 d 31 2 d 34 1 d 36 2 d 38 1 d 36 2 d 35 2 d 30 1 d 24 2 d 18 1 d 11 2 d 5 2 d 1 Y -4 2 d -7 1 d -10 2 d -11 2 d -12 1 d -12 2 d -13 1 d -12 2 d -12 1 d -12 2 d -12 2 d -11 1 d -11 2 d -11 1 d -10 2 d -10 2 d -9 1 d -9 2 d -9 1 d -9 2 d -8 2 d -9 1 d -7 2 d -8 1 d -8 2 d -7 2 d -7 1 d -7 2 d -6 1 d -7 2 d -6 1 d -6 2 d -6 2 d -6 1 d -6 2 d -5 1 d -6 2 d -5 2 d -5 1 d -5 2 d -5 1 d -5 2 d -5 2 d -4 1 d -5 2 d -4 1 d -5 2 d -4 2 d -4 1 d -4 2 d -4 1 d -4 2 d -3 1 d -4 2 d -4 2 d -3 1 d -4 2 d -3 1 d -3 2 d -3 2 d -4 1 d -3 2 d -3 1 d -3 2 d -3 2 d -2 1 d -3 2 d -3 1 d -2 2 d -3 2 d -3 1 d -2 2 d -2 1 d -3 2 d -2 1 d -2 2 d -3 2 d -2 1 d -2 2 d -2 1 d -2 2 d -2 2 d -2 1 d -2 2 d -2 1 d -2 2 d -2 2 d -1 1 d -2 2 d -2 1 d -1 2 d -2 1 d -2 2 d -1 2 d -2 1 d -1 2 d -2 1 d -1 2 d -2 2 d -1 1 d -1 2 d -2 1 d -1 2 d -1 2 d -1 1 d -2 2 d -1 1 d -1 2 d -1 2 d -1 1 d -2 2 d -1 1 d -1 2 d -1 1 d -1 2 d -1 2 d -1 1 d -1 2 d -1 1 d -1 2 d s 1429 1571 m -1 2 d 1 Y -1 2 d -1 1 d -1 2 d -1 2 d -1 1 d -1 2 d 1 Y -1 2 d -1 2 d -1 1 d 2 Y -1 1 d -1 2 d -1 1 d 2 Y -1 2 d -1 1 d 2 Y -1 1 d -1 2 d 2 Y -1 1 d 2 Y -1 1 d -1 2 d 2 Y -1 1 d 2 Y -1 1 d 2 Y -1 1 d 2 Y -1 2 d 1 Y -1 2 d 1 Y -1 2 d 2 Y -1 1 d 2 Y -1 1 d 2 Y -1 2 d 3 Y -1 1 d 2 Y -1 2 d 3 Y -1 1 d 2 Y -1 1 d 4 Y -1 1 d 3 Y -1 2 d 3 Y -1 2 d 3 Y -1 2 d 3 Y -1 1 d 4 Y -1 1 d 5 Y -1 1 d 4 Y -1 1 d 5 Y -1 2 d 4 Y -1 2 d 6 Y -1 2 d 5 Y -1 1 d 7 Y -1 1 d 7 Y -1 1 d 8 Y -1 2 d 6 Y -1 2 d 8 Y -1 1 d 10 Y -1 1 d 10 Y -1 1 d 12 Y -1 1 d 11 Y -1 2 d 13 Y -1 1 d 15 Y -1 1 d 16 Y -1 2 d 17 Y -1 2 d 11 Y s 1371 1894 m 9 Y -1 2 d 22 Y -1 2 d 27 Y -1 1 d 29 Y -1 2 d 39 Y -1 2 d 13 Y s 2268 2268 0 0 C 1361 1248 m 2 Y s 1361 1250 m 1 Y s 1361 1251 m 2 Y s 1361 1253 m 2 Y s 1361 1255 m 1 Y s 1361 1256 m 2 Y s 1361 1258 m 1 Y s 1361 1259 m 2 Y s 1361 1261 m 2 Y s 1361 1263 m 1 Y s 1361 1264 m 2 Y s 1361 1266 m 1 Y s 1361 1267 m 2 Y s 1361 1269 m 1 Y s 1361 1270 m 1 Y s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 1361 1282 m20 1361 1282 m20 1361 1294 m s 1361 1294 m 2 Y s 1361 1296 m 1 Y s 1361 1297 m 2 Y s 1361 1299 m 2 Y s 1361 1301 m 1 Y s 1361 1302 m 2 Y s 1361 1304 m 1 Y s 1361 1305 m 2 Y s 1361 1307 m 2 Y s 1361 1309 m 1 Y s 1361 1310 m 2 Y s 1361 1312 m 1 Y s 1361 1313 m 2 Y s 1361 1315 m 1 Y s 1362 1328 m20 1362 1328 m20 1369 1335 m 2 1 d s 1371 1336 m 6 1 d s 1377 1337 m 9 2 d s 1386 1339 m 6 1 d s 1403 1341 m20 1403 1341 m20 1414 1342 m 1 X s 1415 1342 m 20 2 d s 1435 1344 m 2 X s 1448 1345 m20 1448 1345 m20 1459 1345 m 19 2 d s 1478 1347 m 4 X s 1493 1348 m20 1493 1348 m20 1505 1349 m 10 1 d s 1515 1350 m 12 1 d s 1538 1352 m20 1538 1352 m20 1550 1353 m 15 2 d s 1565 1355 m 7 X s 1584 1356 m20 1584 1356 m20 1595 1357 m 9 1 d s 1604 1358 m 14 1 d s 1629 1360 m20 1629 1360 m20 1640 1360 m 15 1 d s 1655 1361 m 8 X s 1674 1362 m20 1674 1362 m20 1686 1363 m s 1686 1363 m 22 1 d s 1719 1364 m20 1719 1364 m20 1731 1365 m 22 1 d s 1765 1366 m20 1765 1366 m20 1776 1367 m 18 X s 1794 1367 m 5 1 d s 1810 1368 m20 1810 1368 m20 1821 1369 m 10 X s 1831 1369 m 13 1 d s 1855 1370 m20 1855 1370 m20 1867 1371 m 22 1 d s 1901 1373 m20 1901 1373 m20 1912 1373 m 8 1 d s 1920 1374 m 15 1 d s 1946 1377 m20 1946 1377 m20 1953 1381 m -3 1 d s 1950 1382 m -7 1 d s 1943 1383 m -10 2 d s 1933 1385 m -2 X s 1920 1387 m20 1920 1387 m20 1909 1388 m -11 2 d s 1898 1390 m -12 1 d s 1875 1393 m20 1875 1393 m20 1864 1394 m -3 X s 1861 1394 m -12 2 d s 1849 1396 m -8 1 d s 1830 1399 m20 1830 1399 m20 1819 1400 m -4 1 d s 1815 1401 m -11 1 d s 1804 1402 m -8 2 d s 1785 1405 m20 1785 1405 m20 1774 1407 m -8 2 d s 1766 1409 m -9 1 d s 1757 1410 m -5 1 d s 1740 1413 m20 1740 1413 m20 1729 1416 m -5 1 d s 1724 1417 m -8 1 d s 1716 1418 m -8 2 d s 1708 1420 m -1 X s 1696 1423 m20 1696 1423 m20 1685 1425 m -4 1 d s 1681 1426 m -7 2 d s 1674 1428 m -6 1 d s 1668 1429 m -5 2 d s 1652 1434 m20 1652 1434 m20 1641 1437 m -2 X s 1639 1437 m -6 2 d s 1633 1439 m -5 2 d s 1628 1441 m -5 1 d s 1623 1442 m -4 1 d s 1609 1447 m20 1609 1447 m20 1598 1450 m -4 2 d s 1594 1452 m -4 1 d s 1590 1453 m -5 2 d s 1585 1455 m -4 2 d s 1581 1457 m -4 1 d s 1577 1458 m s 1566 1463 m20 1566 1463 m20 1556 1467 m -2 1 d s 1554 1468 m -3 1 d s 1551 1469 m -4 2 d s 1547 1471 m -3 1 d s 1544 1472 m -3 2 d s 1541 1474 m -3 2 d s 1538 1476 m -3 1 d s 1525 1482 m20 1525 1482 m20 1515 1488 m -1 X s 1514 1488 m -2 2 d s 1512 1490 m -3 2 d s 1509 1492 m -3 1 d s 1506 1493 m -2 2 d s 1504 1495 m -2 1 d s 1502 1496 m -3 2 d s 1499 1498 m -2 1 d s 1497 1499 m -1 1 d s 1487 1507 m20 1487 1507 m20 1478 1514 m s 1478 1514 m -2 1 d s 1476 1515 m -2 2 d s 1474 1517 m -2 2 d s 1472 1519 m -1 1 d s 1471 1520 m -2 2 d s 1469 1522 m -2 1 d s 1467 1523 m -1 2 d s 1466 1525 m -2 1 d s 1464 1526 m -2 2 d s 1462 1528 m -1 1 d s 1454 1537 m20 1454 1537 m20 1446 1546 m 1 Y s 1446 1547 m -2 2 d s 1444 1549 m -1 1 d s 1443 1550 m -1 2 d s 1442 1552 m -1 2 d s 1441 1554 m -1 1 d s 1440 1555 m -2 2 d s 1438 1557 m -1 1 d s 1437 1558 m -1 2 d s 1436 1560 m -1 1 d s 1435 1561 m -1 2 d s 1434 1563 m -1 1 d s 680 794 1361 1247 C 2268 2268 0 0 C 1429 1571 m -1 2 d s 1428 1573 m 1 Y s 1428 1574 m -1 2 d s 1427 1576 m -1 1 d s 1426 1577 m -1 2 d s 1425 1579 m -1 2 d s 1424 1581 m -1 1 d s 1423 1582 m -1 2 d s 1422 1584 m 1 Y s 1422 1585 m -1 2 d s 1421 1587 m -1 2 d s 1420 1589 m -1 1 d s 1419 1590 m 1 Y s 1414 1601 m20 1414 1601 m20 1410 1612 m s 1410 1612 m -1 2 d s 1409 1614 m 2 Y s 1409 1616 m -1 1 d s 1408 1617 m 2 Y s 1408 1619 m -1 1 d s 1407 1620 m 2 Y s 1407 1622 m -1 1 d s 1406 1623 m 2 Y s 1406 1625 m -1 2 d s 1405 1627 m 1 Y s 1405 1628 m -1 2 d s 1404 1630 m 1 Y s 1404 1631 m -1 2 d s 1403 1633 m 1 Y s 1400 1644 m20 1400 1644 m20 1397 1655 m 2 Y s 1397 1657 m -1 1 d s 1396 1658 m 2 Y s 1396 1660 m 2 Y s 1396 1662 m -1 1 d s 1395 1663 m 2 Y s 1395 1665 m 1 Y s 1395 1666 m -1 2 d s 1394 1668 m 2 Y s 1394 1670 m 1 Y s 1394 1671 m -1 2 d s 1393 1673 m 1 Y s 1393 1674 m 2 Y s 1393 1676 m -1 2 d s 1392 1678 m s 1390 1689 m20 1390 1689 m20 1388 1700 m 1 Y s 1388 1701 m 2 Y s 1388 1703 m -1 2 d s 1387 1705 m 1 Y s 1387 1706 m 2 Y s 1387 1708 m 1 Y s 1387 1709 m -1 2 d s 1386 1711 m 2 Y s 1386 1713 m 1 Y s 1386 1714 m 2 Y s 1386 1716 m 1 Y s 1386 1717 m -1 2 d s 1385 1719 m 1 Y s 1385 1720 m 2 Y s 1385 1722 m s 1383 1734 m20 1383 1734 m20 1382 1745 m 1 Y s 1382 1746 m 2 Y s 1382 1748 m 1 Y s 1382 1749 m -1 2 d s 1381 1751 m 1 Y s 1381 1752 m 2 Y s 1381 1754 m 1 Y s 1381 1755 m 2 Y s 1381 1757 m -1 2 d s 1380 1759 m 1 Y s 1380 1760 m 2 Y s 1380 1762 m 1 Y s 1380 1763 m 2 Y s 1380 1765 m 2 Y s 1380 1767 m s 1379 1779 m20 1379 1779 m20 1378 1790 m -1 X s 1377 1790 m 2 Y s 1377 1792 m 2 Y s 1377 1794 m 1 Y s 1377 1795 m 2 Y s 1377 1797 m 1 Y s 1377 1798 m 2 Y s 1377 1800 m 2 Y s 1377 1802 m -1 1 d s 1376 1803 m 2 Y s 1376 1805 m 1 Y s 1376 1806 m 2 Y s 1376 1808 m 2 Y s 1376 1810 m 1 Y s 1376 1811 m 2 Y s 1375 1824 m20 1375 1824 m20 1374 1835 m 2 Y s 1374 1837 m 1 Y s 1374 1838 m 2 Y s 1374 1840 m 1 Y s 1374 1841 m 2 Y s 1374 1843 m 2 Y s 1374 1845 m -1 1 d s 1373 1846 m 2 Y s 1373 1848 m 1 Y s 1373 1849 m 2 Y s 1373 1851 m 1 Y s 1373 1852 m 2 Y s 1373 1854 m 2 Y s 1373 1856 m 1 Y s 1373 1857 m 1 Y s 1372 1869 m20 1372 1869 m20 1372 1881 m s 1372 1881 m -1 2 d s 1371 1883 m 1 Y s 1371 1884 m 2 Y s 1371 1886 m 1 Y s 1371 1887 m 2 Y s 1371 1889 m 2 Y s 1371 1891 m 1 Y s 1371 1892 m 2 Y s 680 794 1361 1247 C 2268 2268 0 0 C 1371 1894 m 1 Y s 1371 1895 m 2 Y s 1371 1897 m 2 Y s 1371 1899 m 1 Y s 1371 1900 m 2 Y s 1371 1902 m 1 Y s 1371 1903 m -1 2 d s 1370 1905 m 2 Y s 1370 1907 m 1 Y s 1370 1908 m 2 Y s 1370 1910 m 1 Y s 1370 1911 m 2 Y s 1370 1913 m 2 Y s 1370 1915 m 1 Y s 1370 1916 m s 1369 1928 m20 1369 1928 m20 1369 1939 m 1 Y s 1369 1940 m 2 Y s 1369 1942 m 1 Y s 1369 1943 m 2 Y s 1369 1945 m 1 Y s 1369 1946 m 2 Y s 1369 1948 m 1 Y s 1369 1949 m 2 Y s 1369 1951 m 2 Y s 1369 1953 m 1 Y s 1369 1954 m 2 Y s 1369 1956 m -1 1 d s 1368 1957 m 2 Y s 1368 1959 m 2 Y s 1368 1961 m 1 Y s 1368 1973 m20 1368 1973 m20 1368 1984 m 2 Y s 1368 1986 m -1 2 d s 1367 1988 m 1 Y s 1367 1989 m 2 Y s 1367 1991 m 1 Y s 1367 1992 m 2 Y s 1367 1994 m 2 Y s 1367 1996 m 1 Y s 1367 1997 m 2 Y s 1367 1999 m 1 Y s 1367 2000 m 2 Y s 1367 2002 m 2 Y s 1367 2004 m 1 Y s 1367 2005 m 2 Y s 1367 2007 m s 1367 2018 m20 1367 2018 m20 1366 2030 m 1 Y s 1366 2031 m 1 Y s 1366 2032 m 2 Y s 1366 2034 m 1 Y s 1366 2035 m 2 Y s 1366 2037 m 2 Y s 1366 2039 m 1 Y s 1366 2040 m 1 Y s 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C gsave 1208 1962 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show gr 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (c.) /Times-Roman 48 stwn gsave 2007 1289 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (c.) show gr 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (CV) /Times-Roman 48 stwn gsave 2007 1332 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (CV) show gr 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (valence) /Times-Roman 48 stwn gsave 2007 1454 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (valence) show gr 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (tail) /Times-Roman 48 stwn gsave 2007 1914 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (tail) show gr 680 794 1361 1247 C 2268 2268 0 0 C 1 lw 1361 1323 m 11 X s 1383 1323 m 12 X s 1406 1323 m 12 X s 1429 1323 m 11 X s 1452 1323 m 11 X s 1474 1323 m 12 X s 1497 1323 m 11 X s 1520 1323 m 11 X s 1542 1323 m 12 X s 1565 1323 m 11 X s 1588 1323 m 11 X s 1610 1323 m 12 X s 1633 1323 m 11 X s 1656 1323 m 11 X s 1678 1323 m 12 X s 1701 1323 m 11 X s 1724 1323 m 11 X s 1746 1323 m 12 X s 1769 1323 m 11 X s 1792 1323 m 11 X s 1814 1323 m 12 X s 1837 1323 m 11 X s 1860 1323 m 11 X s 1882 1323 m 12 X s 1905 1323 m 11 X s 1928 1323 m 11 X s 1950 1323 m 12 X s 1973 1323 m 11 X s 1996 1323 m 11 X s 2019 1323 m 11 X s 680 794 1361 1247 C 2268 2268 0 0 C 1361 1374 m 11 X s 1383 1374 m 12 X s 1406 1374 m 12 X s 1429 1374 m 11 X s 1452 1374 m 11 X s 1474 1374 m 12 X s 1497 1374 m 11 X s 1520 1374 m 11 X s 1542 1374 m 12 X s 1565 1374 m 11 X s 1588 1374 m 11 X s 1610 1374 m 12 X s 1633 1374 m 11 X s 1656 1374 m 11 X s 1678 1374 m 12 X s 1701 1374 m 11 X s 1724 1374 m 11 X s 1746 1374 m 12 X s 1769 1374 m 11 X s 1792 1374 m 11 X s 1814 1374 m 12 X s 1837 1374 m 11 X s 1860 1374 m 11 X s 1882 1374 m 12 X s 1905 1374 m 11 X s 1928 1374 m 11 X s 1950 1374 m 12 X s 1973 1374 m 11 X s 1996 1374 m 11 X s 2019 1374 m 11 X s 680 794 1361 1247 C 2268 2268 0 0 C 1361 1567 m 11 X s 1383 1567 m 12 X s 1406 1567 m 12 X s 1429 1567 m 11 X s 1452 1567 m 11 X s 1474 1567 m 12 X s 1497 1567 m 11 X s 1520 1567 m 11 X s 1542 1567 m 12 X s 1565 1567 m 11 X s 1588 1567 m 11 X s 1610 1567 m 12 X s 1633 1567 m 11 X s 1656 1567 m 11 X s 1678 1567 m 12 X s 1701 1567 m 11 X s 1724 1567 m 11 X s 1746 1567 m 12 X s 1769 1567 m 11 X s 1792 1567 m 11 X s 1814 1567 m 12 X s 1837 1567 m 11 X s 1860 1567 m 11 X s 1882 1567 m 12 X s 1905 1567 m 11 X s 1928 1567 m 11 X s 1950 1567 m 12 X s 1973 1567 m 11 X s 1996 1567 m 11 X s 2019 1567 m 11 X s 680 794 1361 1247 C NC 680 794 454 227 bl 680 794 454 227 C NC 454 227 m 794 Y s 488 227 m -34 X s 471 259 m -17 X s 471 290 m -17 X s 471 322 m -17 X s 471 354 m -17 X s 488 386 m -34 X s 471 417 m -17 X s 471 449 m -17 X s 471 481 m -17 X s 471 513 m -17 X s 488 544 m -34 X s 471 576 m -17 X s 471 608 m -17 X s 471 640 m -17 X s 471 671 m -17 X s 488 703 m -34 X s 471 735 m -17 X s 471 767 m -17 X s 471 798 m -17 X s 471 830 m -17 X s 488 862 m -34 X s 471 894 m -17 X s 471 925 m -17 X s 471 957 m -17 X s 471 989 m -17 X s 488 1021 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 408 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 408 363 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 408 522 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 408 680 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 408 839 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr /xs 0 def (5) /Times-Roman 68 stwn gsave 408 998 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (5) show gr 454 227 m 680 X s 454 261 m -34 Y s 488 244 m -17 Y s 522 244 m -17 Y s 556 244 m -17 Y s 590 244 m -17 Y s 624 261 m -34 Y s 658 244 m -17 Y s 692 244 m -17 Y s 726 244 m -17 Y s 760 244 m -17 Y s 794 261 m -34 Y s 828 244 m -17 Y s 862 244 m -17 Y s 896 244 m -17 Y s 930 244 m -17 Y s 964 261 m -34 Y s 998 244 m -17 Y s 1032 244 m -17 Y s 1066 244 m -17 Y s 1100 244 m -17 Y s 1134 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 624 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 794 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 964 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 1134 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr 680 794 454 227 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn gsave 1134 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show gr 680 794 454 227 C 3 lw 454 227 m -1 5 d 31 Y 1 7 d 15 Y 1 4 d 5 Y 1 1 d 1 -3 d 1 X 1 Y 1 2 d 1 4 d 1 2 d 1 1 d 2 3 d 2 4 d 1 Y 2 5 d 2 5 d 2 5 d 2 4 d 2 5 d 2 6 d 2 6 d 2 7 d 2 6 d 2 7 d 2 6 d 2 7 d 2 6 d 3 7 d 2 7 d 2 6 d 2 7 d 2 6 d 2 5 d 2 5 d 2 4 d 2 2 d 1 Y 1 1 d 3 X 1 -1 d 1 -1 d 1 -3 d 1 -1 d 2 -4 d -1 Y 2 -6 d -1 Y 2 -9 d 2 -9 d 2 -10 d 2 -11 d 2 -11 d 2 -10 d 2 -11 d 3 -10 d 2 -9 d 2 -8 d 2 -8 d 2 -6 d 2 -6 d 2 -5 d 2 -5 d 2 -3 d 2 -3 d 2 -3 d 2 -2 d 2 -1 d 2 -1 d 2 -1 d 8 X 2 1 d 2 1 d 2 1 d 2 X 3 2 d 2 1 d 2 1 d 2 1 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 3 1 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 3 2 d 2 1 d 2 2 d 2 1 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 2 d 2 1 d 2 2 d 2 1 d 2 2 d 2 2 d 3 1 d 2 2 d 2 2 d 2 2 d 2 1 d 2 2 d 2 2 d 2 2 d 2 2 d 2 1 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 1 d 2 2 d 2 2 d 3 2 d 2 2 d 2 3 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 3 d 2 2 d 2 2 d 2 2 d 2 2 d 3 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 3 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 3 2 d 2 2 d 2 3 d 2 2 d 2 2 d 2 2 d 2 2 d s 869 520 m 2 2 d 2 2 d 2 2 d 2 2 d 2 2 d 2 3 d 2 2 d 2 2 d 2 2 d 2 2 d 2 3 d 2 2 d 2 2 d 2 2 d 2 3 d 3 2 d 2 2 d 2 3 d 2 2 d 2 3 d 2 2 d 2 2 d 2 3 d 2 3 d 2 2 d 2 3 d 2 3 d 2 2 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 2 3 d 3 3 d 2 3 d 2 4 d 2 3 d 2 3 d 2 4 d 2 3 d 2 4 d 2 4 d 2 3 d 2 4 d 2 4 d 2 4 d 2 4 d 2 4 d 2 4 d 2 5 d 2 4 d 2 4 d 2 5 d 2 4 d 2 5 d 3 5 d 2 4 d 2 5 d 2 5 d 2 5 d 2 5 d 2 6 d 2 5 d 2 5 d 2 6 d 2 5 d 2 6 d 2 6 d 2 6 d 2 6 d 2 6 d 2 6 d 2 6 d 2 6 d 2 7 d 2 6 d 2 7 d 3 7 d 2 7 d 2 7 d 2 7 d 2 7 d 2 8 d 2 7 d 2 8 d 2 7 d 2 8 d 2 8 d 2 8 d 2 8 d 2 9 d 2 8 d 2 9 d 2 8 d 2 9 d 2 9 d 2 9 d 2 9 d 2 10 d 3 9 d 2 10 d 2 9 d s 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 301 941 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 471 894 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (c.) show gr 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 513 894 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (CV) show gr 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 590 894 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (valence) show gr 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 811 894 t 0 r 0 0 m /Times-Roman findfont 48 sf 0 0 m (tail) show gr 680 794 454 227 C 2268 2268 0 0 C 1 lw 513 227 m 22 Y s 513 272 m 23 Y s 513 318 m 22 Y s 513 363 m 23 Y s 513 408 m 23 Y s 513 454 m 22 Y s 513 499 m 23 Y s 513 544 m 23 Y s 513 590 m 22 Y s 513 635 m 23 Y s 513 680 m 23 Y s 513 726 m 22 Y s 513 771 m 23 Y s 513 816 m 23 Y s 513 862 m 23 Y s 513 907 m 23 Y s 513 953 m 22 Y s 513 998 m 23 Y s 680 794 454 227 C 2268 2268 0 0 C 572 227 m 22 Y s 572 272 m 23 Y s 572 318 m 22 Y s 572 363 m 23 Y s 572 408 m 23 Y s 572 454 m 22 Y s 572 499 m 23 Y s 572 544 m 23 Y s 572 590 m 22 Y s 572 635 m 23 Y s 572 680 m 23 Y s 572 726 m 22 Y s 572 771 m 23 Y s 572 816 m 23 Y s 572 862 m 23 Y s 572 907 m 23 Y s 572 953 m 22 Y s 572 998 m 23 Y s 680 794 454 227 C 2268 2268 0 0 C 786 227 m 22 Y s 786 272 m 23 Y s 786 318 m 22 Y s 786 363 m 23 Y s 786 408 m 23 Y s 786 454 m 22 Y s 786 499 m 23 Y s 786 544 m 23 Y s 786 590 m 22 Y s 786 635 m 23 Y s 786 680 m 23 Y s 786 726 m 22 Y s 786 771 m 23 Y s 786 816 m 23 Y s 786 862 m 23 Y s 786 907 m 23 Y s 786 953 m 22 Y s 786 998 m 23 Y s 680 794 454 227 C 2268 2268 0 0 C 454 436 m 11 X s 476 436 m 12 X s 499 436 m 11 X s 522 436 m 11 X s 544 436 m 12 X s 567 436 m 11 X s 590 436 m 11 X s 612 436 m 12 X s 635 436 m 11 X s 658 436 m 11 X s 680 436 m 12 X s 703 436 m 11 X s 726 436 m 11 X s 748 436 m 12 X s 771 436 m 11 X s 794 436 m 11 X s 816 436 m 12 X s 839 436 m 11 X s 862 436 m 11 X s 885 436 m 11 X s 907 436 m 12 X s 930 436 m 11 X s 953 436 m 11 X s 975 436 m 12 X s 998 436 m 11 X s 1021 436 m 11 X s 1043 436 m 12 X s 1066 436 m 11 X s 1089 436 m 11 X s 1111 436 m 12 X s 680 794 454 227 C 2268 2268 0 0 C 454 276 m 11 X s 476 276 m 12 X s 499 276 m 11 X s 522 276 m 11 X s 544 276 m 12 X s 567 276 m 11 X s 590 276 m 11 X s 612 276 m 12 X s 635 276 m 11 X s 658 276 m 11 X s 680 276 m 12 X s 703 276 m 11 X s 726 276 m 11 X s 748 276 m 12 X s 771 276 m 11 X s 794 276 m 11 X s 816 276 m 12 X s 839 276 m 11 X s 862 276 m 11 X s 885 276 m 11 X s 907 276 m 12 X s 930 276 m 11 X s 953 276 m 11 X s 975 276 m 12 X s 998 276 m 11 X s 1021 276 m 11 X s 1043 276 m 12 X s 1066 276 m 11 X s 1089 276 m 11 X s 1111 276 m 12 X s 680 794 454 227 C /w 20 def /w2 {w 2 div} def /w3 {w 3 div} def 513 434 m20 572 274 m20 NC 680 794 1361 227 bl 680 794 1361 227 C NC 1361 227 m 794 Y s 1395 227 m -34 X s 1378 259 m -17 X s 1378 290 m -17 X s 1378 322 m -17 X s 1378 354 m -17 X s 1395 386 m -34 X s 1378 417 m -17 X s 1378 449 m -17 X s 1378 481 m -17 X s 1378 513 m -17 X s 1395 544 m -34 X s 1378 576 m -17 X s 1378 608 m -17 X s 1378 640 m -17 X s 1378 671 m -17 X s 1395 703 m -34 X s 1378 735 m -17 X s 1378 767 m -17 X s 1378 798 m -17 X s 1378 830 m -17 X s 1395 862 m -34 X s 1378 894 m -17 X s 1378 925 m -17 X s 1378 957 m -17 X s 1378 989 m -17 X s 1395 1021 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 1315 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 1315 363 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1315 522 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1315 680 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 1315 839 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr /xs 0 def (5) /Times-Roman 68 stwn gsave 1315 998 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (5) show gr 1361 227 m 680 X s 1361 261 m -34 Y s 1395 244 m -17 Y s 1429 244 m -17 Y s 1463 244 m -17 Y s 1497 244 m -17 Y s 1531 261 m -34 Y s 1565 244 m -17 Y s 1599 244 m -17 Y s 1633 244 m -17 Y s 1667 244 m -17 Y s 1701 261 m -34 Y s 1735 244 m -17 Y s 1769 244 m -17 Y s 1803 244 m -17 Y s 1837 244 m -17 Y s 1871 261 m -34 Y s 1905 244 m -17 Y s 1939 244 m -17 Y s 1973 244 m -17 Y s 2007 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 1361 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1531 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 1701 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr /xs 0 def (6) /Times-Roman 68 stwn gsave 1871 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (6) show gr /xs 0 def (8) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (8) show gr 680 794 1361 227 C 2268 2268 0 0 C /xs 0 def (g) /Times-Roman 86 stwn (3) /Times-Roman 60 stwn (\(s\)) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (g) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (3) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(s\)) show gr 680 794 1361 227 C 3 lw 1361 228 m 23 Y 1 2 d 1 2 d 1 1 d 2 2 d 3 1 d 5 2 d 8 2 d 13 1 d 21 2 d 32 1 d 48 2 d 69 2 d 90 1 d 104 2 d 103 1 d 84 2 d 50 1 d 16 2 d -8 2 d -20 1 d -25 2 d -22 1 d -17 2 d -12 2 d -7 1 d -2 2 d 2 1 d 5 2 d 9 2 d 13 1 d 13 2 d 14 1 d 10 2 d 8 2 d 5 1 d 3 2 d 3 1 d 4 2 d 4 1 d 6 2 d 6 2 d 7 1 d 5 2 d 5 1 d 3 2 d 1 2 d -1 1 d -3 2 d -5 1 d -6 2 d -8 2 d -8 1 d -10 2 d -9 1 d -10 2 d -9 2 d -10 1 d -9 2 d -9 1 d -9 2 d -9 1 d -9 2 d -8 2 d -9 1 d -8 2 d -8 1 d -7 2 d -8 2 d -8 1 d -7 2 d -7 1 d -7 2 d -8 2 d -6 1 d -7 2 d -7 1 d -7 2 d -7 1 d -6 2 d -6 2 d -7 1 d -6 2 d -6 1 d -6 2 d -6 2 d -6 1 d -5 2 d -5 1 d -6 2 d -5 2 d -4 1 d -5 2 d -4 1 d -4 2 d -3 2 d -4 1 d -3 2 d -2 1 d -2 2 d -2 1 d -1 2 d -1 2 d 1 1 d 1 2 d 2 1 d 4 2 d 5 2 d 7 1 d 8 2 d 11 1 d 12 2 d 12 2 d 9 1 d 2 Y -13 1 d -29 2 d -42 2 d -47 1 d -44 2 d -37 1 d -26 2 d -19 1 d -13 2 d -9 2 d -6 1 d -4 2 d -3 1 d -2 2 d -2 2 d -2 1 d -1 2 d -1 1 d -2 2 d -1 2 d -1 1 d -1 2 d -1 1 d -1 2 d -2 1 d -1 2 d -1 2 d -1 1 d -1 2 d -1 1 d -1 2 d -1 2 d -1 1 d -1 2 d -1 1 d -1 2 d -1 2 d -1 1 d 2 Y -1 1 d -1 2 d -1 2 d -1 1 d -1 2 d -1 1 d -1 2 d -1 1 d -1 2 d -1 2 d 1 Y -1 2 d -1 1 d -1 2 d -1 2 d -1 1 d -1 2 d -1 1 d 2 Y -1 2 d -1 1 d -1 2 d -1 1 d -1 2 d 2 Y -1 1 d -1 2 d -1 1 d -1 2 d 1 Y -1 2 d -1 2 d -1 1 d 2 Y -1 1 d s 1397 550 m -1 2 d 2 Y -1 1 d -1 2 d 1 Y -1 2 d -1 2 d 1 Y -1 2 d 1 Y -1 2 d -1 1 d 2 Y -1 2 d 1 Y -1 2 d 1 Y -1 2 d 2 Y -1 1 d 2 Y -1 1 d 2 Y -1 2 d 3 Y -1 1 d 2 Y -1 2 d 3 Y -1 1 d 3 Y -1 2 d 3 Y -1 2 d 3 Y -1 2 d 4 Y -1 2 d 3 Y -1 2 d 6 Y -1 2 d 6 Y -1 2 d 6 Y -1 2 d 8 Y -1 1 d 10 Y -1 1 d 11 Y -1 2 d 14 Y -1 2 d 16 Y -1 1 d 21 Y -1 2 d 30 Y -1 1 d 37 Y -1 2 d 58 Y -1 2 d 3 Y s 1363 873 m 2 Y 1 1 d -1 2 d 76 Y -1 2 d 2 Y 1 1 d 6 Y -1 2 d 3 Y 1 2 d 5 Y -1 1 d 5 Y 1 2 d 3 Y -1 1 d 7 Y 1 1 d 2 Y -1 1 d 21 Y s 2268 2268 0 0 C 1361 228 m 1 Y s 1361 229 m 2 Y s 1361 231 m 1 Y s 1361 232 m 2 Y s 1361 234 m 2 Y s 1361 236 m 1 Y s 1361 237 m 2 Y s 1361 239 m 1 Y s 1361 240 m 2 Y s 1361 242 m 1 Y s 1361 243 m 2 Y s 1361 245 m 2 Y s 1361 247 m 1 Y s 1361 248 m 2 Y s 1361 250 m s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 1368 259 m20 1368 259 m20 1378 262 m 4 1 d s 1382 263 m 13 1 d s 1395 264 m 6 1 d s 1412 266 m20 1412 266 m20 1424 266 m 22 1 d s 1458 268 m20 1458 268 m20 1469 268 m 23 1 d s 1503 269 m20 1503 269 m20 1514 269 m 23 1 d s 1548 270 m20 1548 270 m20 1560 270 m 5 1 d s 1565 271 m 17 X s 1594 271 m20 1594 271 m20 1605 271 m 23 1 d s 1639 272 m20 1639 272 m20 1650 272 m 4 X s 1654 272 m 19 X s 1684 273 m20 1684 273 m20 1696 273 m 22 X s 1730 273 m20 1730 273 m20 1741 273 m 18 1 d s 1759 274 m 5 X s 1775 274 m20 1775 274 m20 1786 274 m 23 X s 1820 275 m20 1820 275 m20 1832 275 m 22 X s 1866 275 m20 1866 275 m20 1877 276 m 23 X s 1911 276 m20 1911 276 m20 1922 276 m 23 1 d s 1945 277 m s 1956 277 m20 1956 277 m20 1968 278 m 21 X s 1989 278 m 1 X s 2002 279 m20 2002 279 m20 2008 281 m -1 X s 2007 281 m -6 1 d s 2001 282 m -15 1 d s 1974 284 m20 1974 284 m20 1963 284 m -11 1 d s 1952 285 m -12 1 d s 1929 286 m20 1929 286 m20 1918 287 m -14 1 d s 1904 288 m -9 1 d s 1884 290 m20 1884 290 m20 1873 291 m -3 X s 1870 291 m -12 2 d s 1858 293 m -8 1 d s 1839 297 m20 1839 297 m20 1828 300 m -1 1 d s 1827 301 m -3 1 d s 1824 302 m -2 2 d s 1822 304 m -2 2 d s 1820 306 m -2 1 d s 1818 307 m -1 2 d s 1817 309 m -2 1 d s 1815 310 m -1 2 d s 1814 312 m -2 1 d s 1812 313 m -1 2 d s 1802 322 m20 1802 322 m20 1792 327 m -2 1 d s 1790 328 m -3 1 d s 1787 329 m -4 2 d s 1783 331 m -5 2 d s 1778 333 m -4 1 d s 1774 334 m -3 1 d s 1760 338 m20 1760 338 m20 1749 341 m -2 1 d s 1747 342 m -6 2 d s 1741 344 m -6 1 d s 1735 345 m -7 2 d s 1728 347 m -1 X s 1716 350 m20 1716 350 m20 1705 353 m -2 X s 1703 353 m -6 2 d s 1697 355 m -7 1 d s 1690 356 m -6 2 d s 1684 358 m -1 X s 1672 361 m20 1672 361 m20 1661 364 m -2 X s 1659 364 m -6 2 d s 1653 366 m -5 2 d s 1648 368 m -6 1 d s 1642 369 m -2 1 d s 1629 373 m20 1629 373 m20 1618 377 m -2 X s 1616 377 m -4 2 d s 1612 379 m 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1 d s 1423 501 m -1 2 d s 1422 503 m -1 1 d s 1421 504 m -1 2 d s 1420 506 m -1 1 d s 1419 507 m 1 Y s 1414 518 m20 1414 518 m20 1408 528 m s 1408 528 m -1 2 d s 1407 530 m -1 1 d s 1406 531 m -1 2 d s 1405 533 m 2 Y s 1405 535 m -1 1 d s 1404 536 m -1 2 d s 1403 538 m -1 1 d s 1402 539 m -1 2 d s 1401 541 m 1 Y s 1401 542 m -1 2 d s 1400 544 m -1 2 d s 1399 546 m -1 1 d s 1398 547 m 1 Y s 680 794 1361 227 C 2268 2268 0 0 C 1397 550 m -1 2 d s 1396 552 m 2 Y s 1396 554 m -1 1 d s 1395 555 m -1 2 d s 1394 557 m 1 Y s 1394 558 m -1 2 d s 1393 560 m -1 2 d s 1392 562 m 1 Y s 1392 563 m -1 2 d s 1391 565 m 1 Y s 1391 566 m -1 2 d s 1390 568 m -1 1 d s 1389 569 m 2 Y s 1389 571 m s 1385 582 m20 1385 582 m20 1382 593 m s 1382 593 m 2 Y s 1382 595 m -1 2 d s 1381 597 m 1 Y s 1381 598 m 2 Y s 1381 600 m -1 1 d s 1380 601 m 2 Y s 1380 603 m 1 Y s 1380 604 m -1 2 d s 1379 606 m 2 Y s 1379 608 m 1 Y s 1379 609 m -1 2 d s 1378 611 m 1 Y s 1378 612 m 2 Y s 1378 614 m -1 1 d s 1376 627 m20 1376 627 m20 1374 638 m s 1374 638 m 1 Y s 1374 639 m 2 Y s 1374 641 m -1 2 d s 1373 643 m 1 Y s 1373 644 m 2 Y s 1373 646 m 1 Y s 1373 647 m 2 Y s 1373 649 m -1 2 d s 1372 651 m 1 Y s 1372 652 m 2 Y s 1372 654 m 1 Y s 1372 655 m 2 Y s 1372 657 m 2 Y s 1372 659 m -1 1 d s 1371 660 m s 1370 672 m20 1370 672 m20 1370 683 m -1 1 d s 1369 684 m 2 Y s 1369 686 m 1 Y s 1369 687 m 2 Y s 1369 689 m 1 Y s 1369 690 m 2 Y s 1369 692 m 2 Y s 1369 694 m 1 Y s 1369 695 m 2 Y s 1369 697 m 1 Y s 1369 698 m -1 2 d s 1368 700 m 1 Y s 1368 701 m 2 Y s 1368 703 m 2 Y s 1368 705 m 1 Y s 1367 717 m20 1367 717 m20 1367 728 m 1 Y s 1367 729 m 1 Y s 1367 730 m 2 Y s 1367 732 m 1 Y s 1367 733 m 2 Y s 1367 735 m 1 Y s 1367 736 m 2 Y s 1367 738 m -1 2 d s 1366 740 m 1 Y s 1366 741 m 2 Y s 1366 743 m 1 Y s 1366 744 m 2 Y s 1366 746 m 2 Y s 1366 748 m 1 Y s 1366 749 m 2 Y s 1366 751 m s 1366 762 m20 1366 762 m20 1365 774 m 1 Y s 1365 775 m 1 Y s 1365 776 m 2 Y s 1365 778 m 1 Y s 1365 779 m 2 Y s 1365 781 m 2 Y s 1365 783 m 1 Y s 1365 784 m 2 Y s 1365 786 m 1 Y s 1365 787 m 2 Y s 1365 789 m 2 Y s 1365 791 m 1 Y s 1365 792 m 2 Y s 1365 794 m 1 Y s 1365 795 m 1 Y s 1365 808 m20 1365 808 m20 1364 819 m s 1364 819 m 2 Y s 1364 821 m 1 Y s 1364 822 m 2 Y s 1364 824 m 2 Y s 1364 826 m 1 Y s 1364 827 m 2 Y s 1364 829 m 1 Y s 1364 830 m 2 Y s 1364 832 m 1 Y s 1364 833 m 2 Y s 1364 835 m 2 Y s 1364 837 m 1 Y s 1364 838 m 2 Y s 1364 840 m 1 Y s 1364 841 m 1 Y s 1364 853 m20 1364 853 m20 1364 864 m 1 Y s 1364 865 m 2 Y s 1364 867 m 1 Y s 1364 868 m -1 2 d s 1363 870 m 2 Y s 1363 872 m 1 Y s 680 794 1361 227 C 2268 2268 0 0 C 1363 873 m 2 Y s 1363 875 m 1 1 d s 1364 876 m -1 2 d s 1363 878 m 2 Y s 1363 880 m 1 Y s 1363 881 m 2 Y s 1363 883 m 1 Y s 1363 884 m 2 Y s 1363 886 m 2 Y s 1363 888 m 1 Y s 1363 889 m 2 Y s 1363 891 m 1 Y s 1363 892 m 2 Y s 1363 894 m 2 Y s 1363 896 m s 1363 907 m20 1363 907 m20 1363 919 m s 1363 919 m 2 Y s 1363 921 m 2 Y s 1363 923 m 1 Y s 1363 924 m 2 Y s 1363 926 m 1 Y s 1363 927 m 2 Y s 1363 929 m 1 Y s 1363 930 m 2 Y s 1363 932 m 2 Y s 1363 934 m 1 Y s 1363 935 m 2 Y s 1363 937 m 1 Y s 1363 938 m 2 Y s 1363 940 m 1 Y s 1363 952 m20 1363 952 m20 1363 964 m s 1363 964 m 1 Y s 1363 965 m -1 2 d s 1362 967 m 2 Y s 1362 969 m 1 Y s 1362 970 m 1 2 d s 1363 972 m 1 Y s 1363 973 m 2 Y s 1363 975 m 2 Y s 1363 977 m -1 1 d s 1362 978 m 2 Y s 1362 980 m 1 Y s 1362 981 m 2 Y s 1362 983 m 1 2 d s 1363 985 m 1 Y s 1363 986 m s 1363 998 m20 1363 998 m20 1362 1009 m 1 Y s 1362 1010 m 2 Y s 1362 1012 m 1 Y s 1362 1013 m 2 Y s 1362 1015 m 1 Y s 1362 1016 m 2 Y s 1362 1018 m 2 Y s 1362 1020 m 1 Y s 680 794 1361 227 C 2268 2268 0 0 C 680 794 1361 227 C 2268 2268 0 0 C gsave 1208 941 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 680 794 1361 227 C 2268 2268 0 0 C 680 794 1361 227 C 2268 2268 0 0 C /xs 0 def (combined) /Times-Roman 48 stwn gsave 1999 386 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (combined) show gr 680 794 1361 227 C 2268 2268 0 0 C 680 794 1361 227 C 2268 2268 0 0 C /xs 0 def (tail) /Times-Roman 48 stwn gsave 1999 862 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 48 sf 0 0 m (tail) show gr 680 794 1361 227 C 2268 2268 0 0 C 1 lw 1361 436 m 11 X s 1383 436 m 12 X s 1406 436 m 12 X s 1429 436 m 11 X s 1452 436 m 11 X s 1474 436 m 12 X s 1497 436 m 11 X s 1520 436 m 11 X s 1542 436 m 12 X s 1565 436 m 11 X s 1588 436 m 11 X s 1610 436 m 12 X s 1633 436 m 11 X s 1656 436 m 11 X s 1678 436 m 12 X s 1701 436 m 11 X s 1724 436 m 11 X s 1746 436 m 12 X s 1769 436 m 11 X s 1792 436 m 11 X s 1814 436 m 12 X s 1837 436 m 11 X s 1860 436 m 11 X s 1882 436 m 12 X s 1905 436 m 11 X s 1928 436 m 11 X s 1950 436 m 12 X s 1973 436 m 11 X s 1996 436 m 11 X s 2019 436 m 11 X s 680 794 1361 227 C gr gr showpage end %%EndDocument @endspecial -41 3859 a FE(Figure)24 b(3.3.3:)33 b(Density)25 b(analysis)f(for)f(the)i(N)e(atom.)38 b(Individual)22 b(regions)h(starting)-41 3979 y(from)32 b(the)h(core)g(outwards)g (contain)g(1.77,)f(0.88,)f(3.45)g(and)h(0.90)f(electrons,)j(to-)-41 4099 y(talling)24 b(in)e(7)h(electrons.)37 b(The)23 b(dash-dot)g(lines) f(show)h(the)g(distribution)f(functions)-41 4220 y(without)29 b(the)f(contribution)g(from)g(the)h(core)g(electrons.)106 4528 y(In)d(Fig.)g(3.3.4)f(we)i(plot)g(the)g(density)g(of)f(the)h (exchange-correlation)i(energy)e FC(f)-41 4648 y FE(for)20 b(Ar)h(atom.)36 b(The)20 b(solid)g(line)g(denotes)h(the)g FC(f)34 b FE(functions)20 b(for)g(the)h(LSD)g(exchange-)-41 4769 y(correlation)39 b(energy)h(\(subsection)e(2.5.1\),)h(and)f(the)h (dashed)g(line)f(denotes)h(the)-41 4889 y FC(f)56 b FE(functions)40 b(for)h(the)h(GGA)g(PBE)f(exchange-correlation)j(energy)e(\(subsection) -41 5009 y(2.5.2\).)68 b(Here)38 b(the)i(distribution)d(functions)h (fall)g(even)h(more)g(rapidly)f(to)h(zero,)-41 5130 y(telling)29 b(us)f(that)h(90\045)e(of)h(the)h(GGA)f(exchange-correlation)i(energy)f (is)f(recovered)-41 5250 y(from)g(the)h(contributions)f(of)f FC(r)1192 5264 y FB(s)1257 5250 y FA(\024)e FE(0)p FC(:)p FE(82)i(and)h FC(s)j FA(\024)26 b FE(0)p FC(:)p FE(86.)106 5391 y(From)j(these)i(\256gures,)f(some)g(common)g(features)g(of)g(the) g(distribution)e(func-)1522 5640 y(36)p eop %%Page: 37 45 37 44 bop 2568 275 a Fw(3.3.)27 b(Results)i(and)f(discussion)p 555 315 3238 4 v 639 3547 a @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 3685 @rwi @setspecial %%BeginDocument: fig/arf.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr } def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1587 794 454 1247 bl 1587 794 454 1247 C NC 454 1247 m 794 Y s 488 1247 m -34 X s 471 1300 m -17 X s 471 1353 m -17 X s 471 1406 m -17 X s 471 1459 m -17 X s 488 1512 m -34 X s 471 1565 m -17 X s 471 1618 m -17 X s 471 1671 m -17 X s 471 1724 m -17 X s 488 1777 m -34 X s 471 1830 m -17 X s 471 1882 m -17 X s 471 1935 m -17 X s 471 1988 m -17 X s 488 2041 m -34 X s /xs 0 def (-150) /Times-Roman 68 stwn gsave 408 1225 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-150) show gr /xs 0 def (-100) /Times-Roman 68 stwn gsave 408 1489 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-100) show gr /xs 0 def (-50) /Times-Roman 68 stwn gsave 408 1754 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-50) show gr /xs 0 def (0) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr 454 1247 m 1587 X s 454 1281 m -34 Y s 559 1264 m -17 Y s 665 1264 m -17 Y s 771 1264 m -17 Y s 877 1264 m -17 Y s 983 1281 m -34 Y s 1089 1264 m -17 Y s 1194 1264 m -17 Y s 1300 1264 m -17 Y s 1406 1264 m -17 Y s 1512 1281 m -34 Y s 1618 1264 m -17 Y s 1724 1264 m -17 Y s 1830 1264 m -17 Y s 1935 1264 m -17 Y s 2041 1281 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 983 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1512 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 2041 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 1587 794 454 1247 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn gsave 2041 1102 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 96 1962 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (f) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (1) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\)) show gr 1587 794 454 1247 C 3 lw 456 2027 m 1 -4 d 2 -6 d 1 -5 d 1 -9 d 1 -9 d 2 -12 d 1 -13 d 1 -17 d 1 -21 d 1 -5 d -19 Y 2 -24 d 1 -44 d 1 -9 d 1 -32 d 1 -38 d 1 -67 d 4 -145 d -11 Y 3 -91 d 1 -22 d -19 Y 2 -47 d 1 -11 d 1 -9 d -7 Y 1 -6 d 1 -4 d 1 -2 d 1 X 1 Y 1 3 d 1 6 d 1 10 d 1 18 d 1 14 d 2 24 d 1 25 d 2 30 d 2 40 d 4 56 d 11 Y 3 38 d 1 20 d 2 26 d 2 21 d 2 16 d 2 15 d 4 Y 2 11 d 2 9 d 3 Y 2 6 d 1 4 d 1 2 d 2 1 d 1 -1 d 1 -1 d 2 -4 d 1 -7 d 1 -3 d 2 -10 d 2 -14 d -5 Y 2 -15 d 2 -25 d 4 -50 d 4 -46 d -3 Y 2 -25 d 2 -10 d -3 Y 1 -9 d 2 -6 d 1 -4 d 1 -2 d 2 2 d 1 3 d 1 5 d 2 10 d 1 6 d 2 12 d 2 21 d 2 24 d 2 15 d 4 40 d 4 38 d 4 36 d 3 28 d 1 4 d 3 25 d 1 4 d 4 26 d 4 24 d 4 20 d 4 19 d 4 16 d 4 15 d 4 13 d 4 12 d 4 11 d 4 9 d 4 9 d 4 8 d 4 7 d 4 6 d 4 6 d 4 5 d 3 5 d 4 4 d 4 4 d 4 4 d 4 4 d 4 3 d 4 2 d 4 3 d 4 2 d 4 3 d 4 2 d 4 2 d 4 1 d 4 2 d 4 1 d 4 2 d 4 1 d 4 1 d 4 1 d 4 1 d 4 1 d 4 1 d 4 1 d 4 X 4 1 d 4 X 4 1 d 4 1 d 8 X 4 1 d 16 X 4 1 d 8 X 4 -1 d 12 X 4 -1 d 4 X 4 -1 d 4 -1 d 4 -1 d 4 -2 d 3 -1 d 4 -3 d 4 -2 d 4 -3 d 4 -4 d 4 -3 d 4 -4 d 4 -4 d 4 -3 d 4 -2 d 4 -1 d 4 X 4 1 d 4 1 d 4 2 d 4 2 d 4 2 d 4 2 d 4 1 d 4 2 d 4 2 d 4 1 d 4 2 d 4 1 d 4 1 d 4 1 d 4 2 d 4 1 d 4 1 d 4 1 d 4 X 4 1 d 4 1 d 4 1 d 4 1 d 4 X 4 1 d 4 1 d 4 X 4 1 d 4 X 4 1 d 4 X 4 1 d 4 X 4 1 d 4 X 3 1 d 4 X 4 1 d 8 X 4 1 d 8 X 4 1 d 8 X 4 1 d 8 X 4 1 d 12 X 4 1 d 16 X 4 1 d 16 X 4 1 d 20 X 4 1 d 20 X 4 1 d 31 X 4 1 d 28 X s 1263 2036 m 8 X 4 1 d 48 X 4 1 d 72 X 4 1 d 119 X 4 1 d 270 X 4 1 d 239 X s 2268 2268 0 0 C 456 2027 m 1 -5 d s 457 2022 m 2 -7 d s 459 2015 m 1 -4 d s 460 2011 m 1 -6 d s 463 1982 m 1 -3 d s 464 1979 m 1 -14 d s 465 1965 m -6 Y s 467 1937 m -12 Y s 467 1925 m 1 -5 d s 468 1920 m -6 Y s 469 1891 m 1 -16 d s 470 1875 m -6 Y s 471 1846 m -17 Y s 471 1829 m -6 Y s 472 1801 m 1 -15 d s 473 1786 m -8 Y s 473 1755 m 1 -8 d s 474 1747 m -14 Y s 475 1710 m -23 Y s 476 1665 m -23 Y s 477 1619 m -22 Y s 478 1574 m -23 Y s 479 1529 m -10 Y s 479 1519 m -10 Y s 479 1509 m 1 -3 d s 480 1483 m 1 -22 d s 481 1438 m 1 -23 d s 483 1393 m -7 Y s 483 1386 m -16 Y s 484 1347 m 1 -22 d s 486 1302 m 1 -9 d s 487 1293 m -9 Y s 487 1284 m 1 -5 d s 493 1278 m 1 6 d s 494 1284 m 1 17 d s 497 1323 m 1 14 d s 498 1337 m 9 Y s 499 1368 m 2 23 d s 502 1414 m 1 22 d s 504 1459 m 2 23 d s 507 1504 m 6 Y s 507 1510 m 1 17 d s 510 1550 m 1 22 d s 511 1572 m s 513 1595 m 6 Y s 513 1601 m 2 16 d s 517 1640 m 1 Y s 517 1641 m 2 17 d s 519 1658 m 4 Y s 519 1662 m 1 Y s 522 1685 m 1 1 d s 523 1686 m 3 Y s 523 1689 m 2 8 d s 525 1697 m 2 6 d s 527 1703 m 2 Y s 527 1705 m 1 2 d s 537 1689 m -1 Y s 537 1688 m 2 -12 d s 539 1676 m -4 Y s 539 1672 m 1 -5 d s 542 1644 m 1 -10 d s 543 1634 m 1 -12 d s 546 1599 m 1 -12 d s 547 1587 m 1 -11 d s 550 1554 m 1 -15 d s 551 1539 m 1 -8 d s 554 1509 m 1 -5 d s 555 1504 m -2 Y s 555 1502 m 1 -9 d s 556 1493 m 2 -5 d s 558 1488 m -2 Y s 566 1499 m 3 Y s 566 1502 m 1 6 d s 567 1508 m 2 12 d s 569 1520 m 2 Y s 571 1544 m 3 23 d s 576 1589 m 2 23 d s 581 1634 m 2 22 d s 583 1656 m 1 Y s 586 1679 m 1 13 d s 587 1692 m 1 10 d s 591 1725 m 3 22 d s 597 1769 m 2 10 d s 599 1779 m 2 13 d s 605 1814 m 2 9 d s 607 1823 m 3 13 d s 615 1858 m 4 15 d s 619 1873 m 2 7 d s 628 1902 m 3 8 d s 631 1910 m 4 10 d s 635 1920 m 1 3 d s 646 1943 m 1 1 d s 647 1944 m 4 7 d s 651 1951 m 4 6 d s 655 1957 m 3 5 d s 673 1979 m 1 1 d s 674 1980 m 4 4 d s 678 1984 m 4 3 d s 682 1987 m 4 3 d s 686 1990 m 4 3 d s 690 1993 m 1 1 d s 711 2004 m 3 2 d s 714 2006 m 4 2 d s 718 2008 m 4 1 d s 722 2009 m 4 1 d s 726 2010 m 4 2 d s 730 2012 m 2 X s 754 2018 m 4 X s 758 2018 m 4 1 d s 762 2019 m 4 1 d s 766 2020 m 4 X s 770 2020 m 4 1 d s 774 2021 m 3 X s 799 2023 m 3 X s 802 2023 m 4 X s 806 2023 m 4 X s 810 2023 m 4 X s 814 2023 m 4 X s 818 2023 m 4 X s 822 2023 m s 844 2020 m 2 -1 d s 846 2019 m 4 -1 d s 850 2018 m 3 -2 d s 853 2016 m 4 -2 d s 857 2014 m 4 -3 d s 861 2011 m 3 -2 d s 881 1994 m s 881 1994 m 4 -3 d s 885 1991 m 4 -2 d s 889 1989 m 4 -1 d s 893 1988 m 4 X s 897 1988 m 4 X s 901 1988 m 1 1 d s 923 1998 m 2 1 d s 925 1999 m 4 2 d s 929 2001 m 4 1 d s 933 2002 m 4 2 d s 937 2004 m 4 1 d s 941 2005 m 3 1 d s 965 2012 m 4 1 d s 969 2013 m 4 1 d s 973 2014 m 4 1 d s 977 2015 m 4 1 d s 981 2016 m 4 X s 985 2016 m 3 1 d s 1010 2021 m 3 X s 1013 2021 m 4 X s 1017 2021 m 4 1 d s 1021 2022 m 4 X s 1025 2022 m 4 1 d s 1029 2023 m 4 X s 1055 2026 m 1 X s 1056 2026 m 4 X s 1060 2026 m 4 1 d s 1064 2027 m 4 X s 1068 2027 m 4 X s 1072 2027 m 4 1 d s 1076 2028 m 2 X s 1100 2029 m 4 1 d s 1104 2030 m 4 X s 1108 2030 m 4 X s 1112 2030 m 4 X s 1116 2030 m 4 1 d s 1120 2031 m 3 X s 1146 2032 m 2 X s 1148 2032 m 4 X s 1152 2032 m 4 X s 1156 2032 m 4 1 d s 1160 2033 m 4 X s 1164 2033 m 4 X s 1168 2033 m s 1191 2034 m 1 X s 1192 2034 m 4 X s 1196 2034 m 4 X s 1200 2034 m 4 X s 1204 2034 m 4 X s 1208 2034 m 4 1 d s 1212 2035 m 2 X s 1236 2035 m 3 X s 1239 2035 m 4 1 d s 1243 2036 m 4 X s 1247 2036 m 4 X s 1251 2036 m 4 X s 1255 2036 m 4 X s 1587 794 454 1247 C 2268 2268 0 0 C 1263 2036 m 4 X s 1267 2036 m 4 X s 1271 2036 m 4 X s 1275 2036 m 4 X s 1279 2036 m 4 X s 1283 2036 m 3 1 d s 1309 2037 m 2 X s 1311 2037 m 4 X s 1315 2037 m 4 X s 1319 2037 m 4 X s 1323 2037 m 4 X s 1327 2037 m 4 X s 1331 2037 m s 1354 2038 m 1 X s 1355 2038 m 4 X s 1359 2038 m 4 X s 1363 2038 m 4 X s 1367 2038 m 4 X s 1371 2038 m 4 X s 1375 2038 m 2 X s 1399 2038 m 4 X s 1403 2038 m 4 X s 1407 2038 m 4 X s 1411 2038 m 4 X s 1415 2038 m 3 X s 1418 2038 m 4 1 d s 1445 2039 m 1 X s 1446 2039 m 4 X s 1450 2039 m 4 X s 1454 2039 m 4 X s 1458 2039 m 4 X s 1462 2039 m 4 X s 1466 2039 m 1 X s 1490 2039 m s 1490 2039 m 4 X s 1494 2039 m 4 X s 1498 2039 m 4 X s 1502 2039 m 4 X s 1506 2039 m 4 X s 1510 2039 m 3 X s 1535 2039 m 3 X s 1538 2039 m 4 X s 1542 2039 m 4 X s 1546 2039 m 4 1 d s 1550 2040 m 4 X s 1554 2040 m 4 X s 1558 2040 m s 1581 2040 m 1 X s 1582 2040 m 4 X s 1586 2040 m 4 X s 1590 2040 m 4 X s 1594 2040 m 4 X s 1598 2040 m 4 X s 1602 2040 m 1 X s 1626 2040 m 3 X s 1629 2040 m 4 X s 1633 2040 m 4 X s 1637 2040 m 4 X s 1641 2040 m 4 X s 1645 2040 m 4 X s 1672 2040 m 1 X s 1673 2040 m 4 X s 1677 2040 m 4 X s 1681 2040 m 4 X s 1685 2040 m 4 X s 1689 2040 m 4 X s 1693 2040 m 1 X s 1717 2040 m s 1717 2040 m 4 X s 1721 2040 m 4 X s 1725 2040 m 4 X s 1729 2040 m 4 X s 1733 2040 m 4 X s 1737 2040 m 3 X s 1762 2040 m 3 X s 1765 2040 m 4 X s 1769 2040 m 4 X s 1773 2040 m 4 X s 1777 2040 m 4 X s 1781 2040 m 4 X s 1785 2040 m s 1808 2040 m s 1808 2040 m 4 X s 1812 2040 m 4 X s 1816 2040 m 4 X s 1820 2040 m 4 X s 1824 2040 m 4 X s 1828 2040 m 2 X s 1853 2041 m 3 X s 1856 2041 m 4 X s 1860 2041 m 4 X s 1864 2041 m 4 X s 1868 2041 m 4 X s 1872 2041 m 4 X s 1898 2041 m 2 X s 1900 2041 m 4 X s 1904 2041 m 4 X s 1908 2041 m 4 X s 1912 2041 m 4 X s 1916 2041 m 4 X s 1920 2041 m 1 X s 1944 2041 m s 1944 2041 m 4 X s 1948 2041 m 4 X s 1952 2041 m 4 X s 1956 2041 m 4 X s 1960 2041 m 4 X s 1964 2041 m 2 X s 1989 2041 m 2 X s 1991 2041 m 4 X s 1995 2041 m 4 X s 1999 2041 m 4 X s 2003 2041 m 4 X s 2007 2041 m 4 X s 2011 2041 m 1 X s 2034 2041 m 1 X s 2035 2041 m 4 X s 1587 794 454 1247 C 2268 2268 0 0 C 1 lw 740 2041 m -11 Y s 740 2019 m -12 Y s 740 1996 m -11 Y s 740 1973 m -11 Y s 740 1950 m -11 Y s 740 1928 m -12 Y s 740 1905 m -11 Y s 740 1882 m -11 Y s 740 1860 m -12 Y s 740 1837 m -11 Y s 740 1814 m -11 Y s 740 1792 m -12 Y s 740 1769 m -11 Y s 740 1746 m -11 Y s 740 1724 m -12 Y s 740 1701 m -11 Y s 740 1678 m -11 Y s 740 1656 m -12 Y s 740 1633 m -11 Y s 740 1610 m -11 Y s 740 1588 m -12 Y s 740 1565 m -11 Y s 740 1542 m -11 Y s 740 1520 m -12 Y s 740 1497 m -11 Y s 740 1474 m -11 Y s 740 1452 m -12 Y s 740 1429 m -11 Y s 740 1406 m -11 Y s 740 1383 m -11 Y s 740 1361 m -12 Y s 740 1338 m -11 Y s 740 1315 m -11 Y s 740 1293 m -12 Y s 740 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 890 2041 m -11 Y s 890 2019 m -12 Y s 890 1996 m -11 Y s 890 1973 m -11 Y s 890 1950 m -11 Y s 890 1928 m -12 Y s 890 1905 m -11 Y s 890 1882 m -11 Y s 890 1860 m -12 Y s 890 1837 m -11 Y s 890 1814 m -11 Y s 890 1792 m -12 Y s 890 1769 m -11 Y s 890 1746 m -11 Y s 890 1724 m -12 Y s 890 1701 m -11 Y s 890 1678 m -11 Y s 890 1656 m -12 Y s 890 1633 m -11 Y s 890 1610 m -11 Y s 890 1588 m -12 Y s 890 1565 m -11 Y s 890 1542 m -11 Y s 890 1520 m -12 Y s 890 1497 m -11 Y s 890 1474 m -11 Y s 890 1452 m -12 Y s 890 1429 m -11 Y s 890 1406 m -11 Y s 890 1383 m -11 Y s 890 1361 m -12 Y s 890 1338 m -11 Y s 890 1315 m -11 Y s 890 1293 m -12 Y s 890 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1395 2041 m -11 Y s 1395 2019 m -12 Y s 1395 1996 m -11 Y s 1395 1973 m -11 Y s 1395 1950 m -11 Y s 1395 1928 m -12 Y s 1395 1905 m -11 Y s 1395 1882 m -11 Y s 1395 1860 m -12 Y s 1395 1837 m -11 Y s 1395 1814 m -11 Y s 1395 1792 m -12 Y s 1395 1769 m -11 Y s 1395 1746 m -11 Y s 1395 1724 m -12 Y s 1395 1701 m -11 Y s 1395 1678 m -11 Y s 1395 1656 m -12 Y s 1395 1633 m -11 Y s 1395 1610 m -11 Y s 1395 1588 m -12 Y s 1395 1565 m -11 Y s 1395 1542 m -11 Y s 1395 1520 m -12 Y s 1395 1497 m -11 Y s 1395 1474 m -11 Y s 1395 1452 m -12 Y s 1395 1429 m -11 Y s 1395 1406 m -11 Y s 1395 1383 m -11 Y s 1395 1361 m -12 Y s 1395 1338 m -11 Y s 1395 1315 m -11 Y s 1395 1293 m -12 Y s 1395 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 559 1300 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (core) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 798 1300 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (CV) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 1142 1300 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (valence) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 1671 1300 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (tail) show gr 1587 794 454 1247 C [] 0 sd 3 lw 1512 1830 m 106 X s 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 1671 1830 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (LSD) show gr 1587 794 454 1247 C 2268 2268 0 0 C [] 0 sd 1512 1777 m 23 X s 1557 1777 m 23 X s 1603 1777 m 15 X s 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 1671 1777 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (GGA) show gr 1587 794 454 1247 C NC 1 lw 1587 794 454 227 bl 1587 794 454 227 C NC 454 227 m 794 Y s 488 227 m -34 X s 471 276 m -17 X s 471 326 m -17 X s 471 376 m -17 X s 488 425 m -34 X s 471 475 m -17 X s 471 524 m -17 X s 471 574 m -17 X s 488 624 m -34 X s 471 673 m -17 X s 471 723 m -17 X s 471 773 m -17 X s 488 822 m -34 X s 471 872 m -17 X s 471 921 m -17 X s 471 971 m -17 X s 488 1021 m -34 X s /xs 0 def (-80) /Times-Roman 68 stwn gsave 408 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-80) show gr /xs 0 def (-60) /Times-Roman 68 stwn gsave 408 403 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-60) show gr /xs 0 def (-40) /Times-Roman 68 stwn gsave 408 601 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-40) show gr /xs 0 def (-20) /Times-Roman 68 stwn gsave 408 799 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-20) show gr /xs 0 def (0) /Times-Roman 68 stwn gsave 408 998 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr 454 227 m 1587 X s 454 261 m -34 Y s 559 244 m -17 Y s 665 244 m -17 Y s 771 244 m -17 Y s 877 244 m -17 Y s 983 261 m -34 Y s 1089 244 m -17 Y s 1194 244 m -17 Y s 1300 244 m -17 Y s 1406 244 m -17 Y s 1512 261 m -34 Y s 1618 244 m -17 Y s 1724 244 m -17 Y s 1830 244 m -17 Y s 1935 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 983 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1512 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 1587 794 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 96 941 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (f) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (3) show 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17 d 1 37 d 1 10 d 1 24 d 1 32 d 2 74 d 1 22 d 3 68 d 1 26 d 1 19 d 1 9 d 2 30 d 1 14 d 1 12 d 1 9 d 1 10 d 2 9 d 2 9 d 1 Y 2 5 d 3 6 d 3 4 d 3 2 d 5 3 d 5 1 d 6 1 d 5 2 d 5 X 6 1 d 10 X 5 1 d 6 -1 d 5 -1 d 5 -1 d 6 -2 d 5 -2 d 5 -5 d 5 -6 d 1 -1 d 5 -9 d 5 -12 d 4 -5 d 2 X 1 2 d 2 4 d 2 7 d 1 6 d 4 26 d 4 24 d 1 8 d 3 9 d 2 7 d 1 3 d 2 4 d 3 4 d 3 3 d 2 1 d 6 1 d 5 1 d 11 X 5 1 d 26 X 6 1 d 37 X 5 1 d 48 X 5 1 d 80 X 5 1 d 133 X 5 1 d 5 X 6 -1 d 5 1 d 74 X s 1533 1020 m 455 X 1 1 d 1 -1 d 28 X 1 1 d 5 X 2 -1 d 22 X 2 1 d 9 X 2 -1 d 22 X 1 1 d 12 X 5 -1 d 16 X 2 1 d 14 X 1 -1 d 19 X 1 1 d 16 X 1 -1 d 18 X 1 1 d 17 X 5 -1 d 15 X 1 1 d 21 X 2 -1 d 14 X 2 1 d 21 X 4 -1 d 13 X 2 1 d 22 X 5 -1 d 13 X 3 1 d 27 X 2 -1 d 10 X 3 1 d 27 X 6 -1 d 8 X 2 1 d 34 X 2 -1 d 9 X 2 1 d 35 X 1 -1 d 7 X 1 1 d 42 X s 2268 2268 0 0 C 456 1021 m 4 X s 460 1021 m 4 X s 464 1021 m 4 X s 468 1021 m 4 X s 472 1021 m 3 X s 475 1021 m 3 X s 501 1021 m 2 X s 503 1021 m 4 X s 507 1021 m 4 X s 511 1021 m 4 X s 515 1021 m 4 X s 519 1021 m 4 X s 523 1021 m 1 X s 546 1019 m 1 X s 547 1019 m 4 -2 d s 551 1017 m 3 -3 d s 554 1014 m 1 -2 d s 555 1012 m 3 -5 d s 558 1007 m 1 -3 d s 559 1004 m 1 -2 d s 565 980 m 2 -14 d s 567 966 m 1 -9 d s 572 935 m 2 -13 d s 574 922 m 1 -6 d s 575 916 m 1 -3 d s 587 893 m s 587 893 m 1 -6 d s 588 887 m 1 -7 d s 589 880 m 2 -8 d s 591 872 m -1 Y s 593 848 m -3 Y s 593 845 m 1 -19 d s 594 826 m s 595 803 m 1 -3 d s 596 800 m -19 Y s 597 758 m 1 -14 d s 598 744 m -9 Y s 599 713 m 1 -23 d s 600 667 m 1 -22 d s 602 622 m -23 Y s 603 576 m -22 Y s 604 531 m -4 Y s 604 527 m 1 -19 d s 605 486 m 1 -22 d s 606 464 m -1 Y s 607 440 m 1 -22 d s 609 395 m -1 Y s 609 394 m -12 Y s 609 382 m 1 -8 d s 610 374 m -1 Y s 615 363 m 1 Y s 615 364 m 1 5 d s 616 369 m 1 8 d s 617 377 m 8 Y s 619 408 m 1 10 d s 620 418 m 1 12 d s 623 453 m 2 Y s 623 455 m 1 21 d s 626 498 m 1 6 d s 627 504 m 1 17 d s 631 543 m 2 17 d s 633 560 m 1 6 d s 637 588 m 2 9 d s 639 597 m 2 12 d s 641 609 m 1 Y s 648 632 m 1 4 d s 649 636 m 2 2 d s 651 638 m 2 4 d s 653 642 m 2 2 d s 655 644 m 2 1 d s 657 645 m 2 X s 659 645 m 3 -1 d s 662 644 m -1 Y s 662 643 m 1 X s 674 623 m s 674 623 m 4 -9 d s 678 614 m 4 -10 d s 682 604 m 1 -2 d s 693 582 m 1 -3 d s 694 579 m 4 -7 d s 698 572 m 4 -7 d s 702 565 m 2 -3 d s 721 547 m 1 X s 722 547 m 4 -2 d s 726 545 m 4 X s 730 545 m 4 X s 734 545 m 4 X s 738 545 m 4 1 d s 742 546 m 1 1 d s 763 558 m 3 2 d s 766 560 m 4 4 d s 770 564 m 4 3 d s 774 567 m 4 4 d s 778 571 m 2 1 d s 797 587 m 1 1 d s 798 588 m 4 3 d s 802 591 m 4 4 d s 806 595 m 4 3 d s 810 598 m 4 2 d s 814 600 m 1 1 d s 836 610 m 2 1 d s 838 611 m 4 X s 842 611 m 4 -1 d s 846 610 m 4 -2 d s 850 608 m 3 -3 d s 853 605 m 3 -2 d s 867 583 m 1 -4 d s 868 579 m 1 -4 d s 869 575 m 3 -9 d s 872 566 m 1 -5 d s 877 539 m -2 Y s 877 537 m 2 -15 d s 879 522 m 1 -5 d s 883 494 m -6 Y s 883 488 m 2 -17 d s 887 449 m 2 -22 d s 889 427 m -1 Y s 892 404 m -1 Y s 892 403 m 1 -4 d s 893 399 m -3 Y s 893 396 m 1 X s 894 396 m 1 1 d s 895 397 m 1 4 d s 896 401 m 1 5 d s 897 406 m 2 Y s 897 408 m 1 Y s 899 432 m 1 Y s 899 433 m 1 13 d s 900 446 m 9 Y s 901 477 m 8 Y s 901 485 m 1 15 d s 903 523 m 6 Y s 903 529 m 16 Y s 904 568 m 1 23 d s 905 613 m 1 23 d s 907 659 m 10 Y s 907 669 m 12 Y s 908 704 m 8 Y s 908 712 m 1 15 d s 910 749 m 1 23 d s 912 795 m 7 Y s 912 802 m 1 15 d s 914 840 m 3 Y s 914 843 m 1 15 d s 915 858 m 1 5 d s 918 885 m 1 4 d s 919 889 m 1 10 d s 920 899 m 1 7 d s 921 906 m 1 1 d s 930 928 m 3 4 d s 933 932 m 4 3 d s 937 935 m 4 1 d s 941 936 m 4 1 d s 945 937 m 4 1 d s 949 938 m s 972 941 m 1 X s 973 941 m 4 X s 977 941 m 4 X s 981 941 m 4 X s 985 941 m 4 -1 d s 989 940 m 4 X s 993 940 m 1 -1 d s 1013 927 m 4 -4 d s 1017 923 m 4 -7 d s 1021 916 m 3 -8 d s 1035 889 m 1 1 d s 1036 890 m 1 1 d s 1037 891 m 1 5 d s 1038 896 m 2 7 d s 1040 903 m 4 Y s 1040 907 m 1 4 d s 1044 934 m 2 Y s 1044 936 m 3 20 d s 1051 978 m 1 8 d s 1052 986 m 2 8 d s 1054 994 m 2 5 d s 1056 999 m 1 1 d s 1074 1013 m 2 X s 1076 1013 m 4 1 d s 1080 1014 m 4 X s 1084 1014 m 4 X s 1088 1014 m 4 X s 1092 1014 m 4 X s 1096 1014 m 1 X s 1119 1015 m 1 X s 1120 1015 m 4 X s 1124 1015 m 4 X s 1128 1015 m 4 X s 1132 1015 m 4 X s 1136 1015 m 4 1 d s 1140 1016 m 2 X s 1165 1016 m 3 X s 1168 1016 m 4 X s 1172 1016 m 4 X s 1176 1016 m 4 X s 1180 1016 m 4 1 d s 1184 1017 m 3 X s 1210 1017 m 2 X s 1212 1017 m 4 X s 1216 1017 m 4 X s 1220 1017 m 4 X s 1224 1017 m 4 X s 1228 1017 m 3 X s 1231 1017 m 2 X s 1255 1018 m 4 X s 1259 1018 m 4 X s 1587 794 454 227 C 2268 2268 0 0 C 1263 1018 m 4 X s 1267 1018 m 4 X s 1271 1018 m 4 X s 1275 1018 m 4 X s 1279 1018 m 4 X s 1283 1018 m 3 X s 1309 1018 m 2 X s 1311 1018 m 4 X s 1315 1018 m 4 X s 1319 1018 m 4 X s 1323 1018 m 4 1 d s 1327 1019 m 4 X s 1331 1019 m s 1354 1019 m 1 X s 1355 1019 m 4 X s 1359 1019 m 4 X s 1363 1019 m 4 X s 1367 1019 m 4 X s 1371 1019 m 4 X s 1375 1019 m 2 X s 1399 1019 m 4 X s 1403 1019 m 4 X s 1407 1019 m 4 X s 1411 1019 m 4 X s 1415 1019 m 3 X s 1418 1019 m 4 X s 1445 1019 m 1 X s 1446 1019 m 4 X s 1450 1019 m 4 X s 1454 1019 m 4 X s 1458 1019 m 4 X s 1462 1019 m 4 X s 1466 1019 m 1 X s 1490 1020 m 4 X s 1494 1020 m 4 X s 1498 1020 m 4 X s 1502 1020 m 4 X s 1506 1020 m 4 X s 1510 1020 m 3 X s 1535 1020 m 3 X s 1538 1020 m 4 X s 1542 1020 m 4 X s 1546 1020 m 4 X s 1550 1020 m 4 X s 1554 1020 m 4 X s 1558 1020 m s 1581 1020 m 1 X s 1582 1020 m 4 X s 1586 1020 m 4 X s 1590 1020 m 4 X s 1594 1020 m 4 X s 1598 1020 m 4 X s 1602 1020 m 2 X s 1626 1020 m 3 X s 1629 1020 m 4 X s 1633 1020 m 4 X s 1637 1020 m 4 X s 1641 1020 m 4 X s 1645 1020 m 4 X s 1672 1020 m 1 X s 1673 1020 m 4 X s 1677 1020 m 4 X s 1681 1020 m 4 X s 1685 1020 m 4 X s 1689 1020 m 4 X s 1693 1020 m 1 X s 1717 1020 m 4 X s 1721 1020 m 4 X s 1725 1020 m 4 X s 1729 1020 m 4 X s 1733 1020 m 4 X s 1737 1020 m 3 X s 1762 1020 m 3 X s 1765 1020 m 4 X s 1769 1020 m 4 X s 1773 1020 m 4 X s 1777 1020 m 4 X s 1781 1020 m 4 X s 1785 1020 m s 1808 1020 m s 1808 1020 m 4 X s 1812 1020 m 4 X s 1816 1020 m 4 X s 1820 1020 m 4 X s 1824 1020 m 4 X s 1828 1020 m 2 X s 1853 1020 m 3 X s 1856 1020 m 4 X s 1860 1020 m 4 X s 1864 1020 m 4 X s 1868 1020 m 4 X s 1872 1020 m 4 X s 1898 1020 m 2 X s 1900 1020 m 4 X s 1904 1020 m 4 X s 1908 1020 m 4 X s 1912 1020 m 4 X s 1916 1020 m 4 X s 1920 1020 m 1 X s 1944 1020 m 4 X s 1948 1020 m 4 X s 1952 1020 m 4 X s 1956 1020 m 4 X s 1960 1020 m 4 X s 1964 1020 m 2 X s 1989 1020 m 2 X s 1991 1020 m 4 X s 1995 1020 m 4 X s 1999 1020 m 4 X s 2003 1020 m s 2003 1020 m 4 X s 2007 1020 m 4 X s 2011 1020 m 1 X s 2034 1020 m 1 X s 2035 1020 m s 2035 1020 m 3 X s 2038 1020 m 1 X s 1587 794 454 227 C 2268 2268 0 0 C 1 lw 1041 1021 m -12 Y s 1041 998 m -11 Y s 1041 975 m -11 Y s 1041 953 m -12 Y s 1041 930 m -11 Y s 1041 907 m -11 Y s 1041 885 m -12 Y s 1041 862 m -11 Y s 1041 839 m -11 Y s 1041 816 m -11 Y s 1041 794 m -12 Y s 1041 771 m -11 Y s 1041 748 m -11 Y s 1041 726 m -12 Y s 1041 703 m -11 Y s 1041 680 m -11 Y s 1041 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1671 756 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (GGA) show gr 1587 794 454 227 C gr gr showpage end %%EndDocument @endspecial 555 3859 a FE(Figure)e(3.3.4:)35 b(Energy-weighted)27 b(density-gradient)g(analysis)g(for)e(the)i(Ar)g(atom.)555 3979 y(The)36 b(top)f(plot)h(shows)f(the)h FC(r)1712 3993 y FB(s)1750 3979 y FE(-analysis)g(of)f(the)i(exchange-correlation) g(energy,)555 4099 y(and)28 b(the)h(bottom)f(the)h FC(s)6 b FE(-analysis.)38 b(The)27 b(solid)g(line)h(was)g(obtained)g(with)f (the)i(LSD)555 4220 y(approximation)23 b(for)h(the)g (exchange-correlation)h(energy,)g(the)g(dashed)e(line)h(with)555 4340 y(the)c(GGA)g(approximation.)34 b(The)19 b(area)i(under)d FC(f)2410 4354 y Fz(1)2454 4340 y FC(\204r)2546 4354 y FB(s)2584 4340 y FC(\205)g FE(\(or)i FC(f)2846 4354 y Fz(3)2889 4340 y FC(\204s)6 b(\205)p FE(\))18 b(is)h(-29.29)e (hartree)555 4460 y(\(LSD\))30 b(or)e(-30.89)f(hartree)i(\(GGA\).)555 4789 y(tions)37 b(can)h(be)g(obtained.)65 b(We)37 b(see)h(that)g(the)g FC(r)2448 4803 y FB(s)2524 4789 y FE(dependence)f(of)g(the)h FC(g)i FE(and)e FC(f)555 4910 y FE(curves)20 b(starts)h(at)f FC(r)1314 4875 y FB(min)1302 4933 y(s)1468 4910 y FE(,)h(which)e (corresponds)g(to)h(the)g(maximum)g(electronic)g(den-)555 5030 y(sity)j(at)g(the)f(atomic)h(centre.)37 b(The)22 b FC(g)1943 5044 y Fz(1)1986 5030 y FC(\204r)2078 5044 y FB(s)2116 5030 y FC(\205)g FE(function)f(also)i(clearly)g(shows)e (the)i(shell)555 5150 y(structure)f(of)e(the)i(atom,)h(the)e(number)f (of)h(peaks)f(corresponding)g(to)h(the)h(number)555 5271 y(of)29 b(fully)f(or)g(partially)i(occupied)e(shells)h(in)f(the)h (atom.)40 b(In)28 b(the)i(tail)f(region,)f(the)h FC(g)555 5391 y FE(and)g FC(f)42 b FE(curves)28 b(fall)h(rapidly)f(to)g(zero.) 2118 5640 y(37)p eop %%Page: 38 46 38 45 bop -41 275 a Fw(Chapter)29 b(3.)e(Distributions)h(of)f(density)i (parameters)p -41 315 3238 4 v 106 576 a FE(In)h(the)h FC(s)6 b(\204r)12 b(\205)30 b FE(plots,)h(we)f(observe)h(that)g(each)h 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FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 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t /Times-Roman findfont 86 sf 0 0 m (\)) show gr 1587 794 454 1247 C 3 lw 456 1935 m 8 X 4 1 d 15 X 4 1 d 4 X 4 1 d 4 1 d 4 X 4 1 d 12 X 4 -1 d 4 X 4 -1 d 4 -1 d 4 -1 d 4 X 4 -1 d 4 X 4 -1 d 4 X 4 -1 d 12 X 4 -1 d 20 X 4 -1 d 12 X 4 -1 d 8 X 4 -1 d 3 X 4 -1 d 4 X 4 -1 d 4 -1 d 4 -1 d 4 -1 d 4 -1 d 4 -2 d 4 -2 d 4 -2 d 4 -4 d 4 -4 d 4 -6 d 4 -7 d 3 -8 d 1 -2 d 3 -9 d 1 -5 d 2 -10 d 2 -9 d 2 -11 d 2 -14 d 2 -14 d 2 -19 d 2 -18 d 2 -26 d 2 -24 d 2 -31 d 2 -26 d 2 -39 d 4 -72 d 4 -66 d -5 Y 2 -40 d 2 -18 d -3 Y 2 -23 d 1 -11 d 1 -9 d 1 -8 d 1 -6 d 1 -4 d 1 -1 d 1 -1 d 1 X 2 3 d 1 Y 1 5 d 1 8 d 2 10 d 1 11 d 2 19 d 1 8 d 1 16 d 3 31 d 4 51 d 3 36 d 1 11 d 2 26 d 2 15 d 3 28 d 1 8 d 3 26 d 1 7 d 2 21 d 2 8 d 2 12 d 2 10 d 2 9 d 2 6 d 4 12 d 3 14 d 4 17 d 4 18 d 3 13 d 1 3 d 3 9 d 1 2 d 4 9 d 4 9 d 4 10 d 4 12 d 4 12 d 4 10 d 1 Y 4 6 d 1 Y 4 5 d 4 5 d 4 5 d 4 7 d 4 8 d 4 6 d 4 5 d 4 3 d 4 3 d 4 3 d 4 3 d 4 5 d 4 3 d 4 3 d 4 2 d 4 2 d 4 1 d 4 2 d 4 3 d 4 2 d 4 1 d 4 1 d 4 1 d 4 1 d 4 1 d 4 1 d 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s 464 1935 m 4 X s 468 1935 m 3 X s 471 1935 m 4 X s 475 1935 m 3 X s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 490 1935 m20 490 1935 m20 501 1935 m 2 X s 503 1935 m 4 X s 507 1935 m 4 X s 511 1935 m 4 X s 515 1935 m 4 X s 519 1935 m 4 X s 523 1935 m 1 X s 535 1935 m20 535 1935 m20 546 1935 m 1 X s 547 1935 m 4 X s 551 1935 m 4 X s 555 1935 m 4 X s 559 1935 m 4 X s 563 1935 m 4 X s 567 1935 m 2 X s 580 1935 m20 580 1935 m20 592 1935 m 3 X s 595 1935 m 4 X s 599 1935 m 4 X s 603 1935 m 4 X s 607 1935 m 4 X s 611 1935 m 3 X s 626 1935 m20 626 1935 m20 637 1935 m 1 X s 638 1935 m 4 X s 642 1935 m 4 X s 646 1935 m 4 -1 d s 650 1934 m 4 X s 654 1934 m 4 -2 d s 658 1932 m 1 X s 668 1925 m20 668 1925 m20 675 1916 m 3 -6 d s 678 1910 m 4 -9 d s 682 1901 m 2 -6 d s 689 1885 m20 689 1885 m20 694 1875 m -1 Y s 694 1874 m 4 -9 d s 698 1865 m -1 Y s 698 1864 m 3 -9 d s 701 1855 m -2 Y s 703 1842 m20 703 1842 m20 705 1831 m 1 -4 d s 706 1827 m 2 -13 d s 708 1814 m -5 Y s 710 1797 m20 710 1797 m20 711 1786 m 1 -9 d s 712 1777 m 1 -13 d s 714 1752 m20 714 1752 m20 715 1741 m 1 -13 d s 716 1728 m -10 Y s 717 1707 m20 717 1707 m20 718 1696 m 1 -23 d s 720 1662 m20 720 1662 m20 721 1650 m 1 -19 d s 722 1631 m -3 Y s 723 1616 m20 723 1616 m20 723 1605 m 2 -22 d s 725 1571 m20 725 1571 m20 726 1560 m -1 Y s 726 1559 m 1 -22 d s 728 1526 m20 728 1526 m20 728 1515 m 2 -22 d s 730 1493 m -1 Y s 730 1481 m20 730 1481 m20 731 1469 m 1 -21 d s 732 1448 m -1 Y s 733 1435 m20 733 1435 m20 734 1424 m 2 -20 d s 736 1404 m -3 Y s 737 1390 m20 737 1390 m20 739 1379 m -3 Y s 739 1376 m 1 -6 d s 740 1370 m 1 -4 d s 741 1366 m 1 -1 d s 742 1365 m 1 -1 d s 743 1364 m 1 1 d s 744 1365 m 2 2 d s 746 1367 m 1 Y s 746 1368 m 1 Y s 748 1381 m20 748 1381 m20 750 1392 m 1 10 d s 751 1402 m 1 12 d s 753 1426 m20 753 1426 m20 754 1437 m 1 8 d s 755 1445 m 1 15 d s 757 1471 m20 757 1471 m20 758 1482 m 2 23 d s 761 1516 m20 761 1516 m20 762 1527 m 2 23 d s 765 1561 m20 765 1561 m20 766 1573 m 1 Y s 766 1574 m 2 21 d s 769 1606 m20 769 1606 m20 770 1618 m 2 22 d s 774 1651 m20 774 1651 m20 775 1663 m 2 14 d s 777 1677 m 1 7 d s 778 1684 m 1 Y s 779 1697 m20 779 1697 m20 781 1708 m 1 5 d s 782 1713 m 2 12 d s 784 1725 m 1 5 d s 787 1741 m20 787 1741 m20 790 1752 m 4 10 d s 794 1762 m 3 12 d s 799 1785 m20 799 1785 m20 802 1796 m 3 15 d s 805 1811 m 2 7 d s 810 1829 m20 810 1829 m20 814 1840 m 3 7 d s 817 1847 m 4 9 d s 821 1856 m 2 4 d s 827 1871 m20 827 1871 m20 830 1882 m 3 8 d s 833 1890 m 4 10 d s 837 1900 m 1 Y s 837 1901 m 1 2 d s 845 1912 m20 845 1912 m20 852 1921 m 1 2 d s 853 1923 m 4 7 d s 857 1930 m 4 8 d s 861 1938 m 2 3 d s 870 1950 m20 870 1950 m20 879 1956 m 2 2 d s 881 1958 m 4 3 d s 885 1961 m 4 5 d s 889 1966 m 4 3 d s 893 1969 m 3 2 d s 906 1976 m20 906 1976 m20 916 1981 m 1 1 d s 917 1982 m 4 2 d s 921 1984 m 4 1 d s 925 1985 m 4 1 d s 929 1986 m 4 1 d s 933 1987 m 4 1 d s 937 1988 m 1 X s 949 1991 m20 949 1991 m20 960 1992 m 1 Y s 960 1993 m 4 X s 964 1993 m 4 X s 968 1993 m 4 1 d s 972 1994 m 4 X s 976 1994 m 4 X s 980 1994 m 3 X s 994 1994 m20 994 1994 m20 1005 1994 m 3 X s 1008 1994 m 4 X s 1012 1994 m 4 X s 1016 1994 m 4 -1 d s 1020 1993 m 4 X s 1024 1993 m 4 X s 1039 1992 m20 1039 1992 m20 1051 1991 m 1 X s 1052 1991 m 4 X s 1056 1991 m 4 -1 d s 1060 1990 m 4 X s 1064 1990 m 4 -1 d s 1068 1989 m 4 X s 1072 1989 m 1 X s 1084 1988 m20 1084 1988 m20 1096 1986 m 4 X s 1100 1986 m 4 -1 d s 1104 1985 m 4 X s 1108 1985 m 4 -1 d s 1112 1984 m 4 X s 1116 1984 m 2 X s 1130 1982 m20 1130 1982 m20 1141 1981 m 2 X s 1143 1981 m 4 -1 d s 1147 1980 m 4 X s 1151 1980 m 4 -1 d s 1155 1979 m 4 X s 1159 1979 m 4 X s 1163 1979 m s 1175 1977 m20 1175 1977 m20 1186 1976 m 1 X s 1187 1976 m 4 X s 1191 1976 m 4 -1 d s 1195 1975 m 4 X s 1199 1975 m 4 -1 d s 1203 1974 m 4 X s 1207 1974 m 1 X s 1220 1973 m20 1220 1973 m20 1231 1972 m 4 -1 d s 1235 1971 m 4 X s 1239 1971 m 4 X s 1243 1971 m 4 -1 d s 1247 1970 m 4 X s 1251 1970 m 3 X s 1587 794 454 1247 C 2268 2268 0 0 C 1263 1969 m 4 X s 1267 1969 m 4 -1 d s 1271 1968 m 4 X s 1275 1968 m 4 X s 1279 1968 m 4 -1 d s 1283 1967 m 2 X s 1297 1966 m20 1297 1966 m20 1308 1965 m 2 X s 1310 1965 m 4 X s 1314 1965 m 4 X s 1318 1965 m 4 -1 d s 1322 1964 m 4 X s 1326 1964 m 4 X s 1330 1964 m s 1342 1963 m20 1342 1963 m20 1353 1962 m 1 X s 1354 1962 m 4 X s 1358 1962 m 4 X s 1362 1962 m 4 -1 d s 1366 1961 m 4 X s 1370 1961 m 4 X s 1374 1961 m 2 X s 1387 1960 m20 1387 1960 m20 1398 1960 m 4 -1 d s 1402 1959 m 4 X s 1406 1959 m 4 X s 1410 1959 m 4 X s 1414 1959 m 4 X s 1418 1959 m 3 -1 d s 1432 1958 m20 1432 1958 m20 1444 1957 m 2 X s 1446 1957 m 3 X s 1449 1957 m 4 X s 1453 1957 m 4 X s 1457 1957 m 4 -1 d s 1461 1956 m 4 X s 1465 1956 m 1 X s 1478 1956 m20 1478 1956 m20 1489 1955 m s 1489 1955 m 4 X s 1493 1955 m 4 X s 1497 1955 m 4 X s 1501 1955 m 4 X s 1505 1955 m 4 X s 1509 1955 m 3 -1 d s 1523 1954 m20 1523 1954 m20 1534 1954 m 3 X s 1537 1954 m 4 -1 d s 1541 1953 m 4 X s 1545 1953 m 4 X s 1549 1953 m 4 X s 1553 1953 m 4 X s 1557 1953 m s 1568 1952 m20 1568 1952 m20 1580 1952 m 1 X s 1581 1952 m 4 X s 1585 1952 m 4 X s 1589 1952 m 4 X s 1593 1952 m 4 X s 1597 1952 m 4 X s 1601 1952 m 1 -1 d s 1614 1951 m20 1614 1951 m20 1625 1951 m 3 X s 1628 1951 m 4 X s 1632 1951 m 4 X s 1636 1951 m 4 -1 d s 1640 1950 m 4 X s 1644 1950 m 4 X s 1659 1950 m20 1659 1950 m20 1670 1950 m 2 X s 1672 1950 m 4 X s 1676 1950 m 4 -1 d s 1680 1949 m 4 X s 1684 1949 m 4 X s 1688 1949 m 4 X s 1692 1949 m 1 X s 1704 1949 m20 1704 1949 m20 1716 1949 m s 1716 1949 m 4 X s 1720 1949 m 4 -1 d s 1724 1948 m 4 X s 1728 1948 m 4 X s 1732 1948 m 4 X s 1736 1948 m 2 X s 1750 1948 m20 1750 1948 m20 1761 1948 m 3 X s 1764 1948 m 4 X s 1768 1948 m 4 -1 d s 1772 1947 m 3 X s 1775 1947 m 4 X s 1779 1947 m 4 X s 1783 1947 m 1 X s 1795 1947 m20 1795 1947 m20 1806 1947 m 1 X s 1807 1947 m 4 X s 1811 1947 m 4 X s 1815 1947 m 4 X s 1819 1947 m 4 X s 1823 1947 m 4 -1 d s 1827 1946 m 2 X s 1840 1946 m20 1840 1946 m20 1852 1946 m 3 X s 1855 1946 m 4 X s 1859 1946 m 4 X s 1863 1946 m 4 X s 1867 1946 m 4 X s 1871 1946 m 3 X s 1886 1946 m20 1886 1946 m20 1897 1945 m 2 X s 1899 1945 m 4 X s 1903 1945 m 4 X s 1907 1945 m 4 X s 1911 1945 m 4 X s 1915 1945 m 4 X s 1919 1945 m 1 X s 1931 1945 m20 1931 1945 m20 1942 1945 m 4 X s 1946 1945 m 4 X s 1950 1945 m 4 X s 1954 1945 m 4 -1 d s 1958 1944 m 4 X s 1962 1944 m 3 X s 1976 1944 m20 1976 1944 m20 1988 1944 m 2 X s 1990 1944 m 4 X s 1994 1944 m 4 X s 1998 1944 m 4 X s 2002 1944 m 4 X s 2006 1944 m 4 X s 2010 1944 m 1 X s 2022 1944 m20 2022 1944 m20 2033 1944 m 1 X s 2034 1944 m 4 -1 d s 2038 1943 m 3 X s 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C 1 lw 644 2041 m -11 Y s 644 2019 m -12 Y s 644 1996 m -11 Y s 644 1973 m -11 Y s 644 1950 m -11 Y s 644 1928 m -12 Y s 644 1905 m -11 Y s 644 1882 m -11 Y s 644 1860 m -12 Y s 644 1837 m -11 Y s 644 1814 m -11 Y s 644 1792 m -12 Y s 644 1769 m -11 Y s 644 1746 m -11 Y s 644 1724 m -12 Y s 644 1701 m -11 Y s 644 1678 m -11 Y s 644 1656 m -12 Y s 644 1633 m -11 Y s 644 1610 m -11 Y s 644 1588 m -12 Y s 644 1565 m -11 Y s 644 1542 m -11 Y s 644 1520 m -12 Y s 644 1497 m -11 Y s 644 1474 m -11 Y s 644 1452 m -12 Y s 644 1429 m -11 Y s 644 1406 m -11 Y s 644 1383 m -11 Y s 644 1361 m -12 Y s 644 1338 m -11 Y s 644 1315 m -11 Y s 644 1293 m -12 Y s 644 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 770 2041 m -11 Y s 770 2019 m -12 Y s 770 1996 m -11 Y s 770 1973 m -11 Y s 770 1950 m -11 Y s 770 1928 m -12 Y s 770 1905 m -11 Y s 770 1882 m -11 Y s 770 1860 m -12 Y s 770 1837 m -11 Y s 770 1814 m -11 Y s 770 1792 m -12 Y s 770 1769 m -11 Y s 770 1746 m -11 Y s 770 1724 m -12 Y s 770 1701 m -11 Y s 770 1678 m -11 Y s 770 1656 m -12 Y s 770 1633 m -11 Y s 770 1610 m -11 Y s 770 1588 m -12 Y s 770 1565 m -11 Y s 770 1542 m -11 Y s 770 1520 m -12 Y s 770 1497 m -11 Y s 770 1474 m -11 Y s 770 1452 m -12 Y s 770 1429 m -11 Y s 770 1406 m -11 Y s 770 1383 m -11 Y s 770 1361 m -12 Y s 770 1338 m -11 Y s 770 1315 m -11 Y s 770 1293 m -12 Y s 770 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1251 2041 m -11 Y s 1251 2019 m -12 Y s 1251 1996 m -11 Y s 1251 1973 m -11 Y s 1251 1950 m -11 Y s 1251 1928 m -12 Y s 1251 1905 m -11 Y s 1251 1882 m -11 Y s 1251 1860 m -12 Y s 1251 1837 m -11 Y s 1251 1814 m -11 Y s 1251 1792 m -12 Y s 1251 1769 m -11 Y s 1251 1746 m -11 Y s 1251 1724 m -12 Y s 1251 1701 m -11 Y s 1251 1678 m -11 Y s 1251 1656 m -12 Y s 1251 1633 m -11 Y s 1251 1610 m -11 Y s 1251 1588 m -12 Y s 1251 1565 m -11 Y s 1251 1542 m -11 Y s 1251 1520 m -12 Y s 1251 1497 m -11 Y s 1251 1474 m -11 Y s 1251 1452 m -12 Y s 1251 1429 m -11 Y s 1251 1406 m -11 Y s 1251 1383 m -11 Y s 1251 1361 m -12 Y s 1251 1338 m -11 Y s 1251 1315 m -11 Y s 1251 1293 m -12 Y s 1251 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 485 1306 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (core) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 654 1306 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (CV) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 890 1306 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (valence) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 1406 1306 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (tail) show gr 1587 794 454 1247 C 2268 2268 0 0 C 454 1935 m 45 X s /w 2 def /w2 {w 2 div} def /w3 {w 3 div} def 522 1935 m20 522 1935 m20 544 1935 m 46 X s 612 1935 m20 612 1935 m20 635 1935 m 45 X s 703 1935 m20 703 1935 m20 726 1935 m 45 X s 794 1935 m20 794 1935 m20 816 1935 m 46 X s 885 1935 m20 885 1935 m20 907 1935 m 46 X s 975 1935 m20 975 1935 m20 998 1935 m 45 X s 1066 1935 m20 1066 1935 m20 1089 1935 m 45 X s 1157 1935 m20 1157 1935 m20 1179 1935 m 46 X s 1247 1935 m20 1247 1935 m20 1270 1935 m 45 X s 1338 1935 m20 1338 1935 m20 1361 1935 m 45 X s 1429 1935 m20 1429 1935 m20 1452 1935 m 45 X s 1520 1935 m20 1520 1935 m20 1542 1935 m 46 X s 1610 1935 m20 1610 1935 m20 1633 1935 m 45 X s 1701 1935 m20 1701 1935 m20 1724 1935 m 45 X s 1792 1935 m20 1792 1935 m20 1814 1935 m 46 X s 1882 1935 m20 1882 1935 m20 1905 1935 m 45 X s 1973 1935 m20 1973 1935 m20 1996 1935 m 45 X s 1587 794 454 1247 C NC 1587 794 454 227 bl 1587 794 454 227 C NC 454 227 m 794 Y s 488 361 m -34 X s 471 405 m -17 X s 471 450 m -17 X s 471 494 m -17 X s 488 539 m -34 X s 471 584 m -17 X s 471 628 m -17 X s 471 673 m -17 X s 488 717 m -34 X s 471 762 m -17 X s 471 807 m -17 X s 471 851 m -17 X s 488 896 m -34 X s 488 361 m -34 X s 471 316 m -17 X s 471 271 m -17 X s 471 227 m -17 X s 488 896 m -34 X s 471 940 m -17 X s 471 985 m -17 X s /xs 0 def (-4) /Times-Roman 68 stwn gsave 408 338 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-4) show gr /xs 0 def (-2) /Times-Roman 68 stwn gsave 408 516 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-2) show gr /xs 0 def (0) /Times-Roman 68 stwn gsave 408 695 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 408 873 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr 454 227 m 1587 X s 454 261 m -34 Y s 559 244 m -17 Y s 665 244 m -17 Y s 771 244 m -17 Y s 877 244 m -17 Y s 983 261 m -34 Y s 1089 244 m -17 Y s 1194 244 m -17 Y s 1300 244 m -17 Y s 1406 244 m -17 Y s 1512 261 m -34 Y s 1618 244 m -17 Y s 1724 244 m -17 Y s 1830 244 m -17 Y s 1935 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 983 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1512 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 1587 794 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 96 941 t 0 r 0 0 m /Symbol findfont 86 sf 0 0 m (D) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (g) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (3) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(s\)) show gr 1587 794 454 227 C 3 lw 456 706 m 6 -6 d 5 -8 d 5 -11 d 5 -13 d 6 -14 d 5 -14 d 5 -14 d 6 -15 d 5 -16 d 5 -19 d 6 -21 d 5 -23 d 5 -22 d 5 -19 d 6 -16 d 5 -17 d 4 -14 d 1 -7 d 4 -19 d 2 -8 d 5 -31 d 5 -30 d 4 -16 d 2 -8 d 3 -14 d 2 -5 d 5 -16 d 5 -16 d 5 -14 d 1 -1 d 3 -5 d 1 X 1 1 d 2 3 d 1 6 d 2 8 d 4 Y 2 9 d 1 14 d 2 24 d 1 9 d 1 20 d 2 30 d 2 34 d 2 37 d 2 32 d 1 19 d 3 34 d 1 15 d 1 10 d 1 3 d 1 10 d 2 6 d 1 4 d 1 1 d 1 X 2 -3 d 2 -8 d 5 -19 d 3 -7 d 3 -4 d 2 -1 d 3 2 d 5 6 d 6 4 d 5 1 d 5 2 d 4 4 d 2 4 d 3 8 d 2 5 d 5 16 d 5 12 d 2 Y 4 7 d 2 3 d 5 6 d 5 5 d 6 8 d 5 11 d 5 13 d 6 12 d 5 9 d 5 7 d 5 6 d 6 7 d 5 9 d 5 9 d 6 8 d 5 7 d 5 6 d 6 5 d 5 6 d 5 6 d 6 5 d 5 4 d 5 4 d 5 4 d 6 3 d 5 3 d 5 3 d 6 3 d 5 2 d 5 2 d 6 1 d 5 1 d 5 1 d 5 1 d 6 1 d 26 X 6 -1 d 5 -1 d 5 X 5 -1 d 6 -1 d 5 -1 d 5 -1 d 6 -1 d 5 -1 d 5 -1 d 6 -1 d 5 -2 d 5 -1 d 5 -1 d 6 -2 d 5 -1 d 5 -1 d 6 -2 d 5 -2 d 5 -1 d 6 -2 d 5 -2 d 5 -2 d 5 -2 d 6 -3 d 5 -2 d 5 -4 d 6 -3 d 5 -5 d 5 -5 d 6 -6 d 5 -6 d 5 -6 d 5 -4 d 5 -2 d 1 X 3 1 d 2 2 d 3 4 d 2 4 d 3 7 d 3 7 d 3 11 d 2 10 d 3 16 d 2 11 d 4 22 d 2 10 d 4 30 d 1 7 d 5 40 d 5 36 d 4 Y 4 23 d 2 10 d 2 11 d 2 4 d 1 2 d 2 -1 d 1 -2 d 2 -5 d -4 Y 2 -7 d 1 -11 d 2 -21 d 1 -5 d 1 -13 d 2 -22 d 2 -35 d 5 -77 d 4 -47 d 1 -18 d 1 -3 d 2 -21 d 1 -13 d 2 -11 d 2 -9 d 1 -7 d 2 -5 d 2 -2 d 2 1 d 1 1 d 2 4 d 4 11 d 3 12 d 2 8 d 5 20 d 4 13 d 2 4 d 4 9 d 1 3 d 4 8 d 1 1 d 6 6 d 5 3 d 5 2 d 5 2 d 6 1 d 5 X 5 1 d 22 X 5 1 d 42 X 6 -1 d 26 X 5 -1 d 16 X 6 -1 d 10 X 5 -1 d 6 X 5 -1 d 5 X 6 -1 d 5 X 5 -1 d 6 X 5 -1 d 5 X 6 -1 d 5 X 5 -1 d 5 -1 d 6 X 5 -1 d 5 X 6 -1 d 5 -1 d 5 X 6 -1 d 5 -1 d 5 X 5 -1 d 6 -1 d 5 X 5 -1 d s 1532 747 m 6 X 5 -1 d 5 -1 d 6 X 5 -1 d 5 X 5 -1 d 6 -1 d 5 X 5 -1 d 6 X 5 -1 d 5 X 6 -1 d 5 X 5 -1 d 5 X 6 -1 d 5 X 5 -1 d 11 X 5 -1 d 6 X 5 -1 d 10 X 6 -1 d 10 X 6 -1 d 10 X 6 -1 d 10 X 5 -1 d 16 X 6 -1 d 16 X 5 -1 d 21 X 5 -1 d 27 X 5 -1 d 32 X 5 -1 d 32 X 5 -1 d 48 X 5 -1 d 64 X 5 -1 d 85 X 5 -1 d 128 X 5 -1 d 201 X 6 -1 d 5 X 5 1 d 6 X 5 -1 d 16 X 5 1 d 5 -1 d 106 X s 2608 719 m 159 X 3 -1 d 5 X 1 1 d 27 X 1 -1 d 9 X 2 1 d 25 X 1 -1 d 13 X 1 1 d 19 X 4 -1 d 16 X 1 1 d 16 X 5 -1 d 18 X 2 1 d 18 X 4 -1 d 19 X 1 1 d 14 X 3 -1 d 23 X 2 1 d 14 X 4 -1 d 22 X 2 1 d 15 X 3 -1 d 25 X 1 1 d 13 X 4 -1 d 27 X 1 1 d 15 X 4 -1 d 27 X 1 Y 16 X 5 -1 d 26 X 1 Y 13 X 3 -1 d 15 X 1 -1 d 1 X 1 1 d 15 X 1 1 d 14 X 1 -1 d 14 X -1 Y 4 X 1 1 d 14 X 1 1 d 15 X 3 -1 d 11 X 1 -1 d 6 X 1 1 d 14 X 1 1 d 11 X 3 -1 d 14 X 1 -1 d 8 X 1 Y 15 X 1 1 d 11 X 3 -1 d 13 X 1 -1 d 10 X 1 1 d 14 X 1 1 d 11 X 2 -1 d 13 X 1 -1 d 12 X 1 1 d 15 X 2 1 d 7 X 2 -1 d 15 X 1 -1 d 14 X 2 1 d 13 X 1 1 d 10 X 1 -1 d 1 X s 2268 2268 0 0 C 456 706 m 5 -5 d s 461 701 m 1 -1 d s 462 700 m 4 -7 d s 466 693 m 1 -1 d s 467 692 m 2 -5 d s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 474 677 m20 474 677 m20 478 667 m 5 -13 d s 483 654 m 3 -9 d s 490 635 m20 490 635 m20 494 624 m 5 -13 d s 499 611 m 2 -8 d s 505 592 m20 505 592 m20 508 581 m -2 Y s 508 579 m 1 -3 d s 509 576 m 4 -17 d s 516 548 m20 516 548 m20 519 537 m 1 -5 d s 520 532 m 4 -17 d s 527 504 m20 527 504 m20 530 493 m -2 Y s 530 491 m 6 -16 d s 536 475 m 1 -4 d s 540 461 m20 540 461 m20 543 450 m 1 -4 d s 544 446 m 2 -9 d s 546 437 m 2 -9 d s 550 416 m20 550 416 m20 552 405 m 4 -22 d s 558 372 m20 558 372 m20 560 361 m 2 -12 d s 562 349 m 2 -11 d s 567 327 m20 567 327 m20 570 316 m -1 Y s 570 315 m 3 -9 d s 573 306 m 4 -11 d s 580 284 m20 580 284 m20 584 273 m 4 -13 d s 588 260 m 1 -1 d s 589 259 m 2 -5 d s 591 254 m 2 X s 593 254 m s 597 265 m20 597 265 m20 599 276 m s 599 276 m 1 7 d s 600 283 m 2 11 d s 602 294 m 5 Y s 603 310 m20 603 310 m20 604 321 m 1 11 d s 605 332 m 1 12 d s 606 355 m20 606 355 m20 607 366 m 4 Y s 607 370 m 1 19 d s 609 400 m20 609 400 m20 610 412 m 4 Y s 610 416 m 1 18 d s 612 446 m20 612 446 m20 612 457 m 2 23 d s 614 491 m20 614 491 m20 615 502 m 2 Y s 615 504 m 2 21 d s 618 536 m20 618 536 m20 618 547 m 1 5 d s 619 552 m 1 8 d s 620 560 m 1 6 d s 621 566 m 4 Y s 623 581 m20 623 581 m20 628 584 m 3 -8 d s 631 576 m 2 -6 d s 633 570 m 2 -8 d s 639 552 m20 639 552 m20 646 546 m 1 1 d s 647 547 m 2 2 d s 649 549 m 3 3 d s 652 552 m 5 4 d s 657 556 m 1 X s 658 556 m 5 2 d s 663 558 m 2 X s 673 566 m20 673 566 m20 677 576 m 2 4 d s 679 580 m 5 16 d s 684 596 m 1 1 d s 689 608 m20 689 608 m20 694 618 m 1 1 d s 695 619 m 5 6 d s 700 625 m 5 6 d s 705 631 m 4 4 d s 714 645 m20 714 645 m20 718 656 m 3 8 d s 721 664 m 6 11 d s 727 675 m 2 Y s 733 686 m20 733 686 m20 740 695 m 2 3 d s 742 698 m 6 7 d s 748 705 m 5 9 d s 753 714 m s 759 724 m20 759 724 m20 765 733 m 4 5 d s 769 738 m 5 6 d s 774 744 m 6 5 d s 780 749 m 1 Y s 788 758 m20 788 758 m20 796 766 m 5 5 d s 801 771 m 5 4 d s 806 775 m 5 3 d s 811 778 m 3 2 d s 824 786 m20 824 786 m20 834 791 m 4 2 d s 838 793 m 5 2 d s 843 795 m 6 1 d s 849 796 m 5 2 d s 854 798 m 1 X s 866 800 m20 866 800 m20 878 801 m 2 X s 880 801 m 6 X s 886 801 m 5 X s 891 801 m 5 X s 896 801 m 4 X s 912 801 m20 912 801 m20 923 802 m 5 X s 928 802 m 5 1 d s 933 803 m 6 1 d s 939 804 m 5 X s 944 804 m 2 1 d s 957 806 m20 957 806 m20 968 808 m 2 1 d s 970 809 m 6 1 d s 976 810 m 5 X s 981 810 m 5 1 d s 986 811 m 4 X s 1002 812 m20 1002 812 m20 1013 810 m s 1013 810 m 5 -4 d s 1018 806 m 5 -5 d s 1023 801 m 6 -7 d s 1034 784 m20 1034 784 m20 1040 774 m 5 -6 d s 1045 768 m 5 -7 d s 1050 761 m 5 -4 d s 1065 754 m20 1065 754 m20 1076 756 m 6 2 d s 1082 758 m 5 2 d s 1087 760 m 5 2 d s 1092 762 m 5 2 d s 1108 767 m20 1108 767 m20 1120 768 m 4 X s 1124 768 m 5 X s 1129 768 m 6 -1 d s 1135 767 m 5 X s 1140 767 m 2 X s 1154 766 m20 1154 766 m20 1165 766 m 2 X s 1167 766 m 5 X s 1172 766 m 5 -1 d s 1177 765 m 5 X s 1182 765 m 6 X s 1199 765 m20 1199 765 m20 1210 765 m 4 X s 1214 765 m 6 X s 1220 765 m 5 X s 1225 765 m 5 X s 1230 765 m 3 X s 1244 765 m20 1244 765 m20 1256 765 m 1 X s 1257 765 m 5 X s 1262 765 m 5 X s 1267 765 m 6 1 d s 1273 766 m 5 X s 1278 766 m s 1290 766 m20 1290 766 m20 1301 766 m 3 X s 1304 766 m 6 X s 1310 766 m 5 X s 1315 766 m 5 X s 1320 766 m 4 -1 d s 1335 765 m20 1335 765 m20 1347 765 m s 1347 765 m 5 X s 1352 765 m 5 -1 d s 1357 764 m 6 X s 1363 764 m 5 X s 1368 764 m 1 X s 1380 763 m20 1380 763 m20 1392 762 m 2 X s 1394 762 m 6 X s 1400 762 m 5 -1 d s 1405 761 m 5 X s 1410 761 m 4 X s 1426 759 m20 1426 759 m20 1437 758 m 5 X s 1442 758 m 6 -1 d s 1448 757 m 5 X s 1453 757 m 5 -1 d s 1458 756 m 2 X s 1471 755 m20 1471 755 m20 1482 753 m 3 X s 1485 753 m 5 -1 d s 1490 752 m 5 X s 1495 752 m 6 -1 d s 1501 751 m 4 X s 1516 749 m20 1516 749 m20 1527 748 m 5 -1 d s 1587 794 454 227 C 2268 2268 0 0 C 1532 747 m 6 X s 1538 747 m 5 -1 d s 1543 746 m 5 -1 d s 1548 745 m 6 X s 1554 745 m 1 X s 1566 743 m20 1566 743 m20 1577 742 m 3 X s 1580 742 m 5 -1 d s 1585 741 m 6 X s 1591 741 m 5 -1 d s 1596 740 m 4 X s 1611 739 m20 1611 739 m20 1623 738 m 5 -1 d s 1628 737 m 5 X s 1633 737 m 5 -1 d s 1638 736 m 6 X s 1644 736 m 1 X s 1656 735 m20 1656 735 m20 1668 734 m 2 X s 1670 734 m 5 X s 1675 734 m 6 -1 d s 1681 733 m 5 X s 1686 733 m 4 X s 1702 732 m20 1702 732 m20 1713 731 m 5 X s 1718 731 m 5 X s 1723 731 m 5 -1 d s 1728 730 m 6 X s 1734 730 m 2 X s 1747 730 m20 1747 730 m20 1758 729 m 2 X s 1760 729 m 6 X s 1766 729 m 5 -1 d s 1771 728 m 5 X s 1776 728 m 5 X s 1792 728 m20 1792 728 m20 1804 727 m 4 X s 1808 727 m 5 X s 1813 727 m 6 X s 1819 727 m 5 X s 1824 727 m 2 -1 d s 1838 726 m20 1838 726 m20 1849 726 m 1 X s 1850 726 m 6 X s 1856 726 m 5 X s 1861 726 m 5 -1 d s 1866 725 m 6 X s 1872 725 m s 1883 725 m20 1883 725 m20 1894 725 m 4 X s 1898 725 m 5 -1 d s 1903 724 m 6 X s 1909 724 m 5 X s 1914 724 m 3 X s 1928 724 m20 1928 724 m20 1940 724 m s 1940 724 m 6 X s 1946 724 m 5 X s 1951 724 m 5 -1 d s 1956 723 m 6 X s 1962 723 m s 1974 723 m20 1974 723 m20 1985 723 m 3 X s 1988 723 m 5 X s 1993 723 m 6 X s 1999 723 m 5 X s 2004 723 m 4 X s 2019 723 m20 2019 723 m20 2030 722 m 1 X s 2031 722 m 5 X s 2036 722 m 5 X s 2041 722 m cl s 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C 1 lw 1151 1021 m -12 Y s 1151 998 m -11 Y s 1151 975 m -11 Y s 1151 953 m -12 Y s 1151 930 m -11 Y s 1151 907 m -11 Y s 1151 885 m -12 Y s 1151 862 m -11 Y s 1151 839 m -11 Y s 1151 816 m -11 Y s 1151 794 m -12 Y s 1151 771 m -11 Y s 1151 748 m -11 Y s 1151 726 m -12 Y s 1151 703 m -11 Y s 1151 680 m -11 Y s 1151 658 m -12 Y s 1151 635 m -11 Y s 1151 612 m -11 Y s 1151 590 m -12 Y s 1151 567 m -11 Y s 1151 544 m -11 Y s 1151 522 m -12 Y s 1151 499 m -11 Y s 1151 476 m -11 Y s 1151 454 m -12 Y s 1151 431 m -11 Y s 1151 408 m -11 Y s 1151 386 m -12 Y s 1151 363 m -11 Y s 1151 340 m -11 Y s 1151 318 m -12 Y s 1151 295 m -11 Y s 1151 272 m -11 Y s 1151 249 m -11 Y s 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 654 334 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (combined) show gr 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 1406 334 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (tail) show gr 1587 794 454 227 C 2268 2268 0 0 C 454 717 m 45 X s /w 2 def /w2 {w 2 div} def /w3 {w 3 div} def 522 717 m20 522 717 m20 544 717 m 46 X s 612 717 m20 612 717 m20 635 717 m 45 X s 703 717 m20 703 717 m20 726 717 m 45 X s 794 717 m20 794 717 m20 816 717 m 46 X s 885 717 m20 885 717 m20 907 717 m 46 X s 975 717 m20 975 717 m20 998 717 m 45 X s 1066 717 m20 1066 717 m20 1089 717 m 45 X s 1157 717 m20 1157 717 m20 1179 717 m 46 X s 1247 717 m20 1247 717 m20 1270 717 m 45 X s 1338 717 m20 1338 717 m20 1361 717 m 45 X s 1429 717 m20 1429 717 m20 1452 717 m 45 X s 1520 717 m20 1520 717 m20 1542 717 m 46 X s 1610 717 m20 1610 717 m20 1633 717 m 45 X s 1701 717 m20 1701 717 m20 1724 717 m 45 X s 1792 717 m20 1792 717 m20 1814 717 m 46 X s 1882 717 m20 1882 717 m20 1905 717 m 45 X s 1973 717 m20 1973 717 m20 1996 717 m 45 X s 2019 717 m20 2019 717 m20 2041 717 m cl s 2019 717 m20 2019 717 m20 2041 717 m cl s 2019 717 m20 2019 717 m20 2041 717 m cl s 2019 717 m20 2019 717 m20 2041 717 m cl s 2019 717 m20 2019 717 m20 2041 717 m cl s 2019 717 m20 2019 717 m20 2041 717 m cl s 1587 794 454 227 C gr gr showpage end %%EndDocument @endspecial 555 3859 a FE(Figure)k(3.3.5:)43 b(Change)33 b(of)e(the)i(distribution)d(functions)h(upon)h(atomization)h(of)555 3979 y(the)39 b(N)808 3993 y Fz(2)889 3979 y FE(molecule.)68 b(The)38 b(regions)g(shown)f(here)h(and)g(in)g(Figs.)f(3.3.6)e(and)j (3.3.7)555 4099 y(are)i(those)f(for)f(the)i(isolated)f(atom.)71 b(Dash-dot)40 b(lines)e(show)g(the)i(distribution)555 4220 y(functions)28 b(without)g(the)h(contribution)f(from)g(core)h (electrons.)555 4549 y(in)h(a)g(tetragonal)i(diamond)c(structure,)j (using)e(the)h(experimental)h(value)f(for)f(the)555 4669 y(lattice)44 b(parameter)f(5.43)1618 4654 y(\312)1618 4669 y(A)1687 4635 y Fz(54)1770 4669 y FE(.)78 b(The)41 b(plots)h(depict)g(the)g(same)g(qualitative)h(be-)555 4789 y(haviour)32 b(as)h(those)g(for)f(atoms)h(and)g(molecules.)52 b(The)32 b(chief)g(difference)g(can)h(be)555 4910 y(seen)g(in)f(the)h (tails)g(of)f(the)h(distributions,)f(where)h(they)g(fall)g(exactly)h (to)f(zero)g(\(at)555 5030 y FC(r)604 5044 y FB(s)669 5030 y FA(\203)25 b FE(4)p FC(:)p FE(8)g(and)h(at)h FC(s)k FA(\203)26 b FE(1)p FC(:)p FE(9\).)37 b(The)25 b(explanation)i(for)e (this)h(feature)h(is)e(simple:)37 b(in)25 b(an)555 5150 y(in\256nite)35 b(periodic)e(system)i(the)h(density)e(never)h(vanishes) f(\(or)h(put)f(it)h(the)g(other)555 5271 y(way,)k FC(r)843 5285 y FB(s)919 5271 y FE(attains)e(its)g(maximum)f(in)g(any)h (periodic)f(system\),)j(and)e(the)g(reduced)555 5391 y(gradient)29 b FC(s)34 b FE(unlike)27 b(in)h(the)h(atom)g(or)f(in)g (the)h(molecule)g(never)f(goes)h(to)f(in\256nity.)2118 5640 y(39)p eop %%Page: 40 48 40 47 bop -41 275 a Fw(Chapter)29 b(3.)e(Distributions)h(of)f(density)i (parameters)p -41 315 3238 4 v 43 3547 a @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 3685 @rwi @setspecial %%BeginDocument: fig/fig3.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr } def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1587 794 454 1247 bl 1587 794 454 1247 C NC 454 1247 m 794 Y s 488 1336 m -34 X s 471 1371 m -17 X s 471 1406 m -17 X s 471 1441 m -17 X s 471 1477 m -17 X s 488 1512 m -34 X s 471 1547 m -17 X s 471 1583 m -17 X s 471 1618 m -17 X s 471 1653 m -17 X s 488 1688 m -34 X s 471 1724 m -17 X s 471 1759 m -17 X s 471 1794 m -17 X s 471 1830 m -17 X s 488 1865 m -34 X s 471 1900 m -17 X s 471 1935 m -17 X s 471 1971 m -17 X s 471 2006 m -17 X s 488 2041 m -34 X s 488 1336 m -34 X s 471 1300 m -17 X s 471 1265 m -17 X s /xs 0 def (-30) /Times-Roman 68 stwn gsave 408 1313 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-30) show gr /xs 0 def (-20) /Times-Roman 68 stwn gsave 408 1489 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-20) show gr /xs 0 def (-10) /Times-Roman 68 stwn gsave 408 1666 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-10) show gr /xs 0 def (0) /Times-Roman 68 stwn gsave 408 1842 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (10) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (10) show gr 454 1247 m 1587 X s 454 1281 m -34 Y s 533 1264 m -17 Y s 612 1264 m -17 Y s 692 1264 m -17 Y s 771 1264 m -17 Y s 851 1281 m -34 Y s 930 1264 m -17 Y s 1009 1264 m -17 Y s 1089 1264 m -17 Y s 1168 1264 m -17 Y s 1247 1281 m -34 Y s 1327 1264 m -17 Y s 1406 1264 m -17 Y s 1486 1264 m -17 Y s 1565 1264 m -17 Y s 1644 1281 m -34 Y s 1724 1264 m -17 Y s 1803 1264 m -17 Y s 1882 1264 m -17 Y s 1962 1264 m -17 Y s 2041 1281 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 851 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1247 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1644 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 2041 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr 1587 794 454 1247 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn gsave 2041 1102 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 96 1957 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (a dg) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (1) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (/da) show gr 1587 794 454 1247 C 3 lw 458 1865 m 39 X 8 -1 d 8 X 8 -1 d 8 -2 d 8 -1 d 8 -1 d 8 -2 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -2 d 8 -2 d 8 -3 d 8 -4 d 8 -5 d 6 -6 d 2 -2 d 5 -7 d 3 -5 d 5 -10 d 3 -8 d 3 -11 d 3 -11 d 2 -7 d 3 -16 d 2 -17 d 3 -14 d 2 -19 d 3 -25 d 3 -26 d 2 -26 d 3 -38 d 2 -34 d 3 -38 d 5 -72 d -7 Y 2 -29 d 3 -34 d 1 -15 d 1 -10 d 1 -10 d -2 Y 3 -17 d 2 -7 d 1 -4 d 1 -1 d 1 X 1 2 d 2 5 d 1 7 d 1 10 d 1 17 d 2 29 d 3 Y 2 21 d 1 21 d 2 30 d 3 63 d 7 Y 4 73 d 3 55 d 1 24 d 4 63 d 2 32 d 2 26 d 3 32 d 2 27 d 3 28 d 3 28 d 3 17 d 2 15 d 2 Y 3 14 d 3 13 d 2 9 d 3 8 d 5 12 d 5 11 d 3 3 d 3 2 d 4 X 1 -1 d 8 -8 d 8 -5 d 7 -4 d 1 -1 d 8 -12 d 8 -10 d 5 -3 d 3 -2 d 8 -6 d 8 -8 d 8 -6 d 8 -4 d 8 -5 d 8 -5 d 8 -4 d 8 -3 d 7 -4 d 8 -3 d 8 -3 d 8 -3 d 8 -2 d 8 -2 d 8 -3 d 8 -2 d 8 -2 d 8 -1 d 8 -2 d 8 -2 d 8 -1 d 8 -2 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 -1 d 8 X 8 -1 d 8 -1 d 7 X 8 -1 d 8 X 8 -1 d 8 X 8 -1 d 8 X 8 -1 d 8 X 8 -1 d 16 X 8 -1 d 16 X 8 -1 d 24 X 8 -1 d 16 X 8 -1 d 32 X 8 -1 d 31 X 8 -1 d 48 X 8 -1 d 56 X 8 -1 d 64 X 8 -1 d 87 X 8 -1 d 120 X 8 -1 d 191 X 8 -1 d 55 X s 2074 1866 m 358 X 1 -1 d 398 X s 2268 2268 0 0 C 458 1865 m 8 X s 466 1865 m 8 X s 474 1865 m 6 X s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 492 1865 m20 492 1865 m20 503 1865 m 2 X s 505 1865 m 8 X s 513 1865 m 8 X s 521 1865 m 5 X s 537 1865 m20 537 1865 m20 548 1865 m 5 X s 553 1865 m 8 X s 561 1865 m 8 X s 569 1865 m 2 X s 582 1865 m20 582 1865 m20 594 1865 m 7 X s 601 1865 m 8 -1 d s 609 1864 m 7 X s 628 1863 m20 628 1863 m20 639 1860 m 2 -1 d s 641 1859 m 6 -3 d s 647 1856 m 2 -1 d s 649 1855 m 5 -6 d s 654 1849 m 2 -3 d s 662 1837 m20 662 1837 m20 666 1826 m 2 -6 d s 668 1820 m 4 -12 d s 672 1808 m 1 -4 d s 675 1793 m20 675 1793 m20 677 1782 m 2 -9 d s 679 1773 m 2 -7 d s 681 1766 m -6 Y s 683 1749 m20 683 1749 m20 685 1738 m 2 -15 d s 687 1723 m 1 -8 d s 689 1704 m20 689 1704 m20 691 1693 m 1 -9 d s 692 1684 m 1 -14 d s 694 1659 m20 694 1659 m20 695 1647 m 2 -11 d s 697 1636 m 1 -11 d s 699 1614 m20 699 1614 m20 699 1602 m 2 -22 d s 702 1568 m20 702 1568 m20 703 1557 m 1 -6 d s 704 1551 m -13 Y s 704 1538 m 1 -4 d s 706 1523 m20 706 1523 m20 706 1512 m 2 -23 d s 709 1478 m20 709 1478 m20 709 1467 m 2 -16 d s 711 1451 m -7 Y s 712 1433 m20 712 1433 m20 713 1421 m 1 -22 d s 715 1387 m20 715 1387 m20 716 1376 m 1 -12 d s 717 1364 m -11 Y s 718 1342 m20 718 1342 m20 720 1331 m -1 Y s 720 1330 m -2 Y s 720 1328 m 3 -16 d s 723 1312 m 1 -3 d s 729 1304 m20 729 1304 m20 731 1315 m 1 2 d s 732 1317 m 1 10 d s 733 1327 m 1 11 d s 734 1349 m20 734 1349 m20 735 1361 m 1 12 d s 736 1373 m 4 Y s 736 1377 m 1 6 d s 738 1395 m20 738 1395 m20 738 1406 m 1 13 d s 739 1419 m 1 10 d s 740 1440 m20 740 1440 m20 741 1451 m 1 23 d s 743 1485 m20 743 1485 m20 743 1497 m 1 16 d s 744 1513 m 6 Y s 745 1531 m20 745 1531 m20 745 1542 m 2 22 d s 747 1576 m20 747 1576 m20 748 1587 m 5 Y s 748 1592 m 1 18 d s 750 1621 m20 750 1621 m20 750 1632 m 1 16 d s 751 1648 m 7 Y s 752 1666 m20 752 1666 m20 753 1678 m 1 22 d s 755 1712 m20 755 1712 m20 755 1723 m 1 12 d s 756 1735 m 1 11 d s 758 1757 m20 758 1757 m20 758 1768 m 2 23 d s 761 1802 m20 761 1802 m20 762 1813 m 1 13 d s 763 1826 m 1 10 d s 765 1847 m20 765 1847 m20 766 1859 m 2 22 d s 768 1881 m s 770 1892 m20 770 1892 m20 771 1904 m 5 Y s 771 1909 m 3 17 d s 774 1926 m s 775 1937 m20 775 1937 m20 777 1949 m 2 8 d s 779 1957 m 3 13 d s 782 1970 m 1 Y s 785 1982 m20 785 1982 m20 789 1992 m 3 7 d s 792 1999 m 5 11 d s 797 2010 m 2 2 d s 809 2013 m20 809 2013 m20 817 2005 m 7 -4 d s 824 2001 m 7 -4 d s 831 1997 m 1 -1 d s 832 1996 m 3 -4 d s 841 1982 m20 841 1982 m20 849 1974 m 7 -5 d s 856 1969 m 8 -6 d s 864 1963 m 3 -3 d s 875 1952 m20 875 1952 m20 885 1946 m 3 -1 d s 888 1945 m 8 -5 d s 896 1940 m 8 -5 d s 904 1935 m s 914 1930 m20 914 1930 m20 925 1925 m 2 -1 d s 927 1924 m 8 -3 d s 935 1921 m 8 -3 d s 943 1918 m 3 -1 d s 957 1914 m20 957 1914 m20 967 1911 m 8 -3 d s 975 1908 m 8 -2 d s 983 1906 m 6 -1 d s 1000 1902 m20 1000 1902 m20 1012 1900 m 3 -1 d s 1015 1899 m 8 -1 d s 1023 1898 m 8 -2 d s 1031 1896 m 3 X s 1045 1894 m20 1045 1894 m20 1056 1893 m 7 -1 d s 1063 1892 m 8 -1 d s 1071 1891 m 8 -1 d s 1090 1888 m20 1090 1888 m20 1101 1887 m 2 X s 1103 1887 m 8 -1 d s 1111 1886 m 8 -1 d s 1119 1885 m 5 X s 1135 1884 m20 1135 1884 m20 1146 1883 m 4 X s 1150 1883 m 8 -1 d s 1158 1882 m 8 X s 1166 1882 m 3 -1 d s 1180 1881 m20 1180 1881 m20 1192 1880 m 6 X s 1198 1880 m 8 -1 d s 1206 1879 m 8 X s 1214 1879 m s 1226 1878 m20 1226 1878 m20 1237 1878 m 1 X s 1238 1878 m 8 -1 d s 1246 1877 m 8 X s 1254 1877 m 6 X s 1271 1876 m20 1271 1876 m20 1282 1876 m 4 X s 1286 1876 m 8 X s 1294 1876 m 8 -1 d s 1302 1875 m 3 X s 1316 1875 m20 1316 1875 m20 1328 1874 m 6 X s 1334 1874 m 8 X s 1342 1874 m 8 X s 1350 1874 m s 1362 1874 m20 1362 1874 m20 1373 1873 m 1 X s 1374 1873 m 7 X s 1381 1873 m 8 X s 1389 1873 m 7 X s 1407 1872 m20 1407 1872 m20 1418 1872 m 3 X s 1421 1872 m 8 X s 1429 1872 m 8 X s 1437 1872 m 4 X s 1452 1872 m20 1452 1872 m20 1464 1871 m 5 X s 1469 1871 m 8 X s 1477 1871 m 8 X s 1485 1871 m 1 X s 1498 1871 m20 1498 1871 m20 1509 1871 m 8 X s 1517 1871 m 8 -1 d s 1525 1870 m 7 X s 1543 1870 m20 1543 1870 m20 1554 1870 m 3 X s 1557 1870 m 8 X s 1565 1870 m 8 X s 1573 1870 m 4 X s 1588 1870 m20 1588 1870 m20 1600 1869 m 4 X s 1604 1869 m 8 X s 1612 1869 m 8 X s 1620 1869 m 2 X s 1634 1869 m20 1634 1869 m20 1645 1869 m 7 X s 1652 1869 m 8 X s 1660 1869 m 8 X s 1679 1869 m20 1679 1869 m20 1691 1868 m 1 X s 1692 1868 m 8 X s 1700 1868 m 8 X s 1708 1868 m 5 X s 1725 1868 m20 1725 1868 m20 1736 1868 m 4 X s 1740 1868 m 8 X s 1748 1868 m 8 X s 1756 1868 m 3 X s 1770 1868 m20 1770 1868 m20 1781 1868 m 7 X s 1788 1868 m 8 X s 1796 1868 m 8 X s 1804 1868 m s 1815 1868 m20 1815 1868 m20 1827 1867 m s 1827 1867 m 8 X s 1835 1867 m 8 X s 1843 1867 m 6 X s 1861 1867 m20 1861 1867 m20 1872 1867 m 3 X s 1875 1867 m 8 X s 1883 1867 m 8 X s 1891 1867 m 4 X s 1906 1867 m20 1906 1867 m20 1917 1867 m 6 X s 1923 1867 m 8 X s 1931 1867 m 8 X s 1939 1867 m 1 X s 1951 1867 m20 1951 1867 m20 1963 1867 m s 1963 1867 m 8 X s 1971 1867 m 8 X s 1979 1867 m 6 X s 1997 1867 m20 1997 1867 m20 2008 1867 m 3 X s 2011 1867 m 8 -1 d s 2019 1866 m 8 X s 2027 1866 m 4 X s 2041 1866 m20 2041 1866 m20 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C 1 lw 644 1247 m 12 Y s 644 1270 m 11 Y s 644 1293 m 11 Y s 644 1315 m 12 Y s 644 1338 m 11 Y s 644 1361 m 11 Y s 644 1383 m 12 Y s 644 1406 m 11 Y s 644 1429 m 11 Y s 644 1452 m 11 Y s 644 1474 m 12 Y s 644 1497 m 11 Y s 644 1520 m 11 Y s 644 1542 m 12 Y s 644 1565 m 11 Y s 644 1588 m 11 Y s 644 1610 m 12 Y s 644 1633 m 11 Y s 644 1656 m 11 Y s 644 1678 m 12 Y s 644 1701 m 11 Y s 644 1724 m 11 Y s 644 1746 m 12 Y s 644 1769 m 11 Y s 644 1792 m 11 Y s 644 1814 m 12 Y s 644 1837 m 11 Y s 644 1860 m 11 Y s 644 1882 m 12 Y s 644 1905 m 11 Y s 644 1928 m 11 Y s 644 1950 m 12 Y s 644 1973 m 11 Y s 644 1996 m 11 Y s 644 2019 m 11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 770 1247 m 12 Y s 770 1270 m 11 Y s 770 1293 m 11 Y s 770 1315 m 12 Y s 770 1338 m 11 Y s 770 1361 m 11 Y s 770 1383 m 12 Y s 770 1406 m 11 Y s 770 1429 m 11 Y s 770 1452 m 11 Y s 770 1474 m 12 Y s 770 1497 m 11 Y s 770 1520 m 11 Y s 770 1542 m 12 Y s 770 1565 m 11 Y s 770 1588 m 11 Y s 770 1610 m 12 Y s 770 1633 m 11 Y s 770 1656 m 11 Y s 770 1678 m 12 Y s 770 1701 m 11 Y s 770 1724 m 11 Y s 770 1746 m 12 Y s 770 1769 m 11 Y s 770 1792 m 11 Y s 770 1814 m 12 Y s 770 1837 m 11 Y s 770 1860 m 11 Y s 770 1882 m 12 Y s 770 1905 m 11 Y s 770 1928 m 11 Y s 770 1950 m 12 Y s 770 1973 m 11 Y s 770 1996 m 11 Y s 770 2019 m 11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1251 1247 m 12 Y s 1251 1270 m 11 Y s 1251 1293 m 11 Y s 1251 1315 m 12 Y s 1251 1338 m 11 Y s 1251 1361 m 11 Y s 1251 1383 m 12 Y s 1251 1406 m 11 Y s 1251 1429 m 11 Y s 1251 1452 m 11 Y s 1251 1474 m 12 Y s 1251 1497 m 11 Y s 1251 1520 m 11 Y s 1251 1542 m 12 Y s 1251 1565 m 11 Y s 1251 1588 m 11 Y s 1251 1610 m 12 Y s 1251 1633 m 11 Y s 1251 1656 m 11 Y s 1251 1678 m 12 Y s 1251 1701 m 11 Y s 1251 1724 m 11 Y s 1251 1746 m 12 Y s 1251 1769 m 11 Y s 1251 1792 m 11 Y s 1251 1814 m 12 Y s 1251 1837 m 11 Y s 1251 1860 m 11 Y s 1251 1882 m 12 Y s 1251 1905 m 11 Y s 1251 1928 m 11 Y s 1251 1950 m 12 Y s 1251 1973 m 11 Y s 1251 1996 m 11 Y s 1251 2019 m 11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 485 1962 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (core) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 654 1962 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (CV) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 890 1962 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (valence) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 1406 1962 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (tail) show gr 1587 794 454 1247 C 2268 2268 0 0 C 454 1865 m 45 X s /w 2 def /w2 {w 2 div} def /w3 {w 3 div} def 522 1865 m20 522 1865 m20 544 1865 m 46 X s 612 1865 m20 612 1865 m20 635 1865 m 45 X s 703 1865 m20 703 1865 m20 726 1865 m 45 X s 794 1865 m20 794 1865 m20 816 1865 m 46 X s 885 1865 m20 885 1865 m20 907 1865 m 46 X s 975 1865 m20 975 1865 m20 998 1865 m 45 X s 1066 1865 m20 1066 1865 m20 1089 1865 m 45 X s 1157 1865 m20 1157 1865 m20 1179 1865 m 46 X s 1247 1865 m20 1247 1865 m20 1270 1865 m 45 X s 1338 1865 m20 1338 1865 m20 1361 1865 m 45 X s 1429 1865 m20 1429 1865 m20 1452 1865 m 45 X s 1520 1865 m20 1520 1865 m20 1542 1865 m 46 X s 1610 1865 m20 1610 1865 m20 1633 1865 m 45 X s 1701 1865 m20 1701 1865 m20 1724 1865 m 45 X s 1792 1865 m20 1792 1865 m20 1814 1865 m 46 X s 1882 1865 m20 1882 1865 m20 1905 1865 m 45 X s 1973 1865 m20 1973 1865 m20 1996 1865 m 45 X s 1587 794 454 1247 C NC 1587 794 454 227 bl 1587 794 454 227 C NC 454 227 m 794 Y s 488 284 m -34 X s 471 312 m -17 X s 471 340 m -17 X s 471 369 m -17 X s 471 397 m -17 X s 488 425 m -34 X s 471 454 m -17 X s 471 482 m -17 X s 471 510 m -17 X s 471 539 m -17 X s 488 567 m -34 X s 471 595 m -17 X s 471 624 m -17 X s 471 652 m -17 X s 471 680 m -17 X s 488 709 m -34 X s 471 737 m -17 X s 471 765 m -17 X s 471 794 m -17 X s 471 822 m -17 X s 488 851 m -34 X s 471 879 m -17 X s 471 907 m -17 X s 471 936 m -17 X s 471 964 m -17 X s 488 992 m -34 X s 488 284 m -34 X s 471 255 m -17 X s 488 992 m -34 X s /xs 0 def (-5) /Times-Roman 68 stwn gsave 408 261 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-5) show gr /xs 0 def (-2.5) /Times-Roman 68 stwn gsave 408 403 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-2.5) show gr /xs 0 def (0) /Times-Roman 68 stwn gsave 408 544 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (2.5) /Times-Roman 68 stwn gsave 408 686 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2.5) show gr /xs 0 def (5) /Times-Roman 68 stwn gsave 408 828 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (5) show gr /xs 0 def (7.5) /Times-Roman 68 stwn gsave 408 970 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (7.5) show gr 454 227 m 1587 X s 454 261 m -34 Y s 559 244 m -17 Y s 665 244 m -17 Y s 771 244 m -17 Y s 877 244 m -17 Y s 983 261 m -34 Y s 1089 244 m -17 Y s 1194 244 m -17 Y s 1300 244 m -17 Y s 1406 244 m -17 Y s 1512 261 m -34 Y s 1618 244 m -17 Y s 1724 244 m -17 Y s 1830 244 m -17 Y s 1935 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 983 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1512 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr 1587 794 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 96 907 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (a dg) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (3) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (/da) show gr 1587 794 454 227 C 3 lw 459 529 m 7 -8 d 4 -5 d 7 -6 d 3 -2 d 5 X 5 2 d 1 X 4 4 d 6 8 d 11 13 d 11 10 d 10 9 d 11 11 d 10 13 d 11 12 d 11 16 d 4 8 d 4 6 d 2 2 d 4 X 2 -1 d 3 -2 d 2 -4 d 2 -6 d 2 -8 d 2 -13 d 5 -25 d 2 -15 d 2 -22 d 6 -54 d 11 -100 d 6 -50 d 2 -11 d 2 -10 d -4 Y 4 -12 d 2 -7 d 2 -4 d 2 -2 d 3 X 2 4 d 3 6 d 4 13 d 2 9 d 3 15 d 5 22 d 10 43 d 1 3 d 8 30 d 3 11 d 7 27 d 3 10 d 7 19 d 4 11 d 5 12 d 5 10 d 7 10 d 4 5 d 11 12 d 10 10 d 11 8 d 9 4 d 1 1 d 11 2 d 11 1 d 10 2 d 11 2 d 11 1 d 10 X 11 -1 d 10 -2 d 11 -1 d 11 -1 d 10 -2 d 11 -2 d 11 -2 d 10 -2 d 11 -2 d 10 -4 d 11 -4 d 11 -6 d 10 -7 d 11 -10 d 8 -9 d 2 -3 d 8 -11 d 3 -5 d 7 -14 d 4 -8 d 8 -19 d 2 -7 d 11 -29 d 8 -20 d 3 -5 d 4 -5 d 3 -1 d 2 X 1 1 d 3 4 d 2 7 d 3 11 d 3 13 d 2 10 d 2 15 d 3 26 d 3 27 d 3 24 d 7 65 d 1 13 d 6 58 d 3 24 d 2 11 d 3 24 d 3 20 d 4 20 d 4 19 d 5 19 d 2 5 d 5 17 d 6 16 d 10 28 d 7 20 d 4 14 d 4 14 d 4 14 d 2 7 d 1 Y 4 7 d 3 3 d 2 1 d 2 -1 d 2 -4 d 2 -5 d 2 -10 d 5 -21 d 2 -13 d 2 -17 d 6 -50 d 11 -87 d 5 -39 d 4 -19 d 2 -11 d 3 -18 d 4 -15 d 3 -13 d 4 -13 d 5 -11 d 2 -4 d 5 -9 d 5 -8 d 7 -6 d 4 -4 d 9 -4 d 2 -1 d 10 -4 d 11 -2 d 10 -1 d 11 -1 d 53 X 11 1 d 10 X 11 1 d 11 X 10 1 d 22 X 10 1 d 21 X 11 1 d 32 X 10 1 d 75 X 10 1 d 999 X s 2615 567 m 38 X 1 1 d 2 X 1 -1 d 28 X 1 1 d 6 X 8 -1 d 21 X 1 1 d 4 X 2 -1 d 116 X 1 1 d 8 X 6 -1 d 24 X 2 1 d 10 X 4 -1 d 21 X 1 1 d 17 X -1 Y 22 X 1 1 d 16 X 1 -1 d 22 X 2 1 d 11 X 4 -1 d 27 X 1 1 d 8 X 1 -1 d 25 X 1 Y 14 X 1 -1 d 24 X 1 1 d 19 X 1 -1 d 23 X 1 Y 23 X -1 Y 3 X 5 -1 d 13 X 1 Y 3 X 1 Y 20 X 1 -1 d 3 X -1 Y 16 X 2 1 d 3 X 1 1 d 24 X -1 Y 5 X 4 -1 d 14 X 1 Y 4 X 1 Y 20 X 1 -1 d 4 X -1 Y 18 X 1 1 d 6 X 1 Y 20 X 1 -1 d 11 X 1 -1 d 5 X 1 1 d 16 X 3 1 d 11 X 7 -1 d 37 X 1 1 d 15 X 2 -1 d 39 X 1 1 d 16 X 2 -1 d 36 X 2 1 d 13 X 6 -1 d 21 X s 2268 2268 0 0 C 459 529 m 5 -6 d s 464 523 m 6 -7 d s 470 516 m 4 -4 d s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 484 508 m20 484 508 m20 494 513 m s 494 513 m 7 9 d s 501 522 m 7 8 d s 516 538 m20 516 538 m20 524 546 m 9 8 d s 533 554 m 8 7 d s 548 570 m20 548 570 m20 555 579 m 10 11 d s 565 590 m 4 7 d s 576 606 m20 576 606 m20 581 616 m 2 2 d s 583 618 m 2 3 d s 585 621 m 1 1 d s 586 622 m 3 X s 589 622 m 3 -1 d s 592 621 m 2 -2 d s 594 619 m 2 -3 d s 596 616 m 1 -1 d s 597 615 m -1 Y s 601 603 m20 601 603 m20 603 592 m 3 -22 d s 608 559 m20 608 559 m20 610 547 m 2 -17 d s 612 530 m 1 -5 d s 614 514 m20 614 514 m20 615 502 m 2 -22 d s 619 468 m20 619 468 m20 620 457 m 2 -22 d s 623 423 m20 623 423 m20 625 412 m 2 -22 d s 628 378 m20 628 378 m20 629 367 m 3 -20 d s 632 347 m -3 Y s 633 333 m20 633 333 m20 635 322 m -4 Y s 635 318 m 2 -8 d s 637 310 m 1 -8 d s 638 302 m 1 -2 d s 642 289 m20 642 289 m20 645 278 m 1 -1 d s 646 277 m 1 -3 d s 647 274 m 2 -2 d s 649 272 m 1 X s 650 272 m 2 X s 652 272 m 1 2 d s 653 274 m 2 4 d s 655 278 m 2 6 d s 661 295 m20 661 295 m20 664 306 m 1 5 d s 665 311 m 3 17 d s 671 339 m20 671 339 m20 673 350 m 5 22 d s 681 383 m20 681 383 m20 683 394 m 5 21 d s 688 415 m 1 1 d s 692 427 m20 692 427 m20 695 438 m 4 17 d s 699 455 m 2 5 d s 704 471 m20 704 471 m20 708 482 m 1 3 d s 709 485 m 4 12 d s 713 497 m 1 2 d s 714 499 m 2 4 d s 720 513 m20 720 513 m20 725 523 m 5 8 d s 730 531 m 5 8 d s 735 539 m 3 3 d s 745 551 m20 745 551 m20 753 559 m 2 3 d s 755 562 m 1 1 d s 756 563 m 8 8 d s 764 571 m 3 2 d s 767 573 m 2 2 d s 780 579 m20 780 579 m20 791 582 m 8 1 d s 799 583 m 10 2 d s 809 585 m 4 1 d s 824 588 m20 824 588 m20 835 590 m 6 1 d s 841 591 m 11 2 d s 852 593 m 6 1 d s 868 598 m20 868 598 m20 879 603 m 2 1 d s 881 604 m 3 2 d s 884 606 m 8 6 d s 892 612 m 2 2 d s 894 614 m 2 2 d s 904 625 m20 904 625 m20 912 633 m 4 4 d s 916 637 m 10 11 d s 926 648 m 2 1 d s 937 656 m20 937 656 m20 946 663 m 1 X s 947 663 m 7 3 d s 954 666 m 4 2 d s 958 668 m 7 X s 965 668 m 3 X s 979 668 m20 979 668 m20 990 670 m 10 4 d s 1000 674 m 11 2 d s 1011 676 m 1 X s 1023 677 m20 1023 677 m20 1034 678 m 8 1 d s 1042 679 m 1 1 d s 1043 680 m 11 3 d s 1054 683 m 2 1 d s 1067 687 m20 1067 687 m20 1078 686 m 2 X s 1080 686 m 5 -3 d s 1085 683 m -1 Y s 1085 682 m 5 -4 d s 1090 678 m 5 -6 d s 1102 662 m20 1102 662 m20 1109 653 m 8 -11 d s 1117 642 m 6 -6 d s 1131 628 m20 1131 628 m20 1140 621 m 9 -7 d s 1149 614 m 10 -5 d s 1169 604 m20 1169 604 m20 1179 599 m 2 -1 d s 1181 598 m 11 -5 d s 1192 593 m 8 -4 d s 1210 585 m20 1210 585 m20 1221 580 m 3 -1 d s 1224 579 m 10 -4 d s 1234 575 m 8 -3 d s 1253 569 m20 1253 569 m20 1264 566 m 2 X s 1266 566 m 11 -2 d s 1277 564 m 9 -2 d s 1297 561 m20 1297 561 m20 1309 560 m 10 X s 1319 560 m 11 X s 1330 560 m 1 X s 1343 560 m20 1343 560 m20 1354 560 m 8 X s 1362 560 m 10 X s 1372 560 m 5 1 d s 1388 561 m20 1388 561 m20 1399 561 m 5 1 d s 1404 562 m 11 X s 1415 562 m 7 X s 1433 563 m20 1433 563 m20 1445 563 m 2 X s 1447 563 m 10 1 d s 1457 564 m 10 X s 1479 564 m20 1479 564 m20 1490 565 m 10 X s 1500 565 m 10 X s 1510 565 m 3 X s 1524 565 m20 1524 565 m20 1535 566 m 7 X s 1542 566 m 11 X s 1553 566 m 5 X s 1569 566 m20 1569 566 m20 1581 566 m 4 X s 1585 566 m 10 X s 1595 566 m 8 X s 1615 567 m20 1615 567 m20 1626 567 m 1 X s 1627 567 m 11 X s 1638 567 m 10 X s 1648 567 m 1 X s 1660 567 m20 1660 567 m20 1671 567 m 9 X s 1680 567 m 11 X s 1691 567 m 3 X s 1706 567 m20 1706 567 m20 1717 567 m 6 X s 1723 567 m 10 X s 1733 567 m 7 X s 1751 567 m20 1751 567 m20 1762 567 m 3 X s 1765 567 m 11 X s 1776 567 m 9 X s 1796 567 m20 1796 567 m20 1808 567 m 10 X s 1818 567 m 11 X s 1829 567 m 1 X s 1842 567 m20 1842 567 m20 1853 567 m 8 X s 1861 567 m 10 X s 1871 567 m 5 X s 1887 567 m20 1887 567 m20 1898 567 m 5 X s 1903 567 m 11 X s 1914 567 m 7 X s 1932 567 m20 1932 567 m20 1944 567 m 2 X s 1946 567 m 10 X s 1956 567 m 10 X s 1978 567 m20 1978 567 m20 1989 567 m 10 X s 1999 567 m 10 X s 2009 567 m 3 X s 2023 567 m20 2023 567 m20 2034 567 m 7 X s 2041 567 m cl s 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C 1 lw 1151 227 m 11 Y s 1151 249 m 12 Y s 1151 272 m 12 Y s 1151 295 m 11 Y s 1151 318 m 11 Y s 1151 340 m 12 Y s 1151 363 m 11 Y s 1151 386 m 11 Y s 1151 408 m 12 Y s 1151 431 m 11 Y s 1151 454 m 11 Y s 1151 476 m 12 Y s 1151 499 m 11 Y s 1151 522 m 11 Y s 1151 544 m 12 Y s 1151 567 m 11 Y s 1151 590 m 11 Y s 1151 612 m 12 Y s 1151 635 m 11 Y s 1151 658 m 11 Y s 1151 680 m 12 Y s 1151 703 m 11 Y s 1151 726 m 11 Y s 1151 748 m 12 Y s 1151 771 m 11 Y s 1151 794 m 11 Y s 1151 816 m 12 Y s 1151 839 m 11 Y s 1151 862 m 11 Y s 1151 885 m 11 Y s 1151 907 m 12 Y s 1151 930 m 11 Y s 1151 953 m 11 Y s 1151 975 m 12 Y s 1151 998 m 11 Y s 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 654 924 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (combined) show gr 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 1406 924 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (tail) show gr 1587 794 454 227 C 2268 2268 0 0 C 454 567 m 45 X s /w 2 def /w2 {w 2 div} def /w3 {w 3 div} def 522 567 m20 522 567 m20 544 567 m 46 X s 612 567 m20 612 567 m20 635 567 m 45 X s 703 567 m20 703 567 m20 726 567 m 45 X s 794 567 m20 794 567 m20 816 567 m 46 X s 885 567 m20 885 567 m20 907 567 m 46 X s 975 567 m20 975 567 m20 998 567 m 45 X s 1066 567 m20 1066 567 m20 1089 567 m 45 X s 1157 567 m20 1157 567 m20 1179 567 m 46 X s 1247 567 m20 1247 567 m20 1270 567 m 45 X s 1338 567 m20 1338 567 m20 1361 567 m 45 X s 1429 567 m20 1429 567 m20 1452 567 m 45 X s 1520 567 m20 1520 567 m20 1542 567 m 46 X s 1610 567 m20 1610 567 m20 1633 567 m 45 X s 1701 567 m20 1701 567 m20 1724 567 m 45 X s 1792 567 m20 1792 567 m20 1814 567 m 46 X s 1882 567 m20 1882 567 m20 1905 567 m 45 X s 1973 567 m20 1973 567 m20 1996 567 m 45 X s 2019 567 m20 2019 567 m20 2041 567 m cl s 2019 567 m20 2019 567 m20 2041 567 m cl s 2019 567 m20 2019 567 m20 2041 567 m cl s 2019 567 m20 2019 567 m20 2041 567 m cl s 2019 567 m20 2019 567 m20 2041 567 m cl s 2019 567 m20 2019 567 m20 2041 567 m cl s 1587 794 454 227 C gr gr showpage end %%EndDocument @endspecial -41 3859 a FE(Figure)19 b(3.3.6:)32 b(The)18 b(derivative)h(of)g(the)h(distribution)d(functions)i FC(g)2534 3873 y Fz(1)2577 3859 y FC(\204r)2669 3873 y FB(s)2707 3859 y FC(\205)f FE(and)i FC(g)3020 3873 y Fz(3)3063 3859 y FC(\204s)6 b(\205)-41 3979 y FE(for)21 b(the)h(N)351 3993 y Fz(2)415 3979 y FE(molecule)g(at)h(its)e (experimental)g(bond)g(length.)36 b(Dash-dot)23 b(lines)e(show)-41 4099 y(the)28 b(distribution)d(functions)i(without)g(the)g (contribution)g(from)f(core)h(electrons.)106 4366 y(The)21 b(range)i(of)f FC(s)27 b FE(that)c(contributes)g(to)f FC(g)1679 4380 y Fz(3)1722 4366 y FC(\204s)6 b(\205)21 b FE(and)h Fu(\321)p FC(g)2205 4380 y Fz(3)2248 4366 y FC(\204s)6 b(\205)21 b FE(seems)h(to)h(coincide)-41 4486 y(with)35 b(that)i(for)e(which)g(the)h(GGA)g(is)e(valid.)59 b(This)35 b(is)g(especially)h(so)f(in)g(the)h(solid)-41 4607 y(state.)1522 5640 y(40)p eop %%Page: 41 49 41 48 bop 2568 275 a Fw(3.3.)27 b(Results)i(and)f(discussion)p 555 315 3238 4 v 639 4132 a @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 3685 @rwi @setspecial %%BeginDocument: fig/fig4.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr } def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1587 794 454 1247 bl 1587 794 454 1247 C NC 454 1247 m 794 Y s 488 1247 m -34 X s 471 1274 m -17 X s 471 1300 m -17 X s 471 1327 m -17 X s 471 1353 m -17 X s 488 1380 m -34 X s 471 1406 m -17 X s 471 1433 m -17 X s 471 1459 m -17 X s 471 1486 m -17 X s 488 1512 m -34 X s 471 1538 m -17 X s 471 1565 m -17 X s 471 1591 m -17 X s 471 1618 m -17 X s 488 1644 m -34 X s 471 1671 m -17 X s 471 1697 m -17 X s 471 1724 m -17 X s 471 1750 m -17 X s 488 1777 m -34 X s 471 1803 m -17 X s 471 1830 m -17 X s 471 1856 m -17 X s 471 1882 m -17 X s 488 1909 m -34 X s 471 1935 m -17 X s 471 1962 m -17 X s 471 1988 m -17 X s 471 2015 m -17 X s 488 2041 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 408 1225 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (10) /Times-Roman 68 stwn gsave 408 1357 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (10) show gr /xs 0 def (20) /Times-Roman 68 stwn gsave 408 1489 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (20) show gr /xs 0 def (30) /Times-Roman 68 stwn gsave 408 1622 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (30) show gr /xs 0 def (40) /Times-Roman 68 stwn gsave 408 1754 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (40) show gr /xs 0 def (50) /Times-Roman 68 stwn gsave 408 1886 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (50) show gr /xs 0 def (60) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (60) show gr 454 1247 m 1587 X s 454 1281 m -34 Y s 533 1264 m -17 Y s 612 1264 m -17 Y s 692 1264 m -17 Y s 771 1264 m -17 Y s 851 1281 m -34 Y s 930 1264 m -17 Y s 1009 1264 m -17 Y s 1089 1264 m -17 Y s 1168 1264 m -17 Y s 1247 1281 m -34 Y s 1327 1264 m -17 Y s 1406 1264 m -17 Y s 1486 1264 m -17 Y s 1565 1264 m -17 Y s 1644 1281 m -34 Y s 1724 1264 m -17 Y s 1803 1264 m -17 Y s 1882 1264 m -17 Y s 1962 1264 m -17 Y s 2041 1281 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 851 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 1247 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr /xs 0 def (3) /Times-Roman 68 stwn gsave 1644 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (3) show gr /xs 0 def (4) /Times-Roman 68 stwn gsave 2041 1179 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (4) show gr 1587 794 454 1247 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn gsave 2041 1102 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 96 1962 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (g) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (1) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\)) show gr 1587 794 454 1247 C 3 lw 455 1272 m 3 8 d 1 4 d 2 10 d 1 7 d 2 12 d 1 10 d 2 16 d 2 14 d 2 21 d 1 15 d 2 32 d 1 10 d 3 45 d 3 39 d 1 4 d 2 26 d 1 12 d 2 18 d 1 11 d 2 10 d 1 8 d 1 1 d 1 6 d 2 3 d 2 2 d 1 -1 d 2 -3 d 2 -3 d 3 -10 d 3 -12 d 4 -12 d 3 -10 d 3 -8 d -1 Y 3 -4 d 1 X 2 -1 d 1 X 2 3 d 1 2 d 2 6 d 1 5 d 2 9 d 2 9 d 2 12 d 1 13 d 2 17 d 1 16 d 2 22 d 2 18 d 2 32 d 1 16 d 3 51 d 4 53 d 2 42 d 1 7 d 2 27 d 1 15 d 2 19 d 2 13 d 1 10 d 1 8 d 1 3 d 1 4 d 2 3 d 1 Y 2 X 2 -3 d 1 -5 d 2 -7 d 2 -11 d 1 -8 d 3 -18 d -5 Y 4 -26 d 3 -28 d 3 -29 d 4 -29 d 3 -28 d 3 -27 d 4 -26 d 3 -24 d 3 -24 d 4 -22 d 3 -21 d 3 -19 d 4 -19 d 3 -17 d 3 -17 d 3 -15 d 4 -14 d 3 -14 d 3 -13 d 4 -12 d 3 -11 d 3 -11 d 4 -10 d 3 -9 d 3 -9 d 4 -9 d 3 -8 d 3 -7 d 4 -7 d 3 -7 d 3 -7 d 3 -6 d 4 -5 d 3 -6 d 3 -5 d 4 -5 d 3 -5 d 3 -5 d 4 -4 d 3 -4 d 3 -4 d 4 -4 d 3 -3 d 3 -4 d 4 -3 d 3 -3 d 3 -3 d 3 -3 d 4 -3 d 3 -2 d 3 -3 d 4 -2 d 3 -2 d 3 -3 d 4 -2 d 3 -2 d 3 -2 d 4 -1 d 3 -2 d 3 -2 d 4 -2 d 3 -1 d 3 -2 d 3 -1 d 4 -1 d 3 -2 d 3 -1 d 4 -1 d 3 -1 d 3 -1 d 4 -2 d 3 -1 d 3 -1 d 4 -1 d 3 X 3 -1 d 4 -1 d 3 -1 d 3 -1 d 4 X 3 -1 d 3 -1 d 3 X 4 -1 d 3 X 3 -1 d 4 X 3 -1 d 3 X 4 -1 d 3 X 3 -1 d 10 X 4 -1 d 39 X 4 1 d 6 X 4 1 d 3 1 d 3 1 d 3 2 d 4 2 d 3 2 d 3 4 d 4 4 d 3 6 d 3 7 d 4 10 d 3 11 d 3 13 d 4 13 d 3 13 d 3 11 d 4 9 d 3 7 d 3 5 d 3 3 d 4 2 d 3 1 d 7 X 3 -1 d 7 X 3 -1 d 3 -1 d 4 -1 d 3 -1 d 3 -1 d 4 X 3 -1 d 3 -1 d 3 -1 d 4 -1 d 3 -2 d 3 -1 d 4 -1 d 3 -1 d 3 -2 d 4 -2 d 3 -2 d 3 -2 d 4 -2 d 3 -3 d 3 -2 d 4 -3 d 3 -2 d 3 -2 d 3 -3 d 4 -2 d s 1128 1370 m 3 -3 d 3 -2 d 4 -3 d 3 -3 d 3 -2 d 4 -2 d 3 -3 d 3 -2 d 4 -3 d 3 -2 d 3 -3 d 4 -2 d 3 -2 d 3 -2 d 3 -1 d 4 -2 d 3 -2 d 3 -3 d 4 -2 d 3 -2 d 3 -2 d 4 -1 d 3 -2 d 3 -1 d 4 -1 d 3 -2 d 3 -1 d 4 -2 d 3 -1 d 3 -2 d 4 -1 d 3 -2 d 3 -1 d 3 -1 d 4 -1 d 3 -2 d 3 -1 d 4 -1 d 3 -1 d 3 -1 d 4 -1 d 3 -1 d 3 -1 d 4 -1 d 3 -1 d 3 X 4 -1 d 3 -1 d 3 -1 d 3 -1 d 4 -1 d 3 X 3 -1 d 4 -1 d 3 -1 d 3 X 4 -1 d 3 -1 d 3 X 4 -1 d 3 -1 d 3 X 4 -1 d 3 X 3 -1 d 3 X 4 -1 d 3 X 3 -1 d 4 X 3 -1 d 3 X 4 -1 d 3 X 3 -1 d 7 X 3 -1 d 4 X 3 -1 d 3 X 3 -1 d 7 X 3 -1 d 4 X 3 -1 d 7 X 3 -1 d 7 X 3 -1 d 7 X 3 -1 d 6 X 4 -1 d 10 X 3 -1 d 13 X 4 -1 d 19 X 4 -1 d 13 X 3 -1 d 10 X 4 -1 d 13 X 3 -1 d 13 X 4 -1 d 23 X 3 -1 d 20 X 3 -1 d 47 X 3 -1 d 23 X 4 -1 d 36 X 3 -1 d 63 X s 1800 1252 m 14 X 3 -1 d 53 X 3 -1 d 86 X 3 -1 d 77 X 3 -1 d 225 X 4 -1 d 165 X s 2268 2268 0 0 C 455 1247 m 4 X s 459 1247 m 3 X s 462 1247 m 3 X s 465 1247 m 4 X s 469 1247 m 3 X s 472 1247 m 3 X s 475 1247 m 3 X s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 489 1247 m20 489 1247 m20 501 1247 m 1 X s 502 1247 m 3 X s 505 1247 m 3 X s 508 1247 m 4 X s 512 1247 m 3 X s 515 1247 m 3 X s 518 1247 m 4 X s 522 1247 m 1 X s 535 1247 m20 535 1247 m20 546 1247 m 2 X s 548 1247 m 3 X s 551 1247 m 4 X s 555 1247 m 3 X s 558 1247 m 3 X s 561 1247 m 4 X s 565 1247 m 3 X s 568 1247 m 1 X s 580 1247 m20 580 1247 m20 591 1247 m 3 X s 594 1247 m 4 X s 598 1247 m 3 X s 601 1247 m 3 X s 604 1247 m 4 X s 608 1247 m 3 X s 611 1247 m 3 X s 625 1247 m20 625 1247 m20 637 1247 m s 637 1247 m 4 X s 641 1247 m 3 X s 644 1247 m 3 X s 647 1247 m 4 X s 651 1247 m 3 X s 654 1247 m 3 X s 657 1247 m 2 X s 671 1247 m20 671 1247 m20 682 1247 m 2 X s 684 1247 m 3 X s 687 1247 m 3 X s 690 1247 m 4 X s 694 1247 m 3 X s 697 1247 m 3 X s 700 1247 m 4 X s 704 1247 m 1 X s 716 1247 m20 716 1247 m20 727 1247 m 3 X s 730 1247 m 4 X s 734 1247 m 3 X s 737 1247 m 3 X s 740 1247 m 3 X s 743 1247 m 4 X s 747 1247 m 3 X s 761 1247 m20 761 1247 m20 773 1247 m s 773 1247 m 4 X s 777 1247 m 3 X s 780 1247 m 3 X s 783 1247 m 4 X s 787 1247 m 3 X s 790 1247 m 3 X s 793 1247 m 2 X s 807 1247 m20 807 1247 m20 818 1247 m 2 X s 820 1247 m 3 X s 823 1247 m 3 X s 826 1247 m 4 X s 830 1247 m 3 X s 833 1247 m 3 X s 836 1247 m 4 X s 840 1247 m 1 X s 852 1247 m20 852 1247 m20 864 1247 m 2 X s 866 1247 m 3 X s 869 1247 m 4 X s 873 1247 m 3 X s 876 1247 m 3 X s 879 1247 m 4 X s 883 1247 m 3 X s 886 1247 m s 898 1247 m20 898 1247 m20 909 1248 m s 909 1248 m 3 X s 912 1248 m 4 X s 916 1248 m 3 X s 919 1248 m 3 X s 922 1248 m 4 X s 926 1248 m 3 1 d s 929 1249 m 2 X s 942 1253 m20 942 1253 m20 952 1259 m 1 Y s 952 1260 m 4 3 d s 956 1263 m 3 3 d s 959 1266 m 3 4 d s 962 1270 m 3 4 d s 965 1274 m 2 2 d s 973 1285 m20 973 1285 m20 979 1295 m s 979 1295 m 2 5 d s 981 1300 m 1 3 d s 982 1303 m 2 5 d s 984 1308 m 1 4 d s 985 1312 m 2 4 d s 990 1327 m20 990 1327 m20 993 1338 m 2 7 d s 995 1345 m 2 Y s 995 1347 m 4 13 d s 1001 1371 m20 1001 1371 m20 1004 1382 m 1 2 d s 1005 1384 m 2 5 d s 1007 1389 m 2 5 d s 1009 1394 m 1 3 d s 1010 1397 m 2 4 d s 1012 1401 m 1 2 d s 1021 1410 m20 1021 1410 m20 1033 1412 m 2 -1 d s 1035 1411 m 3 X s 1038 1411 m 4 X s 1042 1411 m 3 -1 d s 1045 1410 m 3 -1 d s 1048 1409 m 4 -1 d s 1052 1408 m 3 -1 d s 1066 1405 m20 1066 1405 m20 1077 1401 m 1 -1 d s 1078 1400 m 3 -1 d s 1081 1399 m 4 -1 d s 1085 1398 m 3 -1 d s 1088 1397 m 3 -2 d s 1091 1395 m 4 -2 d s 1095 1393 m 2 -1 d s 1107 1385 m20 1107 1385 m20 1116 1379 m 2 -2 d s 1118 1377 m 3 -2 d s 1121 1375 m 3 -3 d s 1124 1372 m 4 -2 d s 1587 794 454 1247 C 2268 2268 0 0 C 1128 1370 m 3 -3 d s 1131 1367 m 3 -2 d s 1134 1365 m 4 -3 d s 1138 1362 m 3 -3 d s 1141 1359 m 3 -2 d s 1144 1357 m 2 -1 d s 1155 1349 m20 1155 1349 m20 1164 1342 m s 1164 1342 m 4 -2 d s 1168 1340 m 3 -2 d s 1171 1338 m 3 -2 d s 1174 1336 m 3 -1 d s 1177 1335 m 4 -2 d s 1181 1333 m 2 -2 d s 1193 1325 m20 1193 1325 m20 1203 1320 m 1 -1 d s 1204 1319 m 3 -1 d s 1207 1318 m 4 -1 d s 1211 1317 m 3 -2 d s 1214 1315 m 3 -1 d s 1217 1314 m 4 -2 d s 1221 1312 m 3 -1 d s 1234 1306 m20 1234 1306 m20 1245 1302 m 2 -1 d s 1247 1301 m 3 -1 d s 1250 1300 m 4 -1 d s 1254 1299 m 3 -1 d s 1257 1298 m 3 -1 d s 1260 1297 m 4 -1 d s 1264 1296 m 3 -1 d s 1277 1292 m20 1277 1292 m20 1288 1290 m 2 -1 d s 1290 1289 m 3 -1 d s 1293 1288 m 4 -1 d s 1297 1287 m 3 X s 1300 1287 m 3 -1 d s 1303 1286 m 4 -1 d s 1307 1285 m 3 -1 d s 1310 1284 m s 1322 1282 m20 1322 1282 m20 1333 1280 m s 1333 1280 m 4 -1 d s 1337 1279 m 3 X s 1340 1279 m 3 -1 d s 1343 1278 m 3 X s 1346 1278 m 4 -1 d s 1350 1277 m 3 X s 1353 1277 m 2 X s 1366 1275 m20 1366 1275 m20 1378 1273 m 2 X s 1380 1273 m 3 X s 1383 1273 m 3 -1 d s 1386 1272 m 4 X s 1390 1272 m 3 -1 d s 1393 1271 m 3 X s 1396 1271 m 3 -1 d s 1399 1270 m 1 X s 1411 1269 m20 1411 1269 m20 1423 1268 m s 1423 1268 m 3 -1 d s 1426 1267 m 3 X s 1429 1267 m 4 X s 1433 1267 m 3 -1 d s 1436 1266 m 3 X s 1439 1266 m 4 X s 1443 1266 m 2 -1 d s 1456 1264 m20 1456 1264 m20 1468 1264 m 1 -1 d s 1469 1263 m 3 X s 1472 1263 m 4 X s 1476 1263 m 3 X s 1479 1263 m 3 X s 1482 1263 m 4 -1 d s 1486 1262 m 3 X s 1489 1262 m 1 X s 1502 1262 m20 1502 1262 m20 1513 1261 m 2 X s 1515 1261 m 4 X s 1519 1261 m 3 X s 1522 1261 m 3 -1 d s 1525 1260 m 4 X s 1529 1260 m 3 X s 1532 1260 m 3 X s 1535 1260 m 1 X s 1547 1259 m20 1547 1259 m20 1558 1258 m s 1558 1258 m 4 X s 1562 1258 m 3 X s 1565 1258 m 3 X s 1568 1258 m 4 -1 d s 1572 1257 m 3 X s 1575 1257 m 3 X s 1578 1257 m 3 X s 1592 1257 m20 1592 1257 m20 1604 1256 m 1 X s 1605 1256 m 3 X s 1608 1256 m 4 X s 1612 1256 m 3 X s 1615 1256 m 3 X s 1618 1256 m 3 -1 d s 1621 1255 m 4 X s 1625 1255 m 1 X s 1638 1255 m20 1638 1255 m20 1649 1255 m 2 X s 1651 1255 m 4 X s 1655 1255 m 3 X s 1658 1255 m 3 X s 1661 1255 m 4 X s 1665 1255 m 3 X s 1668 1255 m 3 -1 d s 1671 1254 m 1 X s 1683 1254 m20 1683 1254 m20 1694 1254 m 4 -1 d s 1698 1253 m 3 X s 1701 1253 m 3 X s 1704 1253 m 4 X s 1708 1253 m 3 X s 1711 1253 m 3 X s 1714 1253 m 3 X s 1728 1253 m20 1728 1253 m20 1740 1252 m 1 X s 1741 1252 m 3 X s 1744 1252 m 3 X s 1747 1252 m 4 X s 1751 1252 m 3 X s 1754 1252 m 3 X s 1757 1252 m 4 X s 1761 1252 m 1 X s 1774 1252 m20 1774 1252 m20 1785 1252 m 2 X s 1787 1252 m 3 X s 1790 1252 m 4 X s 1794 1252 m 3 X s 1797 1252 m 3 X s 1587 794 454 1247 C 2268 2268 0 0 C 1800 1252 m 4 X s 1804 1252 m 3 X s 1807 1252 m 3 X s 1810 1252 m 4 X s 1814 1252 m 3 -1 d s 1817 1251 m 3 X s 1820 1251 m 3 X s 1834 1251 m20 1834 1251 m20 1846 1251 m 1 X s 1847 1251 m 3 X s 1850 1251 m 3 X s 1853 1251 m 4 X s 1857 1251 m 3 X s 1860 1251 m 3 X s 1863 1251 m 4 X s 1867 1251 m 1 X s 1880 1250 m20 1880 1250 m20 1891 1250 m 2 X s 1893 1250 m 3 X s 1896 1250 m 4 X s 1900 1250 m 3 X s 1903 1250 m 3 X s 1906 1250 m 4 X s 1910 1250 m 3 X s 1913 1250 m 1 X s 1925 1250 m20 1925 1250 m20 1936 1250 m 3 X s 1939 1250 m s 1939 1250 m 3 X s 1942 1250 m 1 X s 1943 1250 m 2 X s 1945 1250 m 1 X s 1946 1250 m 2 X s 1948 1250 m 1 X s 1949 1250 m 4 X s 1953 1250 m 3 X s 1956 1250 m 3 X s 1970 1249 m20 1970 1249 m20 1982 1249 m 1 X s 1983 1249 m 3 X s 1986 1249 m 3 X s 1989 1249 m 3 X s 1992 1249 m 4 X s 1996 1249 m 3 X s 1999 1249 m 3 X s 2002 1249 m 2 X s 2016 1249 m20 2016 1249 m20 2027 1249 m 2 X s 2029 1249 m 3 X s 2032 1249 m 4 X s 2036 1249 m 3 X s 2039 1249 m 2 -1 d s 1587 794 454 1247 C 2268 2268 0 0 C 1 lw 866 2041 m -11 Y s 866 2019 m -12 Y s 866 1996 m -11 Y s 866 1973 m -11 Y s 866 1950 m -11 Y s 866 1928 m -12 Y s 866 1905 m -11 Y s 866 1882 m -11 Y s 866 1860 m -12 Y s 866 1837 m -11 Y s 866 1814 m -11 Y s 866 1792 m -12 Y s 866 1769 m -11 Y s 866 1746 m -11 Y s 866 1724 m -12 Y s 866 1701 m -11 Y s 866 1678 m -11 Y s 866 1656 m -12 Y s 866 1633 m -11 Y s 866 1610 m -11 Y s 866 1588 m -12 Y s 866 1565 m -11 Y s 866 1542 m -11 Y s 866 1520 m -12 Y s 866 1497 m -11 Y s 866 1474 m -11 Y s 866 1452 m -12 Y s 866 1429 m -11 Y s 866 1406 m -11 Y s 866 1383 m -11 Y s 866 1361 m -12 Y s 866 1338 m -11 Y s 866 1315 m -11 Y s 866 1293 m -12 Y s 866 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1115 2041 m -11 Y s 1115 2019 m -12 Y s 1115 1996 m -11 Y s 1115 1973 m -11 Y s 1115 1950 m -11 Y s 1115 1928 m -12 Y s 1115 1905 m -11 Y s 1115 1882 m -11 Y s 1115 1860 m -12 Y s 1115 1837 m -11 Y s 1115 1814 m -11 Y s 1115 1792 m -12 Y s 1115 1769 m -11 Y s 1115 1746 m -11 Y s 1115 1724 m -12 Y s 1115 1701 m -11 Y s 1115 1678 m -11 Y s 1115 1656 m -12 Y s 1115 1633 m -11 Y s 1115 1610 m -11 Y s 1115 1588 m -12 Y s 1115 1565 m -11 Y s 1115 1542 m -11 Y s 1115 1520 m -12 Y s 1115 1497 m -11 Y s 1115 1474 m -11 Y s 1115 1452 m -12 Y s 1115 1429 m -11 Y s 1115 1406 m -11 Y s 1115 1383 m -11 Y s 1115 1361 m -12 Y s 1115 1338 m -11 Y s 1115 1315 m -11 Y s 1115 1293 m -12 Y s 1115 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1786 2041 m -11 Y s 1786 2019 m -12 Y s 1786 1996 m -11 Y s 1786 1973 m -11 Y s 1786 1950 m -11 Y s 1786 1928 m -12 Y s 1786 1905 m -11 Y s 1786 1882 m -11 Y s 1786 1860 m -12 Y s 1786 1837 m -11 Y s 1786 1814 m -11 Y s 1786 1792 m -12 Y s 1786 1769 m -11 Y s 1786 1746 m -11 Y s 1786 1724 m -12 Y s 1786 1701 m -11 Y s 1786 1678 m -11 Y s 1786 1656 m -12 Y s 1786 1633 m -11 Y s 1786 1610 m -11 Y s 1786 1588 m -12 Y s 1786 1565 m -11 Y s 1786 1542 m -11 Y s 1786 1520 m -12 Y s 1786 1497 m -11 Y s 1786 1474 m -11 Y s 1786 1452 m -12 Y s 1786 1429 m -11 Y s 1786 1406 m -11 Y s 1786 1383 m -11 Y s 1786 1361 m -12 Y s 1786 1338 m -11 Y s 1786 1315 m -11 Y s 1786 1293 m -12 Y s 1786 1270 m -11 Y s 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 652 1909 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (core) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 930 1909 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (CV) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 1208 1909 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (valence) show gr 1587 794 454 1247 C 2268 2268 0 0 C 1587 794 454 1247 C 2268 2268 0 0 C gsave 1843 1909 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (tail) show gr 1587 794 454 1247 C 2268 2268 0 0 C 454 1247 m 45 X s /w 2 def /w2 {w 2 div} def /w3 {w 3 div} def 522 1247 m20 522 1247 m20 544 1247 m 46 X s 612 1247 m20 612 1247 m20 635 1247 m 45 X s 703 1247 m20 703 1247 m20 726 1247 m 45 X s 794 1247 m20 794 1247 m20 816 1247 m 46 X s 885 1247 m20 885 1247 m20 907 1247 m 46 X s 975 1247 m20 975 1247 m20 998 1247 m 45 X s 1066 1247 m20 1066 1247 m20 1089 1247 m 45 X s 1157 1247 m20 1157 1247 m20 1179 1247 m 46 X s 1247 1247 m20 1247 1247 m20 1270 1247 m 45 X s 1338 1247 m20 1338 1247 m20 1361 1247 m 45 X s 1429 1247 m20 1429 1247 m20 1452 1247 m 45 X s 1520 1247 m20 1520 1247 m20 1542 1247 m 46 X s 1610 1247 m20 1610 1247 m20 1633 1247 m 45 X s 1701 1247 m20 1701 1247 m20 1724 1247 m 45 X s 1792 1247 m20 1792 1247 m20 1814 1247 m 46 X s 1882 1247 m20 1882 1247 m20 1905 1247 m 45 X s 1973 1247 m20 1973 1247 m20 1996 1247 m 45 X s 1587 794 454 1247 C NC 1587 794 454 227 bl 1587 794 454 227 C NC 454 227 m 794 Y s 488 227 m -34 X s 471 259 m -17 X s 471 290 m -17 X s 471 322 m -17 X s 471 354 m -17 X s 488 386 m -34 X s 471 417 m -17 X s 471 449 m -17 X s 471 481 m -17 X s 471 513 m -17 X s 488 544 m -34 X s 471 576 m -17 X s 471 608 m -17 X s 471 640 m -17 X s 471 671 m -17 X s 488 703 m -34 X s 471 735 m -17 X s 471 767 m -17 X s 471 798 m -17 X s 471 830 m -17 X s 488 862 m -34 X s 471 894 m -17 X s 471 925 m -17 X s 471 957 m -17 X s 471 989 m -17 X s 488 1021 m -34 X s /xs 0 def (0) /Times-Roman 68 stwn gsave 408 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (10) /Times-Roman 68 stwn gsave 408 363 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (10) show gr /xs 0 def (20) /Times-Roman 68 stwn gsave 408 522 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (20) show gr /xs 0 def (30) /Times-Roman 68 stwn gsave 408 680 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (30) show gr /xs 0 def (40) /Times-Roman 68 stwn gsave 408 839 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (40) show gr /xs 0 def (50) /Times-Roman 68 stwn gsave 408 998 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (50) show gr 454 227 m 1587 X s 454 261 m -34 Y s 533 244 m -17 Y s 612 244 m -17 Y s 692 244 m -17 Y s 771 244 m -17 Y s 851 261 m -34 Y s 930 244 m -17 Y s 1009 244 m -17 Y s 1089 244 m -17 Y s 1168 244 m -17 Y s 1247 261 m -34 Y s 1327 244 m -17 Y s 1406 244 m -17 Y s 1486 244 m -17 Y s 1565 244 m -17 Y s 1644 261 m -34 Y s 1724 244 m -17 Y s 1803 244 m -17 Y s 1882 244 m -17 Y s 1962 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (0.5) /Times-Roman 68 stwn gsave 851 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.5) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 1247 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (1.5) /Times-Roman 68 stwn gsave 1644 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.5) show gr /xs 0 def (2) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (2) show gr 1587 794 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 96 941 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (g) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (3) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (\(s\)) show gr 1587 794 454 227 C 3 lw 457 236 m 7 2 d 6 3 d 7 4 d 6 3 d 7 5 d 7 4 d 6 5 d 7 5 d 7 5 d 6 5 d 7 6 d 6 5 d 7 5 d 7 5 d 6 5 d 7 6 d 7 6 d 6 7 d 7 7 d 6 7 d 7 9 d 7 10 d 6 12 d 6 12 d 1 2 d 5 13 d 2 6 d 4 14 d 2 10 d 4 16 d 3 15 d 3 19 d 3 21 d 4 24 d 3 27 d 3 30 d 4 32 d 4 42 d 2 30 d 7 79 d 6 68 d 1 11 d 4 44 d 2 24 d 3 26 d 2 17 d 2 9 d 2 14 d 2 11 d 2 7 d 3 7 d 3 5 d 1 2 d 3 1 d 4 -1 d 3 -4 d 3 -5 d 7 -14 d 7 -16 d 6 -16 d 7 -16 d 6 -16 d 7 -16 d 7 -14 d 6 -14 d 7 -12 d 7 -11 d 6 -10 d 7 -9 d 6 -8 d 7 -8 d 7 -5 d 6 -5 d 7 -3 d 7 -3 d 6 -3 d 7 -4 d 6 -5 d 7 -6 d 7 -7 d 6 -8 d 7 -9 d 7 -8 d 6 -8 d 7 -7 d 6 -7 d 7 -5 d 7 -6 d 6 -5 d 7 -4 d 7 -4 d 6 -4 d 7 -4 d 6 -3 d 7 -4 d 7 -3 d 6 -3 d 7 -4 d 7 -4 d 6 -4 d 7 -4 d 7 -4 d 6 -5 d 7 -4 d 6 -5 d 7 -5 d 7 -4 d 6 -4 d 7 -4 d 7 -4 d 6 -3 d 7 -2 d 6 -2 d 14 X 6 2 d 7 2 d 7 4 d 6 6 d 7 6 d 6 8 d 7 7 d 7 5 d 4 2 d 2 X 4 -2 d 3 -3 d 3 -5 d 4 -8 d 3 -11 d 3 -12 d 3 -14 d 4 -16 d 6 -34 d 7 -34 d 5 -26 d 2 -5 d 4 -19 d 2 -7 d 5 -16 d 2 -5 d 5 -14 d 2 -3 d 6 -14 d 7 -11 d 6 -9 d 7 -8 d 7 -6 d 6 -6 d 7 -4 d 7 -4 d 6 -3 d 7 -3 d 6 -3 d 7 -2 d 7 -3 d 6 -2 d 7 -2 d 7 -2 d 6 -1 d 7 -2 d 6 -2 d 7 -1 d 7 -1 d 6 -1 d 7 -1 d 7 -1 d 6 X 7 -1 d 26 X 7 1 d 7 1 d 6 1 d 7 1 d 6 2 d 7 2 d 7 3 d 6 2 d 7 1 d 7 1 d 6 X 7 -1 d 6 -1 d 7 -2 d 7 -2 d 6 -3 d 7 -3 d 7 -4 d 6 -4 d 7 -5 d 6 -6 d 7 -6 d 7 -7 d 6 -8 d 7 -7 d 7 -8 d 6 -7 d 7 -7 d 6 -6 d 7 -5 d 7 -5 d 6 -5 d 7 -4 d 7 -4 d 6 -3 d 7 -3 d 6 -2 d 7 -2 d 7 -1 d 6 -1 d 14 X 6 -1 d 93 X s 1802 227 m 1345 X s 3147 227 m 1272 X s 2268 2268 0 0 C 457 236 m 7 2 d s 464 238 m 6 3 d s 470 241 m 7 4 d s 477 245 m s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 487 251 m20 487 251 m20 497 257 m 6 5 d s 503 262 m 7 5 d s 510 267 m 5 4 d s 524 278 m20 524 278 m20 533 285 m 3 2 d s 536 287 m 7 5 d s 543 292 m 7 5 d s 550 297 m 1 1 d s 560 305 m20 560 305 m20 568 313 m 2 1 d s 570 314 m 6 6 d s 576 320 m 7 6 d s 583 326 m 2 2 d s 593 336 m20 593 336 m20 601 345 m 2 2 d s 603 347 m 6 7 d s 609 354 m 6 8 d s 622 371 m20 622 371 m20 628 381 m 1 Y s 628 382 m 1 1 d s 629 383 m 7 12 d s 636 395 m 3 6 d s 644 411 m20 644 411 m20 649 421 m 7 12 d s 656 433 m 4 8 d s 666 450 m20 666 450 m20 672 460 m 2 2 d s 674 462 m 2 2 d s 676 464 m 4 5 d s 680 469 m 2 2 d s 682 471 m 5 4 d s 687 475 m 1 1 d s 698 482 m20 698 482 m20 708 486 m 1 X s 709 486 m 6 2 d s 715 488 m 6 1 d s 721 489 m 1 X s 722 489 m 5 X s 727 489 m 2 X s 729 489 m 1 -1 d s 741 484 m20 741 484 m20 750 477 m 5 -6 d s 755 471 m 7 -8 d s 762 463 m 3 -3 d s 772 451 m20 772 451 m20 779 442 m 3 -2 d s 782 440 m 6 -7 d s 788 433 m 7 -7 d s 795 426 m s 803 418 m20 803 418 m20 812 411 m 3 -2 d s 815 409 m 6 -5 d s 821 404 m 7 -4 d s 828 400 m 3 -1 d s 841 393 m20 841 393 m20 851 388 m 3 -2 d s 854 386 m 7 -4 d s 861 382 m 7 -4 d s 868 378 m 3 -1 d s 881 371 m20 881 371 m20 891 366 m 3 -2 d s 894 364 m 7 -3 d s 901 361 m 6 -3 d s 907 358 m 4 -2 d s 922 352 m20 922 352 m20 932 347 m 2 X s 934 347 m 7 -3 d s 941 344 m 6 -3 d s 947 341 m 6 -2 d s 964 335 m20 964 335 m20 974 331 m 6 -1 d s 980 330 m 7 -2 d s 987 328 m 7 -2 d s 994 326 m 2 -1 d s 1007 322 m20 1007 322 m20 1018 319 m 2 -1 d s 1020 318 m 7 -1 d s 1027 317 m 6 -2 d s 1033 315 m 7 -2 d s 1051 310 m20 1051 310 m20 1062 308 m 5 -2 d s 1067 306 m 6 -1 d s 1073 305 m 7 -1 d s 1080 304 m 4 -1 d s 1095 301 m20 1095 301 m20 1107 300 m 6 -1 d s 1113 299 m 7 -1 d s 1120 298 m 6 X s 1126 298 m 3 X s 1141 297 m20 1141 297 m20 1152 296 m 1 X s 1153 296 m 6 X s 1159 296 m 7 X s 1166 296 m 7 X s 1173 296 m 2 X s 1186 295 m20 1186 295 m20 1197 294 m 2 -1 d s 1199 293 m 7 -1 d s 1206 292 m 6 -3 d s 1212 289 m 6 -3 d s 1229 281 m20 1229 281 m20 1238 276 m 1 -1 d s 1239 275 m 6 -3 d s 1245 272 m 7 -4 d s 1252 268 m 7 -3 d s 1269 261 m20 1269 261 m20 1280 257 m 5 -1 d s 1285 256 m 7 -2 d s 1292 254 m 6 -1 d s 1298 253 m 4 -1 d s 1313 250 m20 1313 250 m20 1324 248 m 1 -1 d s 1325 247 m 7 -1 d s 1332 246 m 6 -1 d s 1338 245 m 7 -1 d s 1345 244 m 1 -1 d s 1358 241 m20 1358 241 m20 1369 240 m 2 -1 d s 1371 239 m 7 X s 1378 239 m 7 -1 d s 1385 238 m 6 -1 d s 1391 237 m s 1403 236 m20 1403 236 m20 1414 235 m 4 -1 d s 1418 234 m 6 -1 d s 1424 233 m 7 X s 1431 233 m 5 -1 d s 1448 231 m20 1448 231 m20 1459 230 m 5 X s 1464 230 m 7 X s 1471 230 m 6 -1 d s 1477 229 m 5 X s 1493 228 m20 1493 228 m20 1504 228 m 6 X s 1510 228 m 7 -1 d s 1517 227 m 7 X s 1524 227 m 3 X s 1538 227 m20 1538 227 m20 1550 227 m s 1550 227 m 7 X s 1557 227 m 6 X s 1563 227 m 7 X s 1570 227 m 2 X s 1584 227 m20 1584 227 m20 1595 227 m 2 X s 1597 227 m 6 X s 1603 227 m 7 X s 1610 227 m 6 X s 1616 227 m 2 X s 1629 227 m20 1629 227 m20 1640 227 m 3 X s 1643 227 m 7 X s 1650 227 m 6 X s 1656 227 m 7 X s 1663 227 m s 1674 227 m20 1674 227 m20 1686 227 m 3 X s 1689 227 m 7 X s 1696 227 m 7 X s 1703 227 m 5 X s 1720 227 m20 1720 227 m20 1731 227 m 5 X s 1736 227 m 6 X s 1742 227 m 7 X s 1749 227 m 5 X s 1765 227 m20 1765 227 m20 1776 227 m 6 X s 1782 227 m 7 X s 1789 227 m 6 X s 1795 227 m 4 X s 1587 794 454 227 C 2268 2268 0 0 C 1802 227 m 7 X s 1809 227 m 6 X s 1815 227 m 7 X s 1822 227 m 3 X s 1836 227 m20 1836 227 m20 1847 227 m 1 X s 1848 227 m 7 X s 1855 227 m 7 X s 1862 227 m 6 X s 1868 227 m 2 X s 1881 227 m20 1881 227 m20 1893 227 m 2 X s 1895 227 m 6 X s 1901 227 m 7 X s 1908 227 m 7 X s 1915 227 m s 1927 227 m20 1927 227 m20 1938 227 m 3 X s 1941 227 m 7 X s 1948 227 m 6 X s 1954 227 m 7 X s 1972 227 m20 1972 227 m20 1983 227 m 5 X s 1988 227 m 6 X s 1994 227 m 7 X s 2001 227 m 5 X s 2017 227 m20 2017 227 m20 2029 227 m 5 X s 2034 227 m 7 X s 2041 227 m s 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C 1 lw 1579 227 m 11 Y s 1579 249 m 12 Y s 1579 272 m 12 Y s 1579 295 m 11 Y s 1579 318 m 11 Y s 1579 340 m 12 Y s 1579 363 m 11 Y s 1579 386 m 11 Y s 1579 408 m 12 Y s 1579 431 m 11 Y s 1579 454 m 11 Y s 1579 476 m 12 Y s 1579 499 m 11 Y s 1579 522 m 11 Y s 1579 544 m 12 Y s 1579 567 m 11 Y s 1579 590 m 11 Y s 1579 612 m 12 Y s 1579 635 m 11 Y s 1579 658 m 11 Y s 1579 680 m 12 Y s 1579 703 m 11 Y s 1579 726 m 11 Y s 1579 748 m 12 Y s 1579 771 m 11 Y s 1579 794 m 11 Y s 1579 816 m 12 Y s 1579 839 m 11 Y s 1579 862 m 11 Y s 1579 885 m 11 Y s 1579 907 m 12 Y s 1579 930 m 11 Y s 1579 953 m 11 Y s 1579 975 m 12 Y s 1579 998 m 11 Y s 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 930 889 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (combined) show gr 1587 794 454 227 C 2268 2268 0 0 C 1587 794 454 227 C 2268 2268 0 0 C gsave 1843 889 t 0 r 0 0 m /Times-Roman findfont 60 sf 0 0 m (tail) show gr 1587 794 454 227 C 2268 2268 0 0 C 454 227 m 45 X s /w 2 def /w2 {w 2 div} def /w3 {w 3 div} def 522 227 m20 522 227 m20 544 227 m 46 X s 612 227 m20 612 227 m20 635 227 m 45 X s 703 227 m20 703 227 m20 726 227 m 45 X s 794 227 m20 794 227 m20 816 227 m 46 X s 885 227 m20 885 227 m20 907 227 m 46 X s 975 227 m20 975 227 m20 998 227 m 45 X s 1066 227 m20 1066 227 m20 1089 227 m 45 X s 1157 227 m20 1157 227 m20 1179 227 m 46 X s 1247 227 m20 1247 227 m20 1270 227 m 45 X s 1338 227 m20 1338 227 m20 1361 227 m 45 X s 1429 227 m20 1429 227 m20 1452 227 m 45 X s 1520 227 m20 1520 227 m20 1542 227 m 46 X s 1610 227 m20 1610 227 m20 1633 227 m 45 X s 1701 227 m20 1701 227 m20 1724 227 m 45 X s 1792 227 m20 1792 227 m20 1814 227 m 46 X s 1882 227 m20 1882 227 m20 1905 227 m 45 X s 1973 227 m20 1973 227 m20 1996 227 m 45 X s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 2041 227 m cl s 2019 227 m20 2019 227 m20 1587 794 454 227 C gr gr showpage end %%EndDocument @endspecial 555 4444 a FE(Figure)36 b(3.3.7:)51 b FC(g)1233 4458 y Fz(1)1276 4444 y FC(\204r)1368 4458 y FB(s)1406 4444 y FC(\205)36 b FE(and)g FC(g)1753 4458 y Fz(3)1796 4444 y FC(\204s)6 b(\205)34 b FE(distribution)h(functions)g(for)g(bulk) h(Si)f(in)h(the)555 4564 y(diamond)24 b(structure)h(at)g(the)g (experimental)g(lattice)h(parameter.)38 b(Dash-dot)26 b(lines)555 4685 y(show)e(the)g(distribution)e(functions)h(without)h (the)g(contribution)g(from)f(core)h(elec-)555 4805 y(trons.)2118 5640 y(41)p eop %%Page: 42 50 42 49 bop -41 275 a Fw(Chapter)29 b(3.)e(Distributions)h(of)f(density)i (parameters)p -41 315 3238 4 v 1522 5640 a FE(42)p eop %%Page: 43 51 43 50 bop 555 1242 a Fy(Chapter)59 b(4)555 1659 y(Averages)g(of)f (density)g(parameters)555 2113 y FE(The)38 b(distribution)d(functions)i (from)g(Chapter)h(3)e(yield)i(information)e(about)i Fj(all)555 2233 y FE(values)26 b(of)f(the)h(variable)g(being)f(analysed.)38 b(They)26 b(also)g(give)f(us)g(an)h(estimation)g(of)555 2354 y(the)k(ranges)f(of)f(density)g(parameters)i FC(r)2128 2368 y FB(s)2166 2354 y FE(,)f FC(\020)7 b FE(,)28 b(and)h FC(s)k FE(in)28 b(real)i(electronic)f(systems.)555 2474 y(Unfortunately,)f(the)e(distribution)f(functions)h(are)h(not)f (quantitative)i(enough)e(to)555 2595 y(answer)31 b(clearly)g(the)f (question)g(why)g(and)g(how)f(the)h(nonlocal)h(GGA)f(corrections)555 2715 y(to)f(the)g(exchange-correlation)h(energy)e(in\257uence)g(the)h (calculated)h(physical)e(ob-)555 2835 y(servables.)702 2958 y(In)j(this)g(chapter)i(we)e(de\256ne)h(average)g(values)g(of)e FC(r)2728 2972 y FB(s)2767 2958 y FE(,)i FC(\020)7 b FE(,)32 b(and)f FC(s)36 b FE(for)31 b(any)h(elec-)555 3078 y(tronic)e(system,)g(which)f(summarise)h(\(roughly\))g(the)g (information)f(contained)h(in)555 3198 y(the)h(distribution)d (functions.)41 b(The)30 b(average)h(values)f FA(h)p FC(r)2774 3212 y FB(s)2812 3198 y FA(i)p FE(,)f FA(hj)p FC(\020)7 b FA(ji)p FE(,)28 b(and)i FA(h)p FC(s)6 b FA(i)28 b FE(allow)555 3319 y(us)i(to)g(explain)f(why)g(GGA)h(typically)h(gives)e(longer)h (bond)f(lengths,)h(lower)f(atom-)555 3439 y(isation)38 b(energies,)i(and)f(higher)e(energy)i(barriers)f(at)h(transition)e (states.)69 b(They)555 3559 y(also)25 b(allow)g(us)g(to)f(explain)h (why)f(GGA)h(unexpectedly)g(but)g(correctly)h(shrinks)d(the)555 3680 y(bond)28 b(lengths)h(in)f(the)g(H)1536 3694 y Fz(2)1608 3680 y FE(molecule)h(and)f(at)i(the)e(H)2600 3694 y Fz(3)2672 3680 y FE(transition)g(state)i(point.)555 4047 y FD(4.1)130 b(De\256nition)41 b(of)f(density)h(averages)555 4285 y FE(The)29 b(energy-weighted)g(averages)g FA(h)p FC(r)2036 4299 y FB(s)2074 4285 y FA(i)p FE(,)e FA(hj)p FC(\020)7 b FA(ji)p FE(,)27 b(and)h FA(h)p FC(s)6 b FA(i)27 b FE(are)i(de\256ned) f(by:)1489 4563 y FC(")1537 4577 y FB(x)1591 4563 y FC(\204)p FA(h)p FC(r)1727 4577 y FB(s)1764 4563 y FA(i)p FC(\205)82 b FA(\203)2100 4417 y Fu(R)2166 4498 y FC(d)p Fx(r)15 b FC(\032)20 b(")2419 4512 y FB(x)2473 4498 y FC(\204r)2565 4512 y FB(s)2603 4498 y FC(\205)p 2100 4536 546 4 v 2245 4550 a Fu(R)2311 4630 y FC(d)p Fx(r)15 b FC(\032)1933 4834 y FA(\203)2100 4767 y FC(E)2164 4733 y FB(LS)5 b(D)2159 4791 y(x)2307 4767 y FC(\206\032)t(=)p FE(2)p FC(;)15 b(\032)t(=)p FE(2)p FC(\207)p 2100 4806 676 4 v 2396 4900 a(N)2811 4834 y(;)627 b FE(\(4.1.1a\))1333 5080 y FC(F)1387 5094 y FB(x)1440 5080 y FC(\204)p FA(hj)p FC(\020)7 b FA(ji)p FC(;)15 b FE(0)p FC(\205)81 b FA(\203)2100 4935 y Fu(R)2166 5015 y FC(d)p Fx(r)15 b FC(\032)20 b(")2419 5029 y FB(x)2473 5015 y FC(\204r)2565 5029 y FB(s)2603 5015 y FC(\205F)2700 5029 y FB(x)2752 5015 y FC(\204\020)7 b(;)15 b FE(0)p FC(\205)p 2100 5053 906 4 v 2280 5067 a Fu(R)2346 5147 y FC(d)p Fx(r)h FC(\032)j(")2599 5161 y FB(x)2653 5147 y FC(\204r)2745 5161 y FB(s)2783 5147 y FC(\205)1933 5351 y FA(\203)2171 5284 y FC(E)2235 5250 y FB(LS)5 b(D)2230 5308 y(x)2378 5284 y FC(\206\032)2482 5298 y Ft(")2520 5284 y FC(;)15 b(\032)2623 5298 y Ft(#)2662 5284 y FC(\207)p 2100 5323 676 4 v 2100 5423 a(E)2164 5383 y FB(LS)5 b(D)2159 5434 y(x)2307 5423 y FC(\206\032)t(=)p 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(-0.2) /Times-Roman 68 stwn gsave 408 567 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-0.2) show gr /xs 0 def (-0.15) /Times-Roman 68 stwn gsave 408 930 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-0.15) show gr /xs 0 def (-0.1) /Times-Roman 68 stwn gsave 408 1293 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-0.1) show gr /xs 0 def (-0.05) /Times-Roman 68 stwn gsave 408 1656 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (-0.05) show gr /xs 0 def (0) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr 454 227 m 1587 X s 454 261 m -34 Y s 533 244 m -17 Y s 612 244 m -17 Y s 692 244 m -17 Y s 771 244 m -17 Y s 851 261 m -34 Y s 930 244 m -17 Y s 1009 244 m -17 Y s 1089 244 m -17 Y s 1168 244 m -17 Y s 1247 261 m -34 Y s 1327 244 m -17 Y s 1406 244 m -17 Y s 1486 244 m -17 Y s 1565 244 m -17 Y s 1644 261 m -34 Y s 1724 244 m -17 Y s 1803 244 m -17 Y s 1882 244 m -17 Y s 1962 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (0.25) /Times-Roman 68 stwn gsave 851 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.25) show gr /xs 0 def (0.5) /Times-Roman 68 stwn gsave 1247 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.5) show gr /xs 0 def (0.75) /Times-Roman 68 stwn gsave 1644 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.75) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 96 1860 t 0 r 0 0 m /Symbol findfont 86 sf 0 0 m (D) show gr 1587 1814 454 227 C 3 lw 454 2041 m 111 X 16 -1 d 31 X 16 -1 d 16 -1 d 16 -1 d 16 -2 d 16 -1 d 16 -2 d 16 -3 d 15 -3 d 16 -3 d 16 -3 d 16 -4 d 16 -5 d 16 -5 d 16 -5 d 16 -6 d 15 -6 d 16 -7 d 16 -7 d 16 -8 d 16 -8 d 16 -9 d 16 -10 d 16 -10 d 15 -10 d 16 -11 d 16 -12 d 16 -12 d 16 -13 d 16 -13 d 16 -14 d 16 -14 d 15 -15 d 16 -15 d 16 -16 d 16 -16 d 16 -17 d 16 -17 d 16 -18 d 16 -18 d 15 -19 d 16 -19 d 16 -20 d 16 -20 d 16 -21 d 16 -21 d 16 -22 d 16 -21 d 15 -23 d 16 -23 d 16 -23 d 16 -23 d 16 -24 d 16 -25 d 16 -24 d 16 -25 d 15 -26 d 16 -26 d 16 -26 d 16 -26 d 16 -27 d 16 -27 d 16 -28 d 16 -27 d 16 -28 d 15 -29 d 16 -28 d 16 -29 d 16 -29 d 16 -30 d 16 -29 d 16 -30 d 16 -30 d 15 -31 d 16 -30 d 16 -31 d 16 -31 d 16 -31 d 16 -32 d 16 -31 d 16 -32 d 15 -32 d 16 -32 d 16 -33 d 16 -32 d 16 -33 d 16 -32 d 16 -33 d 16 -33 d 15 -33 d s 454 2041 m 174 X 16 -1 d 32 X 16 -1 d 16 X 16 -1 d 15 -1 d 16 -1 d 16 -1 d 16 -1 d 16 -1 d 16 -2 d 16 -1 d 16 -2 d 15 -2 d 16 -2 d 16 -2 d 16 -3 d 16 -3 d 16 -3 d 16 -3 d 16 -3 d 15 -4 d 16 -4 d 16 -4 d 16 -4 d 16 -5 d 16 -4 d 16 -5 d 16 -5 d 15 -6 d 16 -6 d 16 -6 d 16 -6 d 16 -6 d 16 -7 d 16 -7 d 16 -7 d 15 -7 d 16 -8 d 16 -7 d 16 -8 d 16 -9 d 16 -8 d 16 -9 d 16 -9 d 15 -9 d 16 -9 d 16 -10 d 16 -10 d 16 -10 d 16 -10 d 16 -10 d 16 -11 d 15 -11 d 16 -11 d 16 -11 d 16 -11 d 16 -12 d 16 -11 d 16 -12 d 16 -12 d 16 -12 d 15 -13 d 16 -12 d 16 -13 d 16 -13 d 16 -13 d 16 -13 d 16 -13 d 16 -14 d 15 -13 d 16 -14 d 16 -14 d 16 -14 d 16 -14 d 16 -14 d 16 -14 d 16 -15 d 15 -14 d 16 -15 d 16 -15 d 16 -14 d 16 -15 d 16 -15 d 16 -15 d 16 -16 d 15 -15 d s 454 2041 m 254 X 16 -1 d 47 X 16 -1 d 32 X 16 -1 d 16 X 15 -1 d 16 X 16 -1 d 16 -1 d 16 X 16 -1 d 16 -1 d 16 -1 d 15 -1 d 16 -1 d 16 -1 d 16 -2 d 16 -1 d 16 -2 d 16 -1 d 16 -2 d 15 -1 d 16 -2 d 16 -2 d 16 -2 d 16 -2 d 16 -2 d 16 -3 d 16 -2 d 15 -3 d 16 -2 d 16 -3 d 16 -3 d 16 -2 d 16 -3 d 16 -4 d 16 -3 d 15 -3 d 16 -3 d 16 -4 d 16 -3 d 16 -4 d 16 -4 d 16 -4 d 16 -4 d 15 -4 d 16 -4 d 16 -4 d 16 -4 d 16 -5 d 16 -4 d 16 -5 d 16 -4 d 16 -5 d 15 -5 d 16 -5 d 16 -5 d 16 -5 d 16 -5 d 16 -6 d 16 -5 d 16 -5 d 15 -6 d 16 -6 d 16 -5 d 16 -6 d 16 -6 d 16 -6 d 16 -6 d 16 -6 d 15 -6 d 16 -6 d 16 -6 d 16 -6 d 16 -7 d 16 -6 d 16 -6 d 16 -7 d 15 -6 d s 454 2041 m 381 X 16 -1 d 95 X 16 -1 d 47 X 16 -1 d 32 X 16 -1 d 16 X 16 -1 d 31 X 16 -1 d 16 X 16 -1 d 16 -1 d 16 X 16 -1 d 15 X 16 -1 d 16 -1 d 16 -1 d 16 -1 d 16 X 16 -1 d 16 -1 d 15 -1 d 16 -1 d 16 -1 d 16 -1 d 16 -1 d 16 -1 d 16 -2 d 16 -1 d 15 -1 d 16 -1 d 16 -2 d 16 -1 d 16 -2 d 16 -1 d 16 -1 d 16 -2 d 16 -2 d 15 -1 d 16 -2 d 16 -2 d 16 -1 d 16 -2 d 16 -2 d 16 -2 d 16 -2 d 15 -1 d 16 -2 d 16 -2 d 16 -2 d 16 -2 d 16 -3 d 16 -2 d 16 -2 d 15 -2 d 16 -2 d 16 -3 d 16 -2 d 16 -2 d 16 -3 d 16 -2 d 16 -2 d 15 -3 d s 2268 2268 0 0 C 454 2041 m 16 X s 470 2041 m 6 X s 499 2041 m 2 X s 501 2041 m 16 X s 517 2041 m 5 X s 544 2041 m 5 X s 549 2041 m 16 X s 565 2041 m 2 X s 590 2040 m 7 X s 597 2040 m 15 -1 d s 635 2038 m 9 -1 d s 644 2037 m 14 -1 d s 680 2034 m 12 -2 d s 692 2032 m 11 -1 d s 725 2027 m 14 -3 d s 739 2024 m 8 -2 d s 769 2017 m 2 X s 771 2017 m 16 -5 d s 787 2012 m 4 -1 d s 813 2004 m 6 -1 d s 819 2003 m 15 -6 d s 855 1989 m 11 -5 d s 866 1984 m 10 -4 d s 897 1970 m 1 X s 898 1970 m 16 -8 d s 914 1962 m 3 -2 d s 937 1949 m 9 -4 d s 946 1945 m 11 -7 d s 976 1926 m 2 -1 d s 978 1925 m 15 -10 d s 993 1915 m 2 -1 d s 1014 1901 m 11 -8 d s 1025 1893 m 7 -5 d s 1050 1874 m 7 -5 d s 1057 1869 m 11 -9 d s 1086 1846 m 3 -3 d s 1089 1843 m 14 -12 d s 1120 1816 m -1 Y s 1120 1815 m 16 -14 d s 1136 1801 m 1 X s 1153 1785 m 15 -15 d s 1168 1770 m 1 -1 d s 1185 1753 m 15 -15 d s 1200 1738 m 1 -1 d s 1217 1720 m 15 -16 d s 1232 1704 m s 1247 1687 m s 1247 1687 m 15 -17 d s 1277 1653 m 2 -3 d s 1279 1650 m 13 -15 d s 1306 1618 m 5 -6 d s 1311 1612 m 9 -12 d s 1335 1583 m 8 -11 d s 1343 1572 m 6 -7 d s 1362 1547 m 12 -16 d s 1374 1531 m 2 -2 d s 1390 1511 m -1 Y s 1390 1510 m 13 -18 d s 1417 1474 m 5 -8 d s 1422 1466 m 8 -11 d s 1443 1437 m 11 -16 d s 1454 1421 m 2 -3 d s 1469 1400 m 1 -2 d s 1470 1398 m 11 -17 d s 1494 1362 m 7 -11 d s 1501 1351 m 6 -8 d s 1519 1324 m 12 -19 d s 1544 1286 m 5 -8 d s 1549 1278 m 7 -11 d s 1568 1248 m 12 -19 d s 1592 1209 m 5 -8 d s 1597 1201 m 7 -11 d s 1615 1170 m 12 -19 d s 1639 1132 m 5 -10 d s 1644 1122 m 6 -10 d s 1662 1092 m 11 -19 d s 1685 1053 m 7 -13 d s 1692 1040 m 4 -6 d s 1707 1014 m 1 -1 d s 1708 1013 m 10 -19 d s 1729 974 m 11 -18 d s 1740 956 m -1 Y s 1751 935 m 5 -8 d s 1756 927 m 6 -12 d s 1773 895 m 11 -20 d s 1795 855 m 8 -15 d s 1803 840 m 3 -5 d s 1816 815 m 3 -5 d s 1819 810 m 8 -15 d s 1838 775 m 10 -20 d s 1859 735 m 8 -15 d s 1867 720 m 2 -5 d s 1880 695 m 3 -5 d s 1883 690 m 7 -15 d s 1901 654 m 10 -20 d s 1921 614 m 9 -17 d s 1930 597 m 2 -3 d s 1942 574 m 4 -9 d s 1946 565 m 6 -12 d s 1962 533 m 10 -20 d s 1982 493 m 11 -21 d s 2003 452 m 7 -14 d s 2010 438 m 3 -6 d s 2023 411 m 2 -6 d s 1587 1814 454 227 C 2268 2268 0 0 C 454 2041 m 16 X s 470 2041 m 6 X s 499 2041 m 2 X s 501 2041 m 16 X s 517 2041 m 5 X s 544 2041 m 5 X s 549 2041 m 16 X s 565 2041 m 2 X s 590 2041 m 7 X s 597 2041 m 15 X s 635 2040 m 9 X s 644 2040 m 14 X s 680 2039 m 12 X s 692 2039 m 11 -1 d s 726 2037 m 13 -1 d s 739 2036 m 9 X s 771 2034 m s 771 2034 m 16 -1 d s 787 2033 m 7 -1 d s 816 2030 m 3 -1 d s 819 2029 m 16 -2 d s 835 2027 m 4 X s 861 2024 m 5 -1 d s 866 2023 m 16 -2 d s 882 2021 m 2 -1 d s 906 2017 m 8 -2 d s 914 2015 m 14 -3 d s 950 2008 m 12 -3 d s 962 2005 m 11 -2 d s 995 1997 m 14 -4 d s 1009 1993 m 7 -2 d s 1038 1985 m 3 -1 d s 1041 1984 m 16 -4 d s 1057 1980 m 3 -1 d s 1082 1972 m 7 -3 d s 1089 1969 m 14 -5 d s 1124 1957 m 12 -5 d s 1136 1952 m 10 -3 d s 1167 1940 m 1 -1 d s 1168 1939 m 16 -6 d s 1184 1933 m 4 -2 d s 1208 1922 m 8 -3 d s 1216 1919 m 13 -6 d s 1249 1903 m 14 -7 d s 1263 1896 m 7 -3 d s 1290 1883 m 5 -3 d s 1295 1880 m 15 -8 d s 1330 1861 m 13 -7 d s 1343 1854 m 7 -4 d s 1369 1839 m 5 -3 d s 1374 1836 m 15 -9 d s 1408 1816 m 14 -9 d s 1422 1807 m 6 -3 d s 1447 1791 m 7 -4 d s 1454 1787 m 12 -8 d s 1485 1766 m 1 X s 1486 1766 m 15 -11 d s 1501 1755 m 2 -1 d s 1522 1741 m 11 -8 d s 1533 1733 m 7 -5 d s 1559 1714 m 6 -4 d s 1565 1710 m 12 -9 d s 1595 1687 m 2 -1 d s 1597 1686 m 16 -12 d s 1613 1674 m s 1631 1660 m 13 -11 d s 1644 1649 m 5 -3 d s 1667 1632 m 9 -8 d s 1676 1624 m 8 -7 d s 1702 1603 m 6 -5 d s 1708 1598 m 11 -9 d s 1737 1574 m 3 -2 d s 1740 1572 m 14 -13 d s 1771 1545 m -1 Y s 1771 1544 m 16 -13 d s 1787 1531 m 1 -1 d s 1805 1515 m 14 -12 d s 1819 1503 m 3 -3 d s 1839 1484 m 12 -10 d s 1851 1474 m 5 -5 d s 1873 1454 m 10 -9 d s 1883 1445 m 7 -6 d s 1906 1423 m 8 -7 d s 1914 1416 m 9 -8 d s 1939 1392 m 7 -6 d s 1946 1386 m 10 -10 d s 1972 1361 m 6 -6 d s 1978 1355 m 10 -10 d s 2005 1329 m 5 -5 d s 2010 1324 m 11 -11 d s 1587 1814 454 227 C 2268 2268 0 0 C 454 2041 m 16 X s 470 2041 m 6 X s 499 2041 m 2 X s 501 2041 m 16 X s 517 2041 m 5 X s 544 2041 m 5 X s 549 2041 m 16 X s 565 2041 m 2 X s 590 2041 m 7 X s 597 2041 m 15 X s 635 2041 m 9 X s 644 2041 m 14 X s 680 2041 m 12 X s 692 2041 m 11 -1 d s 726 2040 m 13 X s 739 2040 m 10 X s 771 2039 m 16 X s 787 2039 m 7 X s 817 2038 m 2 X s 819 2038 m 16 -1 d s 835 2037 m 4 X s 862 2036 m 4 X s 866 2036 m 16 -1 d s 882 2035 m 3 X s 907 2034 m 7 X s 914 2034 m 16 -1 d s 952 2031 m 10 -1 d s 962 2030 m 13 -1 d s 998 2027 m 11 -1 d s 1009 2026 m 11 -1 d s 1043 2023 m 14 -1 d s 1057 2022 m 8 -1 d s 1088 2018 m 1 X s 1089 2018 m 16 -2 d s 1105 2016 m 5 -1 d s 1133 2012 m 3 X s 1136 2012 m 16 -3 d s 1152 2009 m 3 X s 1178 2006 m 6 -1 d s 1184 2005 m 16 -3 d s 1200 2002 m s 1222 1998 m 10 -2 d s 1232 1996 m 13 -2 d s 1267 1990 m 12 -3 d s 1279 1987 m 10 -2 d s 1312 1981 m 15 -4 d s 1327 1977 m 7 -1 d s 1356 1971 m 3 -1 d s 1359 1970 m 15 -4 d s 1374 1966 m 4 X s 1400 1960 m 6 -1 d s 1406 1959 m 16 -4 d s 1444 1949 m 10 -3 d s 1454 1946 m 12 -3 d s 1487 1937 m 14 -4 d s 1501 1933 m 8 -3 d s 1531 1924 m 2 -1 d s 1533 1923 m 16 -5 d s 1549 1918 m 4 -1 d s 1574 1910 m 7 -2 d s 1581 1908 m 15 -5 d s 1617 1896 m 12 -4 d s 1629 1892 m 10 -3 d s 1660 1881 m 16 -5 d s 1676 1876 m 6 -2 d s 1703 1866 m 5 -2 d s 1708 1864 m 16 -6 d s 1724 1858 m s 1745 1850 m 11 -4 d s 1756 1846 m 11 -4 d s 1788 1834 m 15 -6 d s 1803 1828 m 6 -3 d s 1830 1817 m 5 -2 d s 1835 1815 m 16 -7 d s 1851 1808 m s 1872 1800 m 11 -5 d s 1883 1795 m 10 -4 d s 1914 1782 m s 1914 1782 m 16 -7 d s 1930 1775 m 4 -2 d s 1955 1764 m 7 -3 d s 1962 1761 m 14 -6 d s 1996 1745 m 14 -6 d s 2010 1739 m 7 -3 d s 1587 1814 454 227 C 2268 2268 0 0 C 454 2041 m 16 X s 470 2041 m 6 X s 499 2041 m 2 X s 501 2041 m 16 X s 517 2041 m 5 X s 544 2041 m 5 X s 549 2041 m 16 X s 565 2041 m 2 X s 590 2041 m 7 X s 597 2041 m 15 X s 635 2041 m 9 X s 644 2041 m 14 X s 680 2041 m 12 X s 692 2041 m 11 X s 726 2041 m 13 X s 739 2041 m 10 X s 771 2041 m 16 X s 787 2041 m 7 X s 817 2040 m 2 X s 819 2040 m 16 X s 835 2040 m 4 X s 862 2040 m 4 X s 866 2040 m 16 X s 882 2040 m 3 X s 907 2039 m 7 X s 914 2039 m 16 X s 953 2038 m 9 X s 962 2038 m 13 X s 998 2037 m 11 X s 1009 2037 m 12 X s 1043 2036 m 14 X s 1057 2036 m 9 -1 d s 1089 2035 m s 1089 2035 m 16 -1 d s 1105 2034 m 6 X s 1134 2033 m 2 X s 1136 2033 m 16 -1 d s 1152 2032 m 5 X s 1179 2030 m 5 X s 1184 2030 m 16 -1 d s 1200 2029 m 2 X s 1225 2028 m 7 X s 1232 2028 m 15 -1 d s 1270 2025 m 9 -1 d s 1279 2024 m 13 X s 1315 2022 m 12 -1 d s 1327 2021 m 11 -1 d s 1360 2018 m 14 -1 d s 1374 2017 m 9 -1 d s 1405 2014 m 1 X s 1406 2014 m 16 -1 d s 1422 2013 m 6 -1 d s 1451 2010 m 3 X s 1454 2010 m 16 -2 d s 1470 2008 m 3 X s 1496 2005 m 5 -1 d s 1501 2004 m 16 -1 d s 1517 2003 m 1 X s 1541 2000 m 8 -1 d s 1549 1999 m 14 -2 d s 1586 1994 m 11 -1 d s 1597 1993 m 11 -2 d s 1631 1988 m 13 -1 d s 1644 1987 m 9 -2 d s 1676 1982 m s 1676 1982 m 16 -2 d s 1692 1980 m 6 -1 d s 1721 1975 m 3 X s 1724 1975 m 16 -3 d s 1740 1972 m 3 X s 1765 1968 m 6 -1 d s 1771 1967 m 16 -2 d s 1787 1965 m 1 X s 1810 1961 m 9 -2 d s 1819 1959 m 13 -2 d s 1855 1953 m 12 -2 d s 1867 1951 m 10 -2 d s 1899 1945 m 15 -3 d s 1914 1942 m 8 -1 d s 1944 1937 m 2 -1 d s 1946 1936 m 16 -3 d s 1962 1933 m 4 X s 1989 1928 m 5 -1 d s 1994 1927 m 16 -3 d s 2010 1924 m 1 X s 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn (=0.5) /Times-Roman 86 stwn gsave 1994 1243 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=0.5) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn (=1.0) /Times-Roman 86 stwn gsave 1994 1678 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=1.0) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn (=2.0) /Times-Roman 86 stwn gsave 1994 1882 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=2.0) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (r) /Times-Roman 86 stwn (s) /Times-Roman 60 stwn (=0.25) /Times-Roman 86 stwn gsave 1978 336 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (r) show currentpoint pop 0 t /Times-Roman findfont 60 sf 0 -29 m (s) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=0.25) show gr 1587 1814 454 227 C [] 0 sd 692 1243 m 159 X s 2268 2268 0 0 C [] 0 sd 692 1149 m 22 X s 737 1149 m 23 X s 782 1149 m 23 X s 828 1149 m 22 X s 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 898 1243 t 0 r 0 0 m /Symbol findfont 86 sf 0 0 m (z) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=0) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 898 1149 t 0 r 0 0 m /Symbol findfont 86 sf 0 0 m (z) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (=1) show gr 1587 1814 454 227 C gr gr showpage end %%EndDocument @endspecial -41 3859 a FE(Figure)33 b(4.2.1:)46 b(GGA)33 b(contributions)g(to)g(the)h(exchange-correlation)h(energy)f(for)-41 3979 y(different)28 b(values)g(of)g FC(r)870 3993 y FB(s)937 3979 y FE(for)f(unpolarised)h(and)g(fully)g(polarised)g(case.)-41 4293 y(changes)h(and)e(insert)h(parameter)h(values)e(that)i(are)f(the)h (arithmetic)f(averages)h(of)-41 4413 y(the)g(initial)f(and)g(\256nal)h (state)h(values.)106 4549 y(An)20 b(immediate)h(application)f(is)g(to)h (atomisation)g(energies)f(of)g(molecules)h(and)-41 4669 y(solids.)37 b(The)25 b(atomisation)h(energy)h(\(a)f(positive)f (value\))h(is)f(de\256ned)h(as)g(the)g(differ-)-41 4789 y(ence)e(between)g(the)g(total)g(energy)g(of)f(the)g(molecule)h(\(or)g (total)g(energy)g(of)f(the)g(unit)-41 4910 y(cell)j(in)e(the)h (crystal\))h(and)f(the)g(total)h(energy)f(of)g(the)g(separated)h (atoms.)37 b(The)25 b(total)-41 5030 y(energy)41 b(includes)e(the)i (exchange-correlation)h(part,)h(which)d(is)f(approximated)-41 5150 y(either)24 b(by)g(LSD)g(or)g(GGA.)f(It)i(is)e(well)h(known)f (that)i(LSD)f(always)h(overestimates)g(the)-41 5271 y(atomisation)h (energy,)g(whereas)g(GGA)f(comes)g(much)g(nearer)h(to)g(the)f (experimen-)-41 5391 y(tal)30 b(value)e(\(see)h(for)f(example)h(Ref.)f (62\).)1522 5640 y(48)p eop %%Page: 49 57 49 56 bop 2568 275 a Fw(4.2.)27 b(Results)i(and)f(discussion)p 555 315 3238 4 v 639 3547 a @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 3685 @rwi @setspecial %%BeginDocument: fig/p.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 7F 7F BF B F DF DF EF EF F7 F7 FB FB FD FD FE FE 7F 7F BF BF DF DF EF EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 EF EF EF EF D7 D7 38 38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 EF EF EF EF EF EF 00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D 5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D FE FE 7D 7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF DD DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF F1 F1 EE EE 1F 1F FF FF > } image } if PT 17 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF > } image } if PT 18 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6 B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT 20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image } if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > } image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F > } image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55 > } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00 80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00 00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1 54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def gsave Xcurr Ycurr translate PT DP gr } for } for gr } def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1587 1814 454 227 bl 1587 1814 454 227 C NC 454 227 m 1814 Y s 488 227 m -34 X s 471 287 m -17 X s 471 348 m -17 X s 471 408 m -17 X s 471 469 m -17 X s 488 529 m -34 X s 471 590 m -17 X s 471 650 m -17 X s 471 711 m -17 X s 471 771 m -17 X s 488 832 m -34 X s 471 892 m -17 X s 471 953 m -17 X s 471 1013 m -17 X s 471 1074 m -17 X s 488 1134 m -34 X s 471 1194 m -17 X s 471 1255 m -17 X s 471 1315 m -17 X s 471 1376 m -17 X s 488 1436 m -34 X s 471 1497 m -17 X s 471 1557 m -17 X s 471 1618 m -17 X s 471 1678 m -17 X s 488 1739 m -34 X s 471 1799 m -17 X s 471 1860 m -17 X s 471 1920 m -17 X s 471 1981 m -17 X s 488 2041 m -34 X s 488 2041 m -34 X s /xs 0 def (1) /Times-Roman 68 stwn gsave 408 204 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr /xs 0 def (1.05) /Times-Roman 68 stwn gsave 408 507 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.05) show gr /xs 0 def (1.1) /Times-Roman 68 stwn gsave 408 809 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.1) show gr /xs 0 def (1.15) /Times-Roman 68 stwn gsave 408 1111 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.15) show gr /xs 0 def (1.2) /Times-Roman 68 stwn gsave 408 1414 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.2) show gr /xs 0 def (1.25) /Times-Roman 68 stwn gsave 408 1716 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.25) show gr /xs 0 def (1.3) /Times-Roman 68 stwn gsave 408 2019 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1.3) show gr 454 227 m 1587 X s 454 261 m -34 Y s 533 244 m -17 Y s 612 244 m -17 Y s 692 244 m -17 Y s 771 244 m -17 Y s 851 261 m -34 Y s 930 244 m -17 Y s 1009 244 m -17 Y s 1089 244 m -17 Y s 1168 244 m -17 Y s 1247 261 m -34 Y s 1327 244 m -17 Y s 1406 244 m -17 Y s 1486 244 m -17 Y s 1565 244 m -17 Y s 1644 261 m -34 Y s 1724 244 m -17 Y s 1803 244 m -17 Y s 1882 244 m -17 Y s 1962 244 m -17 Y s 2041 261 m -34 Y s /xs 0 def (0) /Times-Roman 68 stwn gsave 454 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0) show gr /xs 0 def (0.25) /Times-Roman 68 stwn gsave 851 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.25) show gr /xs 0 def (0.5) /Times-Roman 68 stwn gsave 1247 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.5) show gr /xs 0 def (0.75) /Times-Roman 68 stwn gsave 1644 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.75) show gr /xs 0 def (1) /Times-Roman 68 stwn gsave 2041 159 t 0 r xs 2 div neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (1) show gr 1587 1814 454 227 C 2268 2268 0 0 C /xs 0 def (s) /Times-Roman 86 stwn gsave 2041 82 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 86 sf 0 0 m (s) show gr 1587 1814 454 227 C 2268 2268 0 0 C 1587 1814 454 227 C 2268 2268 0 0 C gsave 96 1803 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (P) show gr 1587 1814 454 227 C 3 lw 470 361 m 31 X 16 1 d 16 1 d 16 2 d 16 2 d 16 2 d 16 2 d 15 2 d 16 3 d 16 3 d 16 4 d 16 3 d 16 4 d 16 4 d 16 5 d 15 5 d 16 5 d 16 5 d 16 5 d 16 6 d 16 6 d 16 7 d 16 6 d 15 7 d 16 7 d 16 8 d 16 8 d 16 8 d 16 8 d 16 8 d 16 9 d 15 9 d 16 10 d 16 10 d 16 10 d 16 10 d 16 10 d 16 11 d 16 11 d 15 12 d 16 11 d 16 12 d 16 13 d 16 12 d 16 13 d 16 13 d 16 14 d 15 14 d 16 14 d 16 14 d 16 15 d 16 15 d 16 15 d 16 15 d 16 16 d 15 16 d 16 17 d 16 17 d 16 17 d 16 17 d 16 18 d 16 18 d 16 18 d 15 19 d 16 19 d 16 19 d 16 20 d 16 20 d 16 20 d 16 21 d 16 21 d 16 21 d 15 22 d 16 21 d 16 23 d 16 22 d 16 23 d 16 23 d 16 24 d 16 24 d 15 24 d 16 25 d 16 25 d 16 25 d 16 25 d 16 26 d 16 27 d 16 26 d 15 27 d 16 27 d 16 28 d 16 28 d 16 28 d 16 29 d 16 29 d 16 29 d 15 30 d s 470 504 m 15 2 d 16 1 d 16 X 16 1 d 16 2 d 16 1 d 16 2 d 16 1 d 15 3 d 16 2 d 16 2 d 16 3 d 16 3 d 16 3 d 16 4 d 16 3 d 15 4 d 16 4 d 16 5 d 16 4 d 16 5 d 16 5 d 16 5 d 16 6 d 15 5 d 16 6 d 16 6 d 16 7 d 16 7 d 16 6 d 16 7 d 16 8 d 15 7 d 16 8 d 16 8 d 16 9 d 16 8 d 16 9 d 16 9 d 16 10 d 15 9 d 16 10 d 16 10 d 16 10 d 16 11 d 16 11 d 16 11 d 16 12 d 15 11 d 16 12 d 16 12 d 16 13 d 16 13 d 16 13 d 16 13 d 16 14 d 15 14 d 16 14 d 16 14 d 16 15 d 16 15 d 16 16 d 16 15 d 16 16 d 15 17 d 16 16 d 16 17 d 16 17 d 16 18 d 16 18 d 16 18 d 16 18 d 16 19 d 15 19 d 16 20 d 16 20 d 16 20 d 16 20 d 16 21 d 16 21 d 16 21 d 15 22 d 16 22 d 16 23 d 16 22 d 16 23 d 16 24 d 16 24 d 16 24 d 15 24 d 16 25 d 16 25 d 16 26 d 16 26 d 16 26 d 16 27 d 16 27 d 15 27 d s 470 840 m 15 2 d 16 -1 d 16 1 d 16 X 16 1 d 16 1 d 16 1 d 16 1 d 15 1 d 16 1 d 16 2 d 16 1 d 16 2 d 16 2 d 16 1 d 16 2 d 15 3 d 16 2 d 16 2 d 16 3 d 16 3 d 16 3 d 16 3 d 16 3 d 15 3 d 16 3 d 16 4 d 16 4 d 16 4 d 16 4 d 16 4 d 16 5 d 15 4 d 16 5 d 16 5 d 16 5 d 16 5 d 16 6 d 16 5 d 16 6 d 15 6 d 16 7 d 16 6 d 16 7 d 16 7 d 16 7 d 16 7 d 16 8 d 15 7 d 16 8 d 16 9 d 16 8 d 16 9 d 16 9 d 16 9 d 16 9 d 15 10 d 16 10 d 16 10 d 16 11 d 16 11 d 16 11 d 16 11 d 16 12 d 15 11 d 16 13 d 16 12 d 16 13 d 16 13 d 16 13 d 16 14 d 16 14 d 16 14 d 15 15 d 16 15 d 16 15 d 16 16 d 16 15 d 16 17 d 16 16 d 16 17 d 15 17 d 16 18 d 16 18 d 16 18 d 16 19 d 16 19 d 16 19 d 16 20 d 15 20 d 16 20 d 16 21 d 16 21 d 16 21 d 16 22 d 16 22 d 16 23 d 15 23 d s 470 1738 m 2 6 d 2 5 d 2 5 d 2 5 d 3 4 d 2 3 d 2 2 d 3 1 d 2 1 d 11 -2 d 16 -1 d 16 -1 d 16 -1 d 16 -1 d 16 -2 d 16 -1 d 15 -2 d 16 -2 d 16 -2 d 16 -2 d 16 -2 d 16 -3 d 16 -2 d 16 -3 d 15 -3 d 16 -3 d 16 -3 d 16 -3 d 16 -3 d 16 -4 d 16 -3 d 16 -3 d 15 -4 d 16 -4 d 16 -3 d 16 -4 d 16 -4 d 16 -3 d 16 -4 d 16 -4 d 15 -4 d 16 -3 d 16 -4 d 16 -4 d 16 -3 d 16 -4 d 16 -3 d 16 -4 d 15 -3 d 16 -3 d 16 -3 d 16 -3 d 16 -3 d 16 -3 d 16 -2 d 16 -2 d 15 -3 d 16 -2 d 16 -1 d 16 -2 d 16 -2 d 16 -1 d 16 -1 d 16 -1 d 31 X 16 -1 d 16 1 d 16 X 16 1 d 16 1 d 16 1 d 15 2 d 16 2 d 16 2 d 16 3 d 16 3 d 16 3 d 16 3 d 16 4 d 16 5 d 15 4 d 16 5 d 16 6 d 16 5 d 16 6 d 16 7 d 16 7 d 16 7 d 15 7 d 16 8 d 16 9 d 16 9 d 16 9 d 16 10 d 16 10 d 16 10 d 15 11 d 16 11 d 16 12 d 16 12 d 16 13 d 16 13 d 16 13 d 16 14 d 15 14 d s 2268 2268 0 0 C 470 279 m 15 X s 485 279 m 7 X s 515 279 m 2 X s 517 279 m 16 1 d s 533 280 m 5 X s 560 281 m 5 X s 565 281 m 16 1 d s 581 282 m 2 X s 605 284 m 7 X s 612 284 m 16 2 d s 651 288 m 9 1 d s 660 289 m 13 1 d s 696 293 m 12 1 d s 708 294 m 10 2 d s 741 299 m 14 2 d s 755 301 m 8 1 d s 786 306 m 1 X s 787 306 m 16 3 d s 803 309 m 5 1 d s 830 314 m 5 1 d s 835 315 m 16 3 d s 851 318 m 1 1 d s 875 323 m 7 2 d s 882 325 m 15 3 d s 919 334 m 11 3 d s 930 337 m 11 3 d s 963 345 m 15 5 d s 978 350 m 6 2 d s 1006 358 m 3 1 d s 1009 359 m 16 5 d s 1025 364 m 3 1 d s 1049 372 m 8 3 d s 1057 375 m 14 5 d s 1092 387 m 13 5 d s 1105 392 m 8 3 d s 1134 404 m 2 1 d s 1136 405 m 16 6 d s 1152 411 m 3 1 d s 1176 421 m 8 4 d s 1184 425 m 13 6 d s 1217 440 m 15 7 d s 1232 447 m 6 3 d s 1258 460 m 5 2 d s 1263 462 m 15 8 d s 1298 481 m 13 7 d s 1311 488 m 7 4 d s 1338 503 m 5 2 d s 1343 505 m 15 9 d s 1377 526 m 13 8 d s 1390 534 m 7 4 d s 1416 550 m 6 4 d s 1422 554 m 13 8 d s 1454 575 m s 1454 575 m 16 11 d s 1470 586 m 2 2 d s 1491 601 m 10 7 d s 1501 608 m 8 6 d s 1527 627 m 6 5 d s 1533 632 m 13 9 d s 1563 655 m 2 1 d s 1565 656 m 16 13 d s 1581 669 m s 1599 683 m 14 12 d s 1613 695 m 3 3 d s 1634 712 m 10 9 d s 1644 721 m 7 6 d s 1668 742 m 8 7 d s 1676 749 m 9 8 d s 1702 772 m 6 6 d s 1708 778 m 10 10 d s 1735 803 m 5 5 d s 1740 808 m 11 11 d s 1768 835 m 3 4 d s 1771 839 m 13 12 d s 1800 867 m 3 3 d s 1803 870 m 13 13 d s 1831 899 m 4 4 d s 1835 903 m 12 13 d s 1862 932 m 5 5 d s 1867 937 m 11 12 d s 1893 966 m 5 6 d s 1898 972 m 10 11 d s 1923 1000 m 7 7 d s 1930 1007 m 8 10 d s 1953 1034 m 9 10 d s 1962 1044 m 6 7 d s 1982 1068 m 12 14 d s 1994 1082 m 3 4 d s 2011 1103 m 14 17 d s 1587 1814 454 227 C 2268 2268 0 0 C 470 334 m 15 -2 d s 485 332 m 7 X s 515 332 m 2 X s 517 332 m 16 X s 533 332 m 4 X s 560 333 m 5 X s 565 333 m 16 X s 581 333 m 2 1 d s 605 334 m 7 1 d s 612 335 m 16 X s 651 336 m 9 1 d s 660 337 m 13 X s 696 339 m 12 X s 708 339 m 11 1 d s 741 342 m 14 1 d s 755 343 m 9 1 d s 787 345 m 1 Y s 787 346 m 16 1 d s 803 347 m 6 1 d s 832 350 m 3 X s 835 350 m 16 2 d s 851 352 m 3 1 d s 877 355 m 5 1 d s 882 356 m 16 2 d s 898 358 m 1 X s 922 362 m 8 1 d s 930 363 m 14 2 d s 966 369 m 12 2 d s 978 371 m 11 2 d s 1011 377 m 14 3 d s 1025 380 m 8 2 d s 1055 386 m 2 1 d s 1057 387 m 16 3 d s 1073 390 m 5 2 d s 1100 397 m 5 1 d s 1105 398 m 15 4 d s 1120 402 m 1 1 d s 1143 409 m 9 2 d s 1152 411 m 13 4 d s 1187 422 m 13 4 d s 1200 426 m 8 3 d s 1230 436 m 2 1 d s 1232 437 m 15 6 d s 1247 443 m 4 1 d s 1272 452 m 7 3 d s 1279 455 m 14 5 d s 1314 469 m 13 6 d s 1327 475 m 8 3 d s 1356 488 m 3 1 d s 1359 489 m 15 7 d s 1374 496 m 2 1 d s 1397 507 m 9 5 d s 1406 512 m 11 6 d s 1437 528 m 1 1 d s 1438 529 m 16 9 d s 1454 538 m 3 1 d s 1476 550 m 10 6 d s 1486 556 m 10 6 d s 1515 574 m 2 1 d s 1517 575 m 16 10 d s 1533 585 m 2 1 d s 1554 598 m 11 8 d s 1565 606 m 7 5 d s 1591 624 m 6 4 d s 1597 628 m 13 9 d s 1628 650 m 1 1 d s 1629 651 m 15 11 d s 1644 662 m 2 2 d s 1664 678 m 12 9 d s 1676 687 m 6 5 d s 1699 706 m 9 7 d s 1708 713 m 9 7 d s 1734 735 m 6 4 d s 1740 739 m 11 11 d s 1768 765 m 3 2 d s 1771 767 m 14 13 d s 1802 795 m 1 1 d s 1803 796 m 16 15 d s 1835 826 m 16 16 d s 1851 842 m s 1867 858 m 16 15 d s 1883 873 m 1 Y s 1899 891 m 15 15 d s 1914 906 m 1 1 d s 1930 923 m 16 17 d s 1961 957 m 1 1 d s 1962 958 m 14 16 d s 1991 991 m 3 2 d s 1994 993 m 12 15 d s 2021 1025 m 4 5 d s 1587 1814 454 227 C 2268 2268 0 0 C 470 446 m 15 -2 d s 485 444 m 7 X s 515 444 m 2 -1 d s 517 443 m 16 X s 533 443 m 4 X s 560 443 m 5 X s 565 443 m 16 -1 d s 581 442 m 2 X s 605 441 m 7 X s 612 441 m 16 X s 651 440 m 9 -1 d s 660 439 m 13 X s 696 438 m 12 -1 d s 708 437 m 11 X s 741 436 m 14 -1 d s 755 435 m 9 X s 787 434 m s 787 434 m 16 -1 d s 803 433 m 6 X s 832 432 m 3 X s 835 432 m 16 -1 d s 851 431 m 4 X s 877 430 m 5 X s 882 430 m 16 -1 d s 898 429 m 2 X s 923 429 m 7 X s 930 429 m 15 -1 d s 968 428 m 10 X s 978 428 m 13 X s 1013 428 m 12 X s 1025 428 m 11 X s 1059 429 m 14 X s 1073 429 m 8 X s 1104 430 m 1 X s 1105 430 m 15 1 d s 1120 431 m 7 1 d s 1149 433 m 3 1 d s 1152 434 m 16 1 d s 1168 435 m 4 X s 1195 438 m 5 X s 1200 438 m 16 2 d s 1216 440 m 1 1 d s 1240 444 m 7 1 d s 1247 445 m 15 2 d s 1284 451 m 11 2 d s 1295 453 m 12 3 d s 1329 460 m 14 4 d s 1343 464 m 8 2 d s 1373 471 m 1 1 d s 1374 472 m 16 4 d s 1390 476 m 5 1 d s 1416 484 m 6 2 d s 1422 486 m 16 5 d s 1459 499 m 11 3 d s 1470 502 m 10 4 d s 1501 515 m 16 6 d s 1517 521 m 5 3 d s 1543 533 m 6 3 d s 1549 536 m 15 6 d s 1584 553 m 13 6 d s 1597 559 m 7 4 d s 1624 574 m 5 2 d s 1629 576 m 15 9 d s 1663 596 m 13 8 d s 1676 604 m 7 4 d s 1702 621 m 6 3 d s 1708 624 m 13 9 d s 1739 646 m 1 X s 1740 646 m 16 11 d s 1756 657 m 2 2 d s 1776 672 m 11 9 d s 1787 681 m 7 5 d s 1812 700 m 7 5 d s 1819 705 m 11 9 d s 1848 728 m 3 3 d s 1851 731 m 14 12 d s 1882 758 m 1 X s 1883 758 m 15 14 d s 1898 772 m 1 1 d s 1916 788 m 14 13 d s 1930 801 m 2 3 d s 1949 819 m 13 13 d s 1962 832 m 3 3 d s 1981 851 m 13 12 d s 1994 863 m 3 4 d s 2013 883 m 12 13 d s 1587 1814 454 227 C 2268 2268 0 0 C 470 670 m 2 5 d s 472 675 m 2 6 d s 474 681 m 3 4 d s 477 685 m 3 4 d s 480 689 m 1 Y s 500 693 m 1 X s 501 693 m s 501 693 m 16 X s 517 693 m 6 -1 d s 546 690 m 3 X s 549 690 m 16 -2 d s 565 688 m 3 X s 591 685 m 6 -1 d s 597 684 m 15 -3 d s 612 681 m 1 X s 635 677 m 9 -2 d s 644 675 m 14 -2 d s 680 668 m 12 -3 d s 692 665 m 10 -2 d s 724 657 m 15 -4 d s 739 653 m 7 -2 d s 768 645 m 3 -1 d s 771 644 m 16 -5 d s 787 639 m 2 X s 811 632 m 8 -2 d s 819 630 m 14 -5 d s 854 618 m 12 -4 d s 866 614 m 10 -3 d s 897 604 m 1 -1 d s 898 603 m 16 -5 d s 914 598 m 5 -2 d s 940 589 m 6 -2 d s 946 587 m 16 -5 d s 983 574 m 10 -3 d s 993 571 m 11 -4 d s 1026 560 m 15 -6 d s 1041 554 m 6 -2 d s 1069 545 m 4 -1 d s 1073 544 m 16 -5 d s 1089 539 m 2 -1 d s 1112 532 m 8 -3 d s 1120 529 m 14 -4 d s 1156 519 m 12 -3 d s 1168 516 m 10 -3 d s 1200 507 m s 1200 507 m 16 -4 d s 1216 503 m 6 -1 d s 1244 497 m 3 -1 d s 1247 496 m 16 -3 d s 1263 493 m 3 X s 1288 489 m 7 -2 d s 1295 487 m 16 -2 d s 1333 482 m 10 -1 d s 1343 481 m 13 -2 d s 1378 477 m 12 -1 d s 1390 476 m 11 X s 1424 475 m 14 X s 1438 475 m 8 X s 1469 475 m 1 X s 1470 475 m 16 1 d s 1486 476 m 6 1 d s 1514 479 m 3 X s 1517 479 m 16 2 d s 1533 481 m 4 X s 1559 484 m 6 1 d s 1565 485 m 16 3 d s 1581 488 m 1 X s 1604 493 m 9 2 d s 1613 495 m 13 3 d s 1648 504 m 12 4 d s 1660 508 m 9 3 d s 1691 518 m 1 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def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /@BeginSysCorelDict{systemdict/Corel20Dict known{systemdict/Corel20Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel20Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if/d/setdash ld/j/setlinejoin ld/J /setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W /eoclip ld/c/curveto ld/C/c ld/l/lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n /newpath ld/N/newpath ld/P{11 rp}bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/` {}bd/~{}bd/@{}bd/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd /$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type/stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd/$fil 0 def}bd/K{1 index type /stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def}ifelse/$K xd/$Y xd/$M xd/$C xd }bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{/s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{dup 0 ne{setflat}{pop}ifelse}bd /v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate /$ptm xd matrix scale $ptm dup concatmatrix/$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd{/$scp xd/$sca xd/$scf xd}if }bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd}if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd /$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA}{$dsa}ifelse $SCP @ss}if}bd/p{ /$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def}bd/@MN{2 copy le{pop}{exch pop} ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd/InRange{3 -1 roll @MN @MX}bd /wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd/@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd/cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd/rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll 3 rp}bd/WaldoColor_5 where{ pop}{/SetRgb/setrgbcolor ld/GetRgb/currentrgbcolor ld/SetGry/setgray ld/GetGry /currentgray ld/SetRgb2 systemdict/setrgbcolor get def/GetRgb2 systemdict /currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def/rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5 /setcmykcolor ld}{/SetCmyk_5{cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{ pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse /setoverprint where{pop}{/setoverprint{/$op xd}bd}ifelse/currentoverprint where {pop}{/currentoverprint{$op}bd}ifelse/@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd/@trp{exch pop 5 1 roll @tc_5}bd /setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll 4 rp SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry}ifelse}ifelse}bd/findcmykcustomcolor where {pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{ /setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{ CurrentInkName_5 eq{4 index}{0}ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd }ifelse/@scc_5{dup type/booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor} ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd /colorimage where{pop/ColorImage/colorimage ld}{/ColorImage{/ncolors xd pop /dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image} bd}ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep 4 rp}{2 rp}ifelse @rs}bd/@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit}ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for 2 rp}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for 2 rp}for}bd/@pf{@gs $ctm setmatrix $pm concat @stb eoclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{eofill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{ /$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub/$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add/$tly xd $psx 0 eq{@tv}{@th} ifelse}if @gr @np/$bkg false def}bd/@dlt{$fse $fss sub/nff xd $frb dup 1 eq exch 2 eq or{$frt dup $frc $frm $fry $frk @tc_5 4 copy cmyk2rgb rgb2hsb 3 copy /myb xd/mys xd/myh xd $tot $toc $tom $toy $tok @tc_5 cmyk2rgb rgb2hsb 3 1 roll 4 1 roll 5 1 roll sub neg nff div/kdb xd sub neg nff div/kds xd sub neg dup 0 eq{pop $frb 2 eq{.99}{-.99}ifelse}if dup $frb 2 eq exch 0 lt and{1 add}if dup $frb 1 eq exch 0 gt and{1 sub}if nff div/kdh xd}{$frt dup $frc $frm $fry $frk @tc_5 5 copy $tot dup $toc $tom $toy $tok @tc_5 5 1 roll 6 1 roll 7 1 roll 8 1 roll 9 1 roll sub neg nff dup 1 gt{1 sub}if div/$dk xd sub neg nff dup 1 gt{1 sub}if div/$dy xd sub neg nff dup 1 gt{1 sub}if div/$dm xd sub neg nff dup 1 gt {1 sub}if div/$dc xd sub neg nff dup 1 gt{1 sub}if div/$dt xd}ifelse}bd/ffcol{ 5 copy $fsit 0 eq{setcmykcolor pop}{SepMode_5 0 ne{$frn findcmykcustomcolor exch setcustomcolor}{4 rp $frc $frm $fry $frk $frn findcmykcustomcolor exch setcustomcolor}ifelse}ifelse}bd/@ftl{1 index 4 index sub dup $pad mul dup/$pdw xd 2 mul sub $fst div/$wid xd 2 index sub/$hei xd pop Tl @dlt $fss 0 eq{ffcol n 0 0 m 0 $hei l $pdw $hei l $pdw 0 l @cp $ffpnt{fill}{@np}ifelse}if $fss $wid mul $pdw add 0 Tl nff{ffcol n 0 0 m 0 $hei l $wid $hei l $wid 0 l @cp $ffpnt {fill}{@np}ifelse $wid 0 Tl $frb dup 1 eq exch 2 eq or{4 rp myh mys myb kdb add 3 1 roll kds add 3 1 roll kdh add 3 1 roll 3 copy/myb xd/mys xd/myh xd hsb2rgb rgb2cmyk}{$dk add 5 1 roll $dy add 5 1 roll $dm add 5 1 roll $dc add 5 1 roll $dt add 5 1 roll}ifelse}repeat 5 rp $tot dup $toc $tom $toy $tok @tc_5 ffcol n 0 0 m 0 $hei l $pdw $hei l $pdw 0 l @cp $ffpnt{fill}{@np}ifelse 5 rp}bd/@ftrs{ 1 index 4 index sub dup $rox mul/$row xd 2 div 1 index 4 index sub dup $roy mul /$roh xd 2 div 2 copy dup mul exch dup mul add sqrt $row dup mul $roh dup mul add sqrt add dup/$hei xd $fst div/$wid xd 4 index add $roh add exch 5 index add $row add exch Tl $fan rotate 4 rp @dlt $fss 0 eq{ffcol $fty 3 eq{$hei dup neg dup m 2 mul @sqr}{0 0 m 0 0 $hei 0 360 arc}ifelse $ffpnt{fill}{@np}ifelse}if 1.0 $pad 2 mul sub dup scale $hei $fss $wid mul sub/$hei xd nff{ffcol $fty 3 eq {n $hei dup neg dup m 2 mul @sqr}{n 0 0 m 0 0 $hei 0 360 arc}ifelse $ffpnt {fill}{@np}ifelse/$hei $hei $wid sub def $frb dup 1 eq exch 2 eq or{4 rp myh mys myb kdb add 3 1 roll kds add 3 1 roll kdh add 3 1 roll 3 copy/myb xd/mys xd /myh xd hsb2rgb rgb2cmyk}{$dk add 5 1 roll $dy add 5 1 roll $dm add 5 1 roll $dc add 5 1 roll $dt add 5 1 roll}ifelse}repeat 5 rp}bd/@ftc{1 index 4 index sub dup $rox mul/$row xd 2 div 1 index 4 index sub dup $roy mul/$roh xd 2 div 2 copy dup mul exch dup mul add sqrt $row dup mul $roh dup mul add sqrt add dup /$hei xd $fst div/$wid xd 4 index add $roh add exch 5 index add $row add exch Tl 4 rp @dlt $fss 0 eq{ffcol $ffpnt{fill}{@np}ifelse}{n}ifelse/$dang 180 $fst 1 sub div def/$sang $dang -2 div 180 add def/$eang $dang 2 div 180 add def/$sang $sang $dang $fss mul add def/$eang $eang $dang $fss mul add def/$sang $eang $dang sub def nff{ffcol n 0 0 m 0 0 $hei $sang $fan add $eang $fan add arc $ffpnt{fill}{@np}ifelse 0 0 m 0 0 $hei $eang neg $fan add $sang neg $fan add arc $ffpnt{fill}{@np}ifelse/$sang $eang def/$eang $eang $dang add def $frb dup 1 eq exch 2 eq or{4 rp myh mys myb kdb add 3 1 roll kds add 3 1 roll kdh add 3 1 roll 3 copy/myb xd/mys xd/myh xd hsb2rgb rgb2cmyk}{$dk add 5 1 roll $dy add 5 1 roll $dm add 5 1 roll $dc add 5 1 roll $dt add 5 1 roll}ifelse}repeat 5 rp} bd/@ff{/$fss 0 def $o 1 eq setoverprint 1 1 $fsc 1 sub{dup 1 sub $fsit 0 eq{ $fsa exch 5 mul 5 getinterval aload 2 rp/$frk xd/$fry xd/$frm xd/$frc xd/$frn _ def/$frt 1 def $fsa exch 5 mul 5 getinterval aload pop $fss add/$fse xd/$tok xd /$toy xd/$tom xd/$toc xd/$ton _ def/$tot 1 def}{$fsa exch 7 mul 7 getinterval aload 2 rp/$frt xd/$frn xd/$frk xd/$fry xd/$frm xd/$frc xd $fsa exch 7 mul 7 getinterval aload pop $fss add/$fse xd/$tot xd/$ton xd/$tok xd/$toy xd/$tom xd /$toc xd}ifelse $fsit 0 eq SepMode_5 0 eq or dup not CurrentInkName_5 $frn eq and or{@sv $ctm setmatrix eoclip Bbllx Bblly Bburx Bbury $fty 2 eq{@ftc}{1 index 3 index m 2 copy l 3 index 1 index l 3 index 3 index l @cp $fty dup 1 eq exch 3 eq or{@ftrs}{4 rp $fan rotate pathbbox @ftl}ifelse}ifelse @rs/$fss $fse def}{1 0 0 0 0 _ $o @scc_5{fill}if}ifelse}for @np}bd/@Pf{@sv SepMode_5 0 eq $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry eofill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 eq{@ff}{$fil 3 eq{@Pf}{$t $c $m $y $k $n $o @scc_5{eofill} {@np}ifelse}ifelse}ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix}bd/f{@cp F}bd/S{matrix currentmatrix $ctm setmatrix $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc_5{matrix currentmatrix $ptm concat stroke setmatrix} {@np}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/s{@cp S}bd/B{@gs F @gr S} bd/b{@cp B}bd/E{5 array astore exch cvlit xd}bd/@cc{currentfile $dat readhexstring pop}bd/@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq dup/$vectpat xd{/$pfrg true def}{@gs $t $c $m $y $k $n $o @scc_5/$pfrg xd @gr}ifelse/$pm xd/$psy xd/$psx xd /$pyf xd/$pxf xd/$pn xd}bd/@P{/$fil 3 def/$Psn xd array astore/$Prm xd}bd/@k{ /$fil 2 def/$roy xd/$rox xd/$pad xd/$fty xd/$fan xd $fty 1 eq{/$fan 0 def}if /$frb xd/$fst xd/$fsc xd/$fsa xd/$fsit 0 def}bd/@x{/$fil 2 def/$roy xd/$rox xd /$pad xd/$fty xd/$fan xd $fty 1 eq{/$fan 0 def}if/$frb xd/$fst xd/$fsc xd/$fsa xd/$fsit 1 def}bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip 4 rp}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne{/$frg true def 2 rp}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd }{/$frg false def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd /$urx xd/$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop}repeat}ifelse @gr $ctm setmatrix}bd/@M{@sv}bd/@N {/@cc{}def 1 eq{12 -1 roll neg 12 1 roll @I}{13 -1 roll neg 13 1 roll @i} ifelse @rs}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/z{exch findfont exch scalefont setfont} bd/ZB{9 dict dup begin 4 1 roll/FontType 3 def/FontMatrix xd/FontBBox xd /Encoding 256 array def 0 1 255{Encoding exch/.notdef 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1057 y(sition)f(state)h(or)g(transform)f(a)h (solid)e(to)i(a)g(more)f(open)g(crystal)i(structure.)102 1261 y FA(\017)49 b FE(To)d(understand)h(the)g(origin)f(of)g(these)i (effects,)j(we)c(consider)f(the)h(dif-)203 1381 y(ference)38 b(between)h(LSD)f(and)g(GGA)f(energies.)67 b(We)37 b(derive)g(an)h (inequality)203 1502 y(\(4.2.4a\),)28 b(which)h(shows)g(that,)h (contrary)h(to)e(popular)g(belief,)g(the)h(increase)203 1622 y(in)25 b(inhomogeneity)h FC(d)p FA(h)p FC(s)6 b FA(i)24 b FE(must)i(be)g(greater)h(than)g(some)f Fj(minimum)e FE(value,)203 1742 y(which)k(can)h(be)g(greater)h(than)f(zero,)g(for)f (gradient)h(corrections)g(to)g(favor)f(a)203 1863 y(process.)38 b(If)27 b(the)h(increase)g(in)f(inhomogeneity)h(is)f(insuf\256cient,)f (the)i(gradi-)203 1983 y(ent)23 b(corrections)f(will)f(disfavor)g(the)h (process.)36 b(We)22 b(show)g(that)h(the)f(inequal-)203 2104 y(ity)h(\(4.2.4a\))e(is)h(ful\256lled)g(for)g(most)h(of)e(the)i (cases,)h(and)f(so)f(GGA)h(corrections)203 2224 y(lower)35 b(atomisation)g(energies,)h(stretch)f(bonds,)g(heighten)g(energy)g (barri-)203 2344 y(ers,)21 b(and)e(favour)f(more)h(open)g(crystal)h (structures.)36 b(On)19 b(the)g(other)h(hand,)g(we)203 2465 y(present)g(two)f(cases)h(where)g(gradient)f(corrections)h(cause)g (the)g(bond)e(length)203 2585 y(to)39 b(shrink)e(\(H)763 2599 y Fz(2)845 2585 y FE(molecule)i(and)f(H)1569 2599 y Fz(3)1651 2585 y FE(transition)g(state\),)43 b(even)38 b(though)h(the)203 2705 y(molecule's)f(inhomogeneity)e(increases)i (with)f(increasing)f(bond)h(length.)203 2826 y(In)28 b(these)h(two)g(cases,)g(the)g(inequality)g(\(4.2.4a\))e(is)h (correctly)i(violated.)106 3029 y(Even)h(though)h(a)h(large)f(number)g (of)f(different)h(systems)g(was)g(considered)g(in)-41 3150 y(this)j(work)f(I)h(believe)f(there)i(are)f(systems)g(which)g (will)f(need)h(to)g(be)g(considered)-41 3270 y(to)i(complete)f(the)h (picture.)61 b(I)36 b(am)g(planing)g(to)g(perform)f(the)h(present)h (analysis)-41 3390 y(on)25 b(a)h(number)e(of)h(different)f(phases)h(of) f(crystallised)i(silicon)e(and)h(iron)g(\(metals\),)-41 3511 y(where)37 b(GGA)g(gives)g(good)f(results,)j(and)e(on)f(a)i(set)f (of)f(weakly)i(bound)e(van-der-)-41 3631 y(Waals)h(systems,)g(where)f (GGA)g(fails.)59 b(At)36 b(the)g(moment)g(the)g(work)f(is)g(going)g(on) -41 3752 y(on)28 b(a)h(set)g(of)f(alkali)g(halides)g(crystals,)i(where) e(GGA)h(unexpectedly)g(predicts)f(too)-41 3872 y(long)21 b(bond)f(lengths.)36 b(Unfortunately,)23 b(the)e(present)g (computational)h(framework)-41 3992 y(\(computer)33 b(code)f Fv(Crystal)p FE(\))g(does)g(not)g(allow)h(the)f(treatment)i(of)e (metallic)h(sys-)-41 4113 y(tems.)39 b(A)28 b(new)h(code)f(using)g (plane)g(waves)h(is)f(required)g(to)g(proceed.)1522 5640 y(56)p eop %%Page: 57 65 57 64 bop 555 1256 a Fy(Appendix)59 b(A)555 1687 y(Computer)f(code)f Fc(Crystal)555 2218 y FD(A.1)130 b(Introduction)555 2486 y FE(I)23 b(used)g(the)g(computer)g(code)g Fv(Crystal)f FE(and)h(its)f(DFT)h(extension)g(to)g(calculate)i(the)555 2607 y(HF)36 b(and)g(KS)g(densities)f(of)g(atoms,)k(molecules,)f(and)e (crystals,)i(using)d(different)555 2727 y(exchange-correlation)40 b(potentials.)67 b(I)38 b(also)g(modi\256ed)f(this)g(code)h(to)g (calculate)555 2847 y(the)k(distribution)e(functions)1749 2813 y Fz(48)1872 2847 y FE(de\256ned)h(in)g(Chapter)h(3.)76 b(That)42 b(is)e(the)i(reason)555 2968 y(why)27 b(this)f(chapter)i (with)e(technical)i(details)f(\256nds)f(its)g(place)h(in)f(the)h (appendix)f(of)555 3088 y(my)j(Ph.D.)f(dissertation.)702 3224 y(The)18 b(computer)h(code)f Fv(Crystal)1967 3190 y Fz(49)p FB(;)p Fz(67)2147 3224 y FE(,)i(is)e(an)h(implementation)f (of)g(the)h(Hartree-)555 3345 y(Fock)i(\(HF\))h(method)f(for)g (periodic)f(systems,)i(and)f(has)h(now)e(been)i(under)e(continu-)555 3465 y(ous)h(development)g(for)f(over)h(twenty)h(years.)36 b(It)21 b(is)g(a)g(reliable)g(tool)g(for)g(computing)555 3586 y(the)28 b(electronic)g(structure)g(and)g(associated)g (ground-state)g(properties)f(of)f(up)h(to)555 3706 y (three-dimensionally)33 b(periodic)d(materials)j(within)e(the)i (Hartree-Fock)g(approx-)555 3826 y(imation.)69 b(The)38 b(Bloch)h(functions)f(of)g(the)h(periodic)e(system)i(are)h(expanded)e (as)555 3947 y(linear)43 b(combinations)e(of)h(atom-centred)i(Gaussian) e(functions,)j(and)d(the)g(use)555 4067 y(of)30 b(ef\256cient)h (integral)g(evaluation)g(algorithms)g(and)f(powerful)g(screening)g (tech-)555 4187 y(niques)i(which)g(exploit)g(the)g(real)h(space)f (locality)i(combine)d(to)i(produce)f(a)g(code)555 4308 y(which)g(is)e(both)i(fast,)g(and)g(scales)h(attractively)g(\(linearly) g(for)e(the)h(integrals)g(cal-)555 4428 y(culation)i(in)d(many)i (cases\))h(with)e(the)h(number)f(of)g(basis)g(functions.)50 b(The)33 b(latest)555 4549 y(version)e(of)g(this)g(code)h Fv(Crystal)56 b(95)2049 4514 y Fz(68)p FB(;)p Fz(50)2261 4549 y FE(includes)31 b(a)h(number)f(of)g(major)h(inno-)555 4669 y(vations,)e(one)f(of)g(the)h(most)f(important)h(of)f(which)g(is)g (the)g(additional)h(capability)555 4789 y(of)i(solving)e(for)h(the)i (electronic)f(structure)h(of)e(periodic)g(materials)h(within)f(den-)555 4910 y(sity)21 b(functional)f(theory)h(\(DFT\))g(or)g(various)e(hybrid) h(approximations)f(containing)555 5030 y(elements)33 b(of)d(both)h(Hartree-Fock)i(and)e(Kohn-Sham)g(Hamiltonians.)46 b(Thus)31 b(the)555 5150 y(new)g(code)g(may)g(be)g(used)f(to)h(perform) e(consistent)i(comparisons)f(between)i(the)555 5271 y(Hartree-Fock)39 b(and)e(Kohn-Sham)g(descriptions)f(of)h(the)g(structural,)j(electronic) 555 5391 y(and)20 b(magnetic)g(properties)e(of)h(molecules,)i (polymers,)g(surfaces)e(and)g(crystalline)2118 5640 y(57)p eop %%Page: 58 66 58 65 bop -41 275 a Fw(Chapter)29 b(A.)f(Computer)g(code)h Fv(Crystal)p -41 315 3238 4 v -41 576 a FE(solids)f(using)f(the)i(same) g(basis)f(set)h(and)f(computational)h(conditions.)106 696 y(In)21 b(the)h(present)g(chapter,)h(the)f(computational)h (implementation)f(of)f(the)h(den-)-41 817 y(sity)j(functional)f(theory) h(within)f Fv(Crystal)g FE(will)g(\256rst)h(be)f(outlined,)h (emphasising)-41 937 y(the)38 b(necessary)g(modi\256cations)f(to)h(the) g(algorithms)f(of)g(the)g(original)g(code.)65 b(In)-41 1057 y(particular,)36 b(the)e(techniques)g(used)g(to)g(carry)h(out)e (the)i(numerical)f(integrations)-41 1178 y(required)k(in)g(the)g (solution)g(of)f(the)i(Kohn-Sham)f(equations)h(are)g(discussed)e(in)-41 1298 y(detail.)47 b(Finally,)31 b(results)g(are)h(presented)f(to)g (demonstrate)h(the)g(dependence)f(of)-41 1419 y(various)38 b(calculated)j(observables)e(on)g(the)g(computational)h(parameters)g (used)-41 1539 y(to)33 b(control)g(the)h(accuracy)g(of)e(the)h (calculation.)53 b(Speci\256cally,)35 b(the)e(dependence)-41 1659 y(of)h(the)g(calculated)i(equilibrium)d(geometries,)j(bulk)d (moduli,)h(atomisation)h(en-)-41 1780 y(ergies)28 b(and)h(band)f (structures)h(of)e(Si,)h(NaCl)g(and)g(Al)h(on)f(the)h(accuracy)h(of)d (the)i(nu-)-41 1900 y(merical)f(integration)f(of)g(the)h(total)g (energy)g(and)f(Kohn-Sham)g(matrix)g(elements,)-41 2021 y(and)34 b(on)f(the)h(auxiliary)f(basis)g(set)g(used)g(to)h(expand)f (the)h(exchange-correlation)-41 2141 y(potential)i(are)f(reported.)57 b(These)35 b(results)g(are)g(used)f(to)h(de\256ne)g(default)g(values) -41 2261 y(for)28 b(the)h(computational)g(parameters.)-41 2609 y FD(A.2)130 b(Theoretical)40 b(and)g(computational)g(method)-41 2872 y Fi(A.2.1)108 b(Basic)33 b(equations)-41 3066 y FE(The)d(crystalline-orbital)h(method)f(upon)f(which)g(our)h(treatment) i(is)d(based)h(is)f(an)-41 3186 y(extension)45 b(of)g(standard)g(LCAO)g (molecular-orbital)i(techniques)f(to)f(periodic)-41 3307 y(systems,)29 b(where)f(the)h(wave)g(function)e(must)i(obey)f(the)h (Bloch)f(theorem:)914 3483 y Fu(\331)976 3497 y Fe(k)1023 3483 y FC(\204)p Fx(r)20 b FA(\202)h Fx(g)r FC(\205)k FA(\203)h Fu(\331)1512 3497 y Fe(k)1559 3483 y FC(\204)p Fx(r)p FC(\205)15 b FE(exp)p FC(\204i)p Fx(k)k FA(\001)i Fx(g)r FC(\205)26 b(:)664 b FE(\(A.2.1\))-41 3659 y(The)26 b(wave)g(vector)g Fx(k)g FE(is)f(the)h(generating)h(vector)f(of)g(the)g (irreducible)f(representa-)-41 3779 y(tion)33 b(of)f(the)h(group)f(of)g (crystal)i(translations)g FA(f)p Fx(g)r FA(g)p FE(.)51 b(The)33 b(electron)g(density)g FC(\032)k FE(of)-41 3900 y(an)f(N-electron)h(system)f(described)e(by)i(such)f(a)h(wave)f (function)g(is)g(given)g(from)-41 4020 y(the)29 b(optimum)f (one-electron)i(crystalline)f(orbitals)g FC(')2122 4034 y Fe(k)p FB(i)2224 4020 y FE(by)345 4323 y FC(\032)t(\204)p Fx(r)p FC(\205)d FA(\203)665 4192 y Fu(Z)727 4367 y Fg(B)s(r)7 b(illo)q(uine)806 4423 y(z)q(o)q(ne)1047 4323 y FC(d)p Fx(k)1198 4152 y Fg(o)q(c)s(c)s(up)r(ie)q(d)1240 4211 y(b)q(ands)1272 4232 y Fu(X)1312 4432 y FB(i)1479 4323 y FA(j)p FC(')1600 4337 y Fe(k)p FB(i)1674 4323 y FC(\204)p Fx(r)p FC(\205)p FA(j)1838 4284 y Fz(2)1880 4323 y FC(\022)t(\204")2035 4337 y FB(F)2105 4323 y FA(\000)20 b FC(")2247 4337 y FB(i)2279 4323 y FC(\204)p Fx(k)p 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Fe(g)q FB(j)1836 5308 y FC(\204)p Fx(r)p FC(\205)15 b FE(exp)p FC(\204i)p Fx(k)k FA(\001)j Fx(g)r FC(\205)2468 5206 y Fu(\021)2545 5308 y FC(;)335 b FE(\(A.2.3\))1522 5640 y(58)p eop %%Page: 59 67 59 66 bop 1824 275 a Fw(A.2.)27 b(Theoretical)i(and)g(computational)g (method)p 555 315 3238 4 v 555 576 a FE(and)g(are)g(solutions)e(of)h (the)h(one-particle)h(equations)1814 773 y FC(h)1881 787 y FB(i)1913 773 y FC(')1999 787 y Fe(k)p FB(i)2099 773 y FA(\203)c FC(")2247 787 y Fe(k)p FB(i)2322 773 y FC(')2408 787 y Fe(k)p FB(i)2508 773 y FC(:)968 b FE(\(A.2.4\))702 971 y(The)33 b(principal)f(difference)g(between)i(the)g(Kohn-Sham)f (density)g(functional)555 1091 y(and)d(Hartree-Fock)h(methods)f(lies)f (in)g(the)i(form)e(of)g(the)h(one-electron)i(operator)555 1212 y FC(h)p FE(.)39 b(The)28 b(Hartree-Fock)h(mono-electronic)h (operator)f(is)e(given)h(by)1312 1409 y FC(h)1379 1423 y FB(H)5 b(F)1513 1409 y FA(\203)26 b FC(t)f FA(\202)c FC(v)28 b FA(\202)20 b FC(J)7 b(\206\032)t(\204)p Fx(r)p 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FC(E)614 2497 y FB(x)s(c)734 2483 y FE(with)28 b(respect)h(to)g(the)g(density)f(at)h(a)g(point)f Fx(r)p FE(:)1817 2725 y FC(v)1881 2739 y FB(x)s(c)1998 2725 y FA(\203)2108 2659 y FC(\016E)2228 2673 y FB(x)s(c)2319 2659 y FC(\206\032)t(\207)p 2108 2697 362 4 v 2161 2791 a(\016\032)t(\204)p Fx(r)p FC(\205)2505 2725 y(:)971 b FE(\(A.2.7\))702 2968 y(In)26 b(a)h(local)h(density)e(approximation)g (\(LDA\),)h FC(E)2543 2982 y FB(x)s(c)2661 2968 y FE(is)f(de\256ned)g (in)g(terms)h(of)f(the)555 3088 y(exchange)j(correlation)f(energy)g (per)f(particle)h FC(")2447 3102 y FB(x)s(c)2566 3088 y FE(in)f(the)h(uniform)d(electron)k(gas)555 3208 y(of)f(density)g FC(\032)t FE(:)1597 3366 y FC(E)1656 3380 y FB(x)s(c)1773 3366 y FA(\203)1873 3235 y Fu(Z)1935 3410 y Fg(unit)1949 3466 y(c)s(e)q(ll)2090 3366 y FC(d)p Fx(r)16 b FC(\032)t(\204)p Fx(r)p FC(\205")2457 3380 y FB(x)s(c)2549 3366 y FC(\204\032)t(\205)25 b(:)751 b FE(\(A.2.8\))702 3592 y(Thus)28 b(modi\256cation)h(of)g(the)h 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Fx(g)h FE(labels)g(the)f(cell)g(containing)g(the)g FC(j)5 b FE(th)30 b(basis)555 4675 y(function)e(at)h(atomic)g(position) f Fx(s)1865 4689 y FB(j)1904 4675 y FE(,)g(take)h(the)g(form:)1227 4919 y FC(v)1299 4866 y FB(i;j)t Fe(g)1291 4930 y FB(x)s(c)1451 4919 y FA(\203)1551 4788 y Fu(Z)1636 4919 y FC(d)p Fx(r)15 b FC(\037)1821 4933 y FB(i)1854 4919 y FC(\204)p Fx(r)20 b FA(\000)h Fx(s)2104 4933 y FB(i)2135 4919 y FC(\205v)2242 4933 y FB(x)s(c)2333 4919 y FC(\204)p Fx(r)p FC(\205\037)2523 4933 y FB(j)2563 4919 y FC(\204)p Fx(r)g FA(\000)f Fx(s)2813 4933 y FB(j)2874 4919 y FA(\000)g Fx(g)r FC(\205)26 b(:)381 b FE(\(A.2.9\))702 5150 y(A)37 b(great)h(many)f(analytic)i(forms)d(for) g(the)i(exchange-correlation)g(potential)555 5271 y FC(v)619 5285 y FB(x)s(c)730 5271 y FE(have)19 b(been)h(suggested.)35 b(To)19 b(allow)h(comparisons)e(between)i(the)g(various)f(pro-)555 5391 y(posals,)30 b(the)h(most)f(important)g(of)g(these)g(have)g(been)h (implemented)f(in)f(the)h(new)2118 5640 y(59)p eop %%Page: 60 68 60 67 bop -41 275 a Fw(Chapter)29 b(A.)f(Computer)g(code)h Fv(Crystal)p -41 315 3238 4 v -41 576 a FE(code;)f(for)e(the)i (complete)h(list)e(see)g(the)h(paper)f(of)g(Towler,)g(Zupan,)g(and)g (Caus)3036 575 y(\301)3039 576 y(a)3089 542 y Fz(50)3172 576 y FE(.)-41 696 y(In)j(general)h(however,)e(the)h FC(v)1110 710 y FB(x)s(c)1231 696 y FE(potentials)g(have)g(an)g (exceedingly)g(complex)g(an-)-41 817 y(alytic)g(form,)e(even)h(at)h(a)f (local)h(level,)f(and)g(so)g(for)f(periodic)g(systems)i(the)f(matrix) -41 937 y(elements)24 b(must)g(be)f(evaluated)h(numerically.)37 b(Performing)23 b(the)g(numerical)h(inte-)-41 1057 y(gration)j (directly)g(over)g(each)g(pair)g(of)f(real)h(space)h(basis)e(functions) g(is)g(expensive)-41 1178 y(in)i(crystalline)h(calculations,)g(and)g (in)e(the)i(present)f(work)g(a)h(more)f(ef\256cient)g(pro-)-41 1298 y(cedure)k(has)g(been)f(adopted.)48 b(In)32 b(this)f(method,)h (the)g(exchange-correlation)h(po-)-41 1419 y(tential)c(is)e(expanded)g (in)f(an)i(auxiliary)f(basis)g(set)h(of)f(contracted)i(Gaussian-type) -41 1539 y(functions)f FA(f)p FC(G)r(\204)p Fx(r)p FC(\205)p FA(g)p FE(:)1110 1737 y FC(v)1174 1751 y FB(x)s(c)1265 1737 y FC(\204)p Fx(r)p FC(\205)e FA(\203)1544 1618 y FB(N)1520 1646 y Fu(X)1550 1835 y FB(a)1642 1737 y FC(c)1692 1751 y FB(a)1741 1737 y FC(G)1814 1751 y FB(a)1865 1737 y FC(\204)p Fx(r)p FC(\205)f(:)804 b FE(\(A.2.10\))-41 1979 y(This)37 b(expansion)g(allows)g(the)i(evaluation)f(of)f(the)h (DFT)f(potential)i(integrals)f(in)-41 2111 y(\(A.2.9\))30 b(as)h(a)g(linear)g(combination)f(of)g(integrals)h FC(g)1988 2058 y FB(i;j)t Fe(g)1984 2121 y FB(a)2145 2111 y FE(over)f(the)h (auxiliary)g(basis)-41 2231 y(functions.)63 b(These)36 b(primitive)g(integrals)h(need)g(only)f(be)h(calculated)i(once)e(and) -41 2351 y(stored:)128 2633 y FC(v)200 2580 y FB(i;j)t Fe(g)192 2643 y FB(x)s(c)351 2633 y FA(\203)490 2514 y FB(N)466 2542 y Fu(X)451 2739 y FB(a)p Ft(\203)p Fz(1)603 2633 y FC(c)653 2647 y FB(a)703 2633 y FC(g)770 2580 y FB(i;j)t Fe(g)766 2643 y FB(a)922 2633 y FC(;)108 b FE(where)93 b FC(g)1489 2580 y FB(i;j)t Fe(g)1485 2643 y FB(a)1641 2633 y FA(\203)1741 2501 y Fu(Z)1826 2633 y FC(d)p Fx(r)p FC(\037)1996 2647 y FB(i)2028 2633 y FC(\204)p Fx(r)p FC(\205G)2230 2647 y FB(a)2280 2633 y FC(\204)p Fx(r)p FC(\205\037)2470 2647 y FB(j)2510 2633 y FC(\204)p Fx(r)21 b FA(\000)g Fx(s)f FA(\000)h Fx(g)r FC(\205)k(:)2850 2830 y FE(\(A.2.11\))106 2950 y(At)42 b(each)h(SCF)f(iteration)h(the)f(auxiliary)g(basis)g(set)g(is)g (\256tted)g(to)h(the)f(actual)-41 3070 y(analytic)30 b(form)d(of)g(the)h(exchange-correlation)i(potential,)f(which)e (changes)h(with)-41 3191 y(the)f(evolving)e(charge)j(density.)37 b(The)26 b(best-\256t)h(coef\256cients)g FC(c)2386 3205 y FB(a)2462 3191 y FE(are)g(evaluated)g(by)-41 3311 y(solving)h(the)h (linear)f(least-squares)i(equation:)1362 3527 y Fb(A)22 b FA(\001)f Fb(c)26 b FA(\203)g Fb(b)f FC(;)1055 b FE(\(A.2.12\))-41 3743 y(where)29 b Fb(A)h 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b(question)h(arises)f(of)h(what)g(\256tting)g(functions)f (to)h(use)f(in)g(the)h(auxiliary)555 1178 y(basis)c(set)g(for)f(the)h (expansion)f(of)h(the)g(exchange-correlation)i(potential.)46 b(Since)555 1298 y FC(v)619 1312 y FB(x)s(c)737 1298 y FE(is)26 b(a)i(basis)e(for)g(the)h(totally)i(symmetric)e(irreducible) f(representation)h(of)g(the)555 1419 y(space)35 b(group,)f(the)h (chosen)f(auxiliary)f(basis)h(functions)f(must)h(be)f(totally)j(sym-) 555 1539 y(metric)g(with)e(respect)i(to)f(all)g(operations)g(of)f(the)i (space)f(group.)57 b(In)35 b(this)f(work,)555 1659 y(a)39 b(universal)e(set)i(of)f(atom-independent)g(Gaussian)g(functions)f(has) i(been)f(em-)555 1780 y(ployed,)g(with)e(even-tempered)h(exponents)f (chosen)h(to)f(span)g(the)h(range)g(from)555 1900 y(1000)k(down)g(to)h (0.1)f(following)g(earlier)h(work)g(by)g(Baerends)g(and)g(te)g(Velde) 3685 1866 y Fz(69)3769 1900 y FE(.)555 2021 y(Only)34 b(\256tting)f(functions)f(with)g(angular)i FC(s)k FE(symmetry)33 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5150 y(A)g(and)h(the)f(total)i(energy)e(by)h (less)f(than)555 5271 y(0.1)d(kcal/mol.)702 5391 y(In)40 b(addition)f(to)h(the)h(standard)f(HF)g(and)g(DFT)g(methods,)i(it)e(is) g(possible)f(to)2118 5640 y(61)p eop %%Page: 62 70 62 69 bop -41 275 a Fw(Chapter)29 b(A.)f(Computer)g(code)h Fv(Crystal)p -41 315 3238 4 v -41 576 a FE(de\256ne)41 b(various)f(approximations)g(which)g(combine)g(elements)i(of)e(both.)75 b(The)-41 696 y(simplest)41 b(of)f(these)i(are)f(the)g(so-called)h Fj(a)e(posteriori)g FE(methods,)k(whereby)d(the)-41 817 y(correlation)30 b(and/or)e(exchange)h(energies)g(are)g(evaluated)h (through)f(integration)-41 937 y(of)g(exchange-correlation)i(density)e (functionals)g(with)g(the)h(converged)f(HF)g(den-)-41 1057 y(sity:)830 1215 y FC(E)889 1229 y FB(x)s(c)981 1215 y FC(\204\032)1089 1176 y FB(H)5 b(F)1196 1215 y FC(\205)25 b FA(\203)1364 1084 y Fu(Z)1449 1215 y FC(d)p Fx(r)16 b FC(\032)1639 1176 y FB(H)5 b(F)1747 1215 y FC(\204)p Fx(r)p FC(\205")1924 1229 y FB(x)s(c)2015 1215 y FC(\204\032)2123 1176 y FB(H)g(F)2231 1215 y FC(\205)25 b(:)524 b FE(\(A.2.15\))106 1420 y(Advanced)18 b(quantum-chemical)i (methods)e(of)g(including)f(correlation)h(effects)-41 1540 y(in)35 b Fv(Crystal)g FE(are)h(still)g(under)e(development,)j (and)f(thus)f(the)h Fj(a)f(posteriori)f FE(DFT)-41 1660 y(correlation-only)42 b(technique)g(is)e(extremely)i(valuable)g(for)e (the)h(estimation)h(of)-41 1781 y(correlation)32 b(effects)e(in)g (periodic)f(Hartree-Fock)j(calculations.)46 b(Results)31 b(of)f(cal-)-41 1901 y(culations)44 b(where)f(the)h(HF)e(exchange)i (energy)g(is)e(subtracted)j(from)d(the)i(total)-41 2021 y(energy,)26 b(and)f(replaced)g(with)f(both)h Fj(a)f(posteriori)f FE(correlation)j Fj(and)d FE(exchange)j(en-)-41 2142 y(ergies)j(have)g(been)g(presented)g(for)f(a)i(set)f(of)f(twenty)i (covalent)g(and)f(ionic)f(solids)-41 2262 y(in)37 b(reference)g(70.)63 b(Finally,)39 b(one)e(may)h(de\256ne)f(a)g Fj(correlation-only)f FE(Kohn-Sham)-41 2383 y(mono-electronic)28 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16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /@BeginSysCorelDict{systemdict/Corel20Dict known{systemdict/Corel20Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel20Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if/d/setdash ld/j/setlinejoin ld/J /setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W /eoclip ld/c/curveto ld/C/c ld/l/lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n /newpath ld/N/newpath ld/P{11 rp}bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/` {}bd/~{}bd/@{}bd/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd /$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type/stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd/$fil 0 def}bd/K{1 index type /stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def}ifelse/$K xd/$Y xd/$M xd/$C xd }bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{/s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{dup 0 ne{setflat}{pop}ifelse}bd /v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate /$ptm xd matrix scale $ptm dup concatmatrix/$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd{/$scp xd/$sca xd/$scf xd}if }bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd}if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd /$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA}{$dsa}ifelse $SCP @ss}if}bd/p{ /$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def}bd/@MN{2 copy le{pop}{exch pop} ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd/InRange{3 -1 roll @MN @MX}bd /wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd/@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd/cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd/rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll 3 rp}bd/WaldoColor_5 where{ pop}{/SetRgb/setrgbcolor ld/GetRgb/currentrgbcolor ld/SetGry/setgray ld/GetGry /currentgray ld/SetRgb2 systemdict/setrgbcolor get def/GetRgb2 systemdict /currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def/rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5 /setcmykcolor ld}{/SetCmyk_5{cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{ pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse /setoverprint where{pop}{/setoverprint{/$op xd}bd}ifelse/currentoverprint where {pop}{/currentoverprint{$op}bd}ifelse/@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd/@trp{exch pop 5 1 roll @tc_5}bd /setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll 4 rp SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry}ifelse}ifelse}bd/findcmykcustomcolor where {pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{ /setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{ CurrentInkName_5 eq{4 index}{0}ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd }ifelse/@scc_5{dup type/booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor} ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd /colorimage where{pop/ColorImage/colorimage ld}{/ColorImage{/ncolors xd pop /dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image} bd}ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep 4 rp}{2 rp}ifelse @rs}bd/@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit}ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for 2 rp}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for 2 rp}for}bd/@pf{@gs $ctm setmatrix $pm concat @stb eoclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{eofill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{ /$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub/$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add/$tly xd $psx 0 eq{@tv}{@th} ifelse}if @gr @np/$bkg false def}bd/@dlt{$fse $fss sub/nff xd $frb dup 1 eq exch 2 eq or{$frt dup $frc $frm $fry $frk @tc_5 4 copy cmyk2rgb rgb2hsb 3 copy /myb xd/mys xd/myh xd $tot $toc $tom $toy $tok @tc_5 cmyk2rgb rgb2hsb 3 1 roll 4 1 roll 5 1 roll sub neg nff div/kdb xd sub neg nff div/kds xd sub neg dup 0 eq{pop $frb 2 eq{.99}{-.99}ifelse}if dup $frb 2 eq exch 0 lt and{1 add}if dup $frb 1 eq exch 0 gt and{1 sub}if nff div/kdh xd}{$frt dup $frc $frm $fry $frk @tc_5 5 copy $tot dup $toc $tom $toy $tok @tc_5 5 1 roll 6 1 roll 7 1 roll 8 1 roll 9 1 roll sub neg nff dup 1 gt{1 sub}if div/$dk xd sub neg nff dup 1 gt{1 sub}if div/$dy xd sub neg nff dup 1 gt{1 sub}if div/$dm xd sub neg nff dup 1 gt {1 sub}if div/$dc xd sub neg nff dup 1 gt{1 sub}if div/$dt xd}ifelse}bd/ffcol{ 5 copy $fsit 0 eq{setcmykcolor pop}{SepMode_5 0 ne{$frn findcmykcustomcolor exch setcustomcolor}{4 rp $frc $frm $fry $frk $frn findcmykcustomcolor exch setcustomcolor}ifelse}ifelse}bd/@ftl{1 index 4 index sub dup $pad mul dup/$pdw xd 2 mul sub $fst div/$wid xd 2 index sub/$hei xd pop Tl @dlt $fss 0 eq{ffcol n 0 0 m 0 $hei l $pdw $hei l $pdw 0 l @cp $ffpnt{fill}{@np}ifelse}if $fss $wid mul $pdw add 0 Tl nff{ffcol n 0 0 m 0 $hei l $wid $hei l $wid 0 l @cp $ffpnt {fill}{@np}ifelse $wid 0 Tl $frb dup 1 eq exch 2 eq or{4 rp myh mys myb kdb add 3 1 roll kds add 3 1 roll kdh add 3 1 roll 3 copy/myb xd/mys xd/myh xd hsb2rgb rgb2cmyk}{$dk add 5 1 roll $dy add 5 1 roll $dm add 5 1 roll $dc add 5 1 roll $dt add 5 1 roll}ifelse}repeat 5 rp $tot dup $toc $tom $toy $tok @tc_5 ffcol n 0 0 m 0 $hei l $pdw $hei l $pdw 0 l @cp $ffpnt{fill}{@np}ifelse 5 rp}bd/@ftrs{ 1 index 4 index sub dup $rox mul/$row xd 2 div 1 index 4 index sub dup $roy mul /$roh xd 2 div 2 copy dup mul exch dup mul add sqrt $row dup mul $roh dup mul add sqrt add dup/$hei xd $fst div/$wid xd 4 index add $roh add exch 5 index add $row add exch Tl $fan rotate 4 rp @dlt $fss 0 eq{ffcol $fty 3 eq{$hei dup neg dup m 2 mul @sqr}{0 0 m 0 0 $hei 0 360 arc}ifelse $ffpnt{fill}{@np}ifelse}if 1.0 $pad 2 mul sub dup scale $hei $fss $wid mul sub/$hei xd nff{ffcol $fty 3 eq {n $hei dup neg dup m 2 mul @sqr}{n 0 0 m 0 0 $hei 0 360 arc}ifelse $ffpnt {fill}{@np}ifelse/$hei $hei $wid sub def $frb dup 1 eq exch 2 eq or{4 rp myh mys myb kdb add 3 1 roll kds add 3 1 roll kdh add 3 1 roll 3 copy/myb xd/mys xd /myh xd hsb2rgb rgb2cmyk}{$dk add 5 1 roll $dy add 5 1 roll $dm add 5 1 roll $dc add 5 1 roll $dt add 5 1 roll}ifelse}repeat 5 rp}bd/@ftc{1 index 4 index sub dup $rox mul/$row xd 2 div 1 index 4 index sub dup $roy mul/$roh xd 2 div 2 copy dup mul exch dup mul add sqrt $row dup mul $roh dup mul add sqrt add dup /$hei xd $fst div/$wid xd 4 index add $roh add exch 5 index add $row add exch Tl 4 rp @dlt $fss 0 eq{ffcol $ffpnt{fill}{@np}ifelse}{n}ifelse/$dang 180 $fst 1 sub div def/$sang $dang -2 div 180 add def/$eang $dang 2 div 180 add def/$sang $sang $dang $fss mul add def/$eang $eang $dang $fss mul add def/$sang $eang $dang sub def nff{ffcol n 0 0 m 0 0 $hei $sang $fan add $eang $fan add arc $ffpnt{fill}{@np}ifelse 0 0 m 0 0 $hei $eang neg $fan add $sang neg $fan add arc $ffpnt{fill}{@np}ifelse/$sang $eang def/$eang $eang $dang add def $frb dup 1 eq exch 2 eq or{4 rp myh mys myb kdb add 3 1 roll kds add 3 1 roll kdh add 3 1 roll 3 copy/myb xd/mys xd/myh xd hsb2rgb rgb2cmyk}{$dk add 5 1 roll $dy add 5 1 roll $dm add 5 1 roll $dc add 5 1 roll $dt add 5 1 roll}ifelse}repeat 5 rp} bd/@ff{/$fss 0 def $o 1 eq setoverprint 1 1 $fsc 1 sub{dup 1 sub $fsit 0 eq{ $fsa exch 5 mul 5 getinterval aload 2 rp/$frk xd/$fry xd/$frm xd/$frc xd/$frn _ def/$frt 1 def $fsa exch 5 mul 5 getinterval aload pop $fss add/$fse xd/$tok xd /$toy xd/$tom xd/$toc xd/$ton _ def/$tot 1 def}{$fsa exch 7 mul 7 getinterval aload 2 rp/$frt xd/$frn xd/$frk xd/$fry xd/$frm xd/$frc xd $fsa exch 7 mul 7 getinterval aload pop $fss add/$fse xd/$tot xd/$ton xd/$tok xd/$toy xd/$tom xd /$toc xd}ifelse $fsit 0 eq SepMode_5 0 eq or dup not CurrentInkName_5 $frn eq and or{@sv $ctm setmatrix eoclip Bbllx Bblly Bburx Bbury $fty 2 eq{@ftc}{1 index 3 index m 2 copy l 3 index 1 index l 3 index 3 index l @cp $fty dup 1 eq exch 3 eq or{@ftrs}{4 rp $fan rotate pathbbox @ftl}ifelse}ifelse @rs/$fss $fse def}{1 0 0 0 0 _ $o @scc_5{fill}if}ifelse}for @np}bd/@Pf{@sv SepMode_5 0 eq $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry eofill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 eq{@ff}{$fil 3 eq{@Pf}{$t $c $m $y $k $n $o @scc_5{eofill} {@np}ifelse}ifelse}ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix}bd/f{@cp F}bd/S{matrix currentmatrix $ctm setmatrix $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc_5{matrix currentmatrix $ptm concat stroke setmatrix} {@np}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/s{@cp S}bd/B{@gs F @gr S} bd/b{@cp B}bd/E{5 array astore exch cvlit xd}bd/@cc{currentfile $dat readhexstring pop}bd/@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq dup/$vectpat xd{/$pfrg true def}{@gs $t $c $m $y $k $n $o @scc_5/$pfrg xd @gr}ifelse/$pm xd/$psy xd/$psx xd /$pyf xd/$pxf xd/$pn xd}bd/@P{/$fil 3 def/$Psn xd array astore/$Prm xd}bd/@k{ /$fil 2 def/$roy xd/$rox xd/$pad xd/$fty xd/$fan xd $fty 1 eq{/$fan 0 def}if /$frb xd/$fst xd/$fsc xd/$fsa xd/$fsit 0 def}bd/@x{/$fil 2 def/$roy xd/$rox xd /$pad xd/$fty xd/$fan xd $fty 1 eq{/$fan 0 def}if/$frb xd/$fst xd/$fsc xd/$fsa xd/$fsit 1 def}bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip 4 rp}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne{/$frg true def 2 rp}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd }{/$frg false def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd /$urx xd/$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop}repeat}ifelse @gr $ctm setmatrix}bd/@M{@sv}bd/@N {/@cc{}def 1 eq{12 -1 roll neg 12 1 roll @I}{13 -1 roll neg 13 1 roll @i} ifelse @rs}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/z{exch findfont exch scalefont setfont} bd/ZB{9 dict dup begin 4 1 roll/FontType 3 def/FontMatrix xd/FontBBox xd /Encoding 256 array def 0 1 255{Encoding exch/.notdef put}for/CharStrings 256 dict def CharStrings/.notdef{}put/Metrics 256 dict def Metrics/.notdef 3 -1 roll put/BuildChar{exch dup/$char exch/Encoding get 3 index get def dup /Metrics get $char get aload pop setcachedevice begin Encoding exch get CharStrings exch get end exec}def end definefont pop}bd/ZBAddChar{findfont begin dup 4 1 roll dup 6 1 roll Encoding 3 1 roll put CharStrings 3 1 roll put Metrics 3 1 roll put end}bd/Z{findfont dup maxlength 2 add dict exch dup{1 index/FID ne{3 index 3 1 roll put}{2 rp}ifelse}forall pop dup dup/Encoding get 256 array copy dup/$fe xd/Encoding exch put dup/Fontname 3 index put 3 -1 roll dup length 0 ne{0 exch{dup type 0 type eq{exch pop}{$fe exch 2 index exch put 1 add}ifelse}forall pop}if dup 256 dict dup/$met xd/Metrics exch put dup /FontMatrix get 0 get 1000 mul 1 exch div 3 index length 256 eq{0 1 255{dup $fe exch get dup/.notdef eq{2 rp}{5 index 3 -1 roll get 2 index mul $met 3 1 roll put}ifelse}for}if pop definefont pop 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(coef\256cient)-41 5030 y FC(\020)21 5044 y FB(A)118 5030 y FE(is)j(de\256ned)i(to)g(reproduce)f(the)h(atomic)g(shape,)j (taking)c(into)h(account)h(the)-41 5150 y(atomic)f(or)e(ionic)g (dimension.)70 b(The)40 b(evaluation)g(of)f(the)h(weight)g FC(W)2731 5164 y FB(A)2825 5150 y FE(requires)-41 5271 y(only)26 b(the)f(summation)g(of)g(exponential)g(functions)g(centred)g (on)g(the)h(neighbours)-41 5391 y(of)31 b(atom)g FC(A)p FE(.)46 b(This)30 b(method)g(can)i(be)f(applied)f(to)h(very)g(complex)g (molecules)g(and)1522 5640 y(68)p eop %%Page: 69 77 69 76 bop 2082 275 a Fw(A.3.)27 b(Numerical)i(integration)g(techniques) p 555 315 3238 4 v 555 576 a FE(crystals,)40 b(and)d(the)h(loss)e(of)h (accuracy)h(is)f(less)g(than)g(one)g(order)g(of)f(magnitude)555 696 y(with)g(respect)h(to)f(the)h(Becke)f(scheme.)61 b(Both)36 b(Savin)g(and)g(Becke)g(weights)g(have)555 817 y(been)29 b(implemented)f(in)g(the)h(new)f(version)g(of)f(the)i Fv(Crystal)f FE(program.)702 937 y(We)37 b(must)g(now)f(consider)h(how) f(to)h(extend)g(the)h(atomic)f(partition)g(method)555 1057 y(to)30 b(a)g(periodic)e(scheme.)42 b(In)30 b(periodic)e(systems)i (the)g(integration)g(is)e(con\256ned)i(to)555 1178 y(the)j(unit)f (cell,)i(which)d(is)h(a)h(\256nite)f(polyhedron)g(in)f(3D)i(periodic)e (systems)h(\(crys-)555 1298 y(tals\),)c(a)f(polyhedron)e(in\256nite)h (in)g(one)g(dimension)e(in)i(2D)g(systems)h(\(slabs\))g(and)f(a)555 1419 y(cylinder)31 b(with)e(in\256nite)h(radius)g(in)f(1D)h(systems)h (\(polymers\).)44 b(The)30 b(same)h(trans-)555 1539 y(formation)37 b(from)f(one)h(multi-centre)h(integral)g(to)f(a)g(sum)g(of)f(atomic)i (integrals)555 1659 y(can)c(be)e(performed)g(as)h(in)f(molecules,)i (but)e(in\256nite)g(lattice)i(sums)e(arise)h(in)f(the)555 1780 y(evaluation)d(of)f(the)h(normalised)f(weight)h(functions:)1609 1997 y FC(W)1693 2011 y FB(A)1748 1997 y FC(\204)p Fx(r)p FC(\205)c FA(\203)2210 1932 y FC(w)2295 1946 y FB(A)2351 1932 y FC(\204)p Fx(r)p FC(\205)p 2012 1969 666 4 v 2012 1989 a Fu(P)2100 2084 y FB(B)2164 1989 y Fu(P)2251 2014 y Ft(1)2251 2087 y Fe(m)2334 2064 y FC(w)2419 2078 y FB(B)s(;)p Fe(m)2549 2064 y FC(\204)p Fx(r)p FC(\205)2713 1997 y(:)706 b FE(\(A.3.33\))555 2220 y(The)29 b(expression)e(for)h (the)g(exchange-correlation)j(energy)e(is)e(thus:)927 2430 y FC(E)991 2391 y FB(D)r(F)7 b(T)1228 2430 y FA(\203)1385 2298 y Fu(Z)1447 2474 y Fg(unit)1461 2529 y(c)s(e)q(ll)1602 2430 y FC(d)p Fx(r)16 b FC(\032)t(\204)p Fx(r)p FC(\205")1971 2391 y FB(D)r(F)7 b(T)2126 2430 y FC(\204)p Fx(r)p FC(\205)25 b FA(\203)2380 2298 y Fu(Z)2443 2474 y Fg(unit)2457 2529 y(c)s(e)q(ll)2598 2430 y FC(d)p Fx(r)15 b FC(\032)t(\204)p Fx(r)p FC(\205")2966 2391 y FB(D)r(F)7 b(T)3121 2430 y FC(\204)p Fx(r)p FC(\205)21 b FA(\002)f FE(1)1228 2724 y FA(\203)1385 2592 y Fu(Z)1447 2768 y Fg(unit)1461 2823 y(c)s(e)q(ll)1602 2724 y FC(d)p Fx(r)c FC(\032)t(\204)p Fx(r)p FC(\205")1971 2685 y FB(D)r(F)7 b(T)2126 2724 y FC(\204)p Fx(r)p FC(\205)2270 2570 y Fu(P)2358 2665 y FB(A)2428 2570 y Fu(P)2516 2596 y Ft(1)2516 2668 y Fe(g)2597 2645 y FC(w)2682 2659 y FB(A;)p Fe(g)2796 2645 y FC(\204)p Fx(r)p FC(\205)p 2265 2696 V 2265 2716 a Fu(P)2352 2811 y FB(B)2416 2716 y Fu(P)2504 2741 y Ft(1)2504 2814 y Fe(m)2586 2791 y FC(w)2671 2805 y FB(B)s(;)p Fe(m)2801 2791 y FC(\204)p Fx(r)p FC(\205)1228 3019 y FA(\203)1385 2928 y Fu(X)1413 3125 y FB(A)1530 2900 y Ft(1)1507 2928 y Fu(X)1540 3117 y Fe(g)1629 2888 y Fu(Z)1692 3063 y Fg(unit)1706 3119 y(c)s(e)q(ll)1847 3019 y FC(d)p Fx(r)15 b FC(\032)t(\204)p Fx(r)p FC(\205")2215 2980 y FB(D)r(F)7 b(T)2371 3019 y FC(\204)p Fx(r)p FC(\205)2678 2950 y(w)2763 2964 y FB(A;)p Fe(g)2877 2950 y FC(\204)p Fx(r)p FC(\205)p 2510 2992 V 2510 3011 a Fu(P)2597 3106 y FB(B)2661 3011 y Fu(P)2748 3037 y Ft(1)2748 3109 y Fe(m)2831 3086 y FC(w)2916 3100 y FB(B)s(;)p Fe(m)3046 3086 y FC(\204)p Fx(r)p FC(\205)1228 3335 y FA(\203)1385 3244 y Fu(X)1413 3441 y FB(A)1530 3217 y Ft(1)1507 3244 y Fu(X)1540 3433 y Fe(g)1629 3204 y Fu(Z)1692 3379 y Fg(unit)1706 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b(tests)h(on)e(three)i(dimensional)e(periodic)g(systems)i(however,)-41 4910 y(we)44 b(have)f(found)f(that)j(a)e(sixth)g(degree)h(polynomial)f (generated)h(by)f(just)h(two)-41 5030 y(iterations)27 b(gives)f(more)g(accurate)i(results.)38 b(This)25 b(difference)h(is)f (presumably)i(re-)-41 5150 y(lated)k(to)e(the)h(higher)f(average)i (coordination)e(of)g(atoms)h(in)f(the)h(solid)e(state)j(and)-41 5271 y(the)c(consequent)g(larger)g(number)f(of)f(vertices)h(in)g(the)g (Voronoi)g(polyhedra.)37 b(The)-41 5391 y(current)e(version)f(of)g(the) h(code)g(thus)f(switches)g(between)i(the)f(different)e(cutoff)1522 5640 y(70)p eop %%Page: 71 79 71 78 bop 2082 275 a Fw(A.3.)27 b(Numerical)i(integration)g(techniques) p 555 315 3238 4 v 555 576 a FE(functions)f(according)h(to)g(the)h (dimensionality)e(of)g(the)h(calculation.)41 b(The)28 b(shape)555 696 y(of)19 b(the)g(smoothed)g(cutoff)g(function)f(allows)h (the)h(lattice)g(sum)e(of)h(weights)g FC(w)3535 710 y FB(B)s(;)p Fe(m)3665 696 y FC(\204)p Fx(r)p FC(\205)555 817 y FE(appearing)33 b(in)f(the)i(denominator)e(of)h(\(A.3.33\),)f (which)g(is)g(in)g(principle)g(in\256nite,)555 937 y(to)f(be)g(limited) f(to)h(a)g(set)g(of)f(atoms)h(within)f(some)h(distance)g FC(B)3018 951 y FB(S)3095 937 y FE(of)f(atom)h FC(A)p FE(.)46 b(The)555 1057 y(question)28 b(of)f(appropriate)g(values)g(for) g(the)h(two)f(parameters)i FC(B)3093 1071 y FB(S)3167 1057 y FE(and)e FC(B)3422 1071 y FB(P)3499 1057 y FE(will)g(be)555 1178 y(addressed)i(in)e(Section)i(A.4.)702 1298 y(Many)j(quadrature)i (techniques)e(exist)g(to)h(evaluate)g(one-dimensional)f(inte-)555 1419 y(grals,)25 b(but)f(the)h(numerical)f(evaluation)h(of)e (multi-dimensional)g(integrals)i(is)e(less)555 1539 y(common,)31 b(and)f(is)f(usually)h(done)g(using)f(direct)i(products)e(of)h (one-dimensional)555 1659 y(quadratures.)61 b(In)35 b(our)g(case,)j (the)d(most)h(ef\256cient)g(numerical)f(integration)h(me-)555 1780 y(thod)f(exploits)f(the)h(atomic,)h(quasi-spherical)f(shape)f(of)g (the)h(integrand)f(by)h(in-)555 1900 y(troducing)29 b(spherical)h (coordinates)f(to)h(separate)h(the)e(radial)h(and)f(angular)h(inte-)555 2021 y(grations:)1062 2140 y Fu(Z)1166 2315 y Fg(all)1124 2370 y(s)s(p)r(ac)s(e)1312 2271 y FC(d)p Fx(r)16 b FC(\032)t(\204)p Fx(r)p FC(\205")1681 2232 y FB(D)r(F)7 b(T)1836 2271 y FC(\204)p Fx(r)p FC(\205W)2049 2285 y FB(A;)p Fe(0)2162 2271 y FC(\204)p Fx(r)p FC(\205)83 b FA(\203)2531 2140 y Fu(Z)2635 2315 y Fg(all)2593 2370 y(s)s(p)r(ac)s(e)2781 2271 y FC(d)p Fx(r)16 b FC(f)e(\204)p Fx(r)p FC(\205)25 b FA(\203)1077 2421 y Fu(Z)1147 2447 y Ft(1)1130 2629 y Fz(0)1227 2553 y FC(dr)1342 2567 y FB(A)1413 2553 y FC(r)1474 2513 y Fz(2)1462 2576 y FB(A)1533 2421 y Fu(Z)1618 2553 y FC(d)p Fu(\332)p FC(f)1816 2567 y FB(A)1871 2553 y FC(\204r)1963 2567 y FB(A)2018 2553 y FC(;)15 b(\022)t(;)g(\036\205) 83 b FA(\203)2531 2421 y Fu(Z)2601 2447 y Ft(1)2583 2629 y Fz(0)2681 2553 y FC(dr)2796 2567 y FB(A)2867 2553 y FC(r)2928 2513 y Fz(2)2916 2576 y FB(A)2972 2553 y FC(A\204r)3137 2567 y FB(A)3192 2553 y FC(\205)25 b(;)159 b FE(\(A.3.39\))555 2803 y(where)38 b FC(r)914 2817 y FB(A)1010 2803 y FA(\203)j(j)p Fx(r)27 b FA(\000)g Fx(R)1398 2817 y FB(A)1453 2803 y FA(j)37 b FE(is)g(the)g(radial)h(distance)f(of)g(the)h(sampling)e (point)h(from)555 2923 y(the)c(nucleus)f FC(A)p FE(,)h(and)e FC(A\204r)1609 2937 y FB(A)1665 2923 y FC(\205)g FE(is)g(the)i(value)f (of)f(the)h(angular)h(integral)g(at)f FC(r)45 b FA(\203)31 b FC(r)3713 2937 y FB(A)3769 2923 y FE(.)555 3044 y(Two-dimensional)18 b(quadrature)i(on)e(the)h(surface)g(of)f(a)h(sphere)f(has)h(been)g (fully)f(de-)555 3164 y(veloped)24 b(by)g(Lebedev)1432 3130 y Fz(81)1515 3164 y FE(,)g(who)g(derived)f(very)h(ef\256cient)g (sets)h(of)e(sampling)h(points)555 3284 y(and)33 b(weights.)50 b(His)31 b(richest)h(set)h(of)f(435)f(points)g(is)h(able)h(to)f (integrate)i(exactly)g(a)555 3405 y(35-degree)c(polynomial)f(in)g(the)h (angular)g(coordinates)g FC(\204\022)t(;)15 b(\036\205)p FE(.)41 b(This)29 b(is)f(enough)555 3525 y(to)e(integrate)g(exactly)g (functionals)e(of)h(the)g(atomic)g(density)g(with)f(angular)i(quan-)555 3645 y(tum)d(numbers)f(of)g(up)g(to)h FC(l)i FA(\203)h FE(6)c(and)h FC(m)j FA(\203)g FE(6)c(\(i.e.)36 b FC(i)22 b FE(functions\))g(and)h(hence)g(allows)555 3766 y(high)j(accuracy)i (for)e(any)g(atomic)h(coordination.)37 b(The)26 b(octahedral)i (symmetry)f(of)555 3886 y(the)h(Lebedev)f(grids)f(confers)h(the)h (additional)e(advantage)j(of)e(a)g(straightforward)555 4007 y(selection)36 b(of)f(irreducible)f(set)i(of)f(points)f(using)h (the)g(local)i(symmetry)f(of)e(each)555 4127 y(atomic)i(site.)58 b(By)35 b(contrast,)i(sampling)e(techniques)h(in)e FC(\204\022)t(;)15 b(\036\205)p FE(,)35 b(based)g(on)g(one-)555 4247 y(dimensional)c (quadrature)j(cannot)e(fully)g(exploit)f(the)i(local)g(symmetry,)g (which)555 4368 y(is)23 b(an)h(important)g(consideration)f(in)g (condensed)g(systems.)37 b(The)23 b(expression)g(for)555 4488 y(the)29 b(angular)g(integral)g FC(A\204r)1638 4502 y FB(A)1694 4488 y FC(\205)f FE(is)f(thus:)943 4738 y FC(A\204r)1108 4752 y FB(A)1163 4738 y FC(\205)e FA(\203)1331 4607 y Fu(Z)1416 4738 y FC(d)p Fu(\332)15 b FC(f)1629 4752 y FB(A)1685 4738 y FC(\204r)1777 4752 y FB(A)1831 4738 y FC(;)g(\022)t(;)g(\036\205)26 b FA(\233)2230 4647 y Fu(X)2270 4847 y FB(i)2352 4738 y FC(!)2445 4752 y FB(i)2477 4738 y FC(f)2532 4752 y FB(A)2587 4738 y FC(\204r)2679 4752 y FB(A)2734 4738 y FC(;)15 b(\022)t(;)g(\036\205)25 b(;)387 b FE(\(A.3.40\))555 5030 y(where)29 b FC(!)949 5044 y FB(i)1009 5030 y FE(are)g(the)f(Lebedev)h(weights.)702 5150 y(We)c(have)g(examined)g(various)f(ways)i(of)e(performing)g(the)h (radial)g(integration.)555 5271 y(Standard)20 b(one-dimensional)e (Gaussian)h(quadrature)g(techniques)3188 5236 y Fz(82)3290 5271 y FE(were)g(found)555 5391 y(to)36 b(be)f(appropriate.)60 b(The)35 b(most)g(critical)h(region)f(of)g(the)h(integration)f(is)g(in) g(the)2118 5640 y(71)p eop %%Page: 72 80 72 79 bop -41 275 a Fw(Chapter)29 b(A.)f(Computer)g(code)h Fv(Crystal)p -41 315 3238 4 v -41 576 a FE(vicinity)34 b(of)g(the)h(nucleus,)h(where)f(the)g(integrand)f(functions,)h(which)f (are)h(func-)-41 696 y(tionals)i(of)e(the)i(electron)h(density,)f(have) g(cusps)f(that)h(span)f(several)h(orders)f(of)-41 817 y(magnitude.)67 b(As)38 b(a)g(result,)i(large)f(numbers)e(of)g (orthogonal)i(polynomials)e(are)-41 937 y(necessary)31 b(for)f(accurate)i(Gaussian)e(quadrature,)i(and)e(therefore)g(a)h(high) e(num-)-41 1057 y(ber)g(of)e(sampling)h(points)g(are)h(required)f(in)g (the)h(calculation.)39 b(The)28 b(most)h(impor-)-41 1178 y(tant)36 b(characteristic)h(of)d(the)h(radial)g(integration)g(is)g (thus)f(the)i Fj(degree)e FE(\(number)-41 1298 y(of)40 b(points\))g(in)f(the)i(quadrature)g(of)f(the)g(cusp.)73 b(A)40 b(natural)i(idea)e(therefore,)j(is)-41 1419 y(the)29 b(subdivision)d(of)i(the)i(integration)f(region)f(into)g(segments,)h (with)g(a)g(separate)-41 1539 y(numerical)g(quadrature)g(for)f(each)h (segment:)516 1662 y Fu(Z)586 1687 y Ft(1)569 1869 y Fz(0)667 1793 y FC(dr)e(f)14 b(\204r)e(\205)83 b FA(\203)1295 1674 y FB(N)1270 1702 y Fu(X)1265 1902 y FB(i)p Ft(\203)p Fz(1)1399 1662 y Fu(Z)1468 1687 y FB(r)1502 1700 y Fg(i)1451 1869 y FB(r)1485 1882 y Fg(i)p Ff(\000)p Fs(1)1602 1793 y FC(dr)27 b(f)14 b(\204r)e(\205)20 b FA(\202)2075 1662 y Fu(Z)2144 1687 y Ft(1)2127 1869 y FB(r)2161 1882 y Fg(i)2225 1793 y FC(dr)27 b(f)14 b(\204r)e(\205)1108 2122 y FA(\233)1295 2003 y FB(N)1270 2031 y Fu(X)1265 2231 y FB(i)p Ft(\203)p Fz(1)1426 1998 y FB(n)1476 2011 y Fg(i)1411 2031 y Fu(X)1399 2231 y FB(k)p Ft(\203)p Fz(1)1546 2122 y FC(f)i(\204r)1719 2082 y FB(i)1707 2149 y(k)1751 2122 y FC(\205w)1879 2136 y FB(k)1944 2122 y FA(\202)2039 2000 y FB(n)2089 2010 y Fg(N)t Ff(\202)p Fs(1)2071 2031 y Fu(X)2066 2231 y FB(l)p Ft(\203)p Fz(1)2225 2122 y FC(f)g(\204r)2398 2082 y FB(i)2386 2149 y(l)2430 2122 y FC(\205w)2558 2136 y FB(l)2613 2122 y FC(:)210 b FE(\(A.3.41\))-41 2374 y(In)29 b(principle,)d(such)j(a)f(procedure)h 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y(merical)e(integration)f(of)f(a)h(function)f(between)i(limits)e (of)g(zero)h(and)g(in\256nity)f(can)-41 3578 y(be)j(performed)e(using)h (the)h(weights)f(and)h(the)g(nodes)f(of)f(polynomials)i(orthogo-)-41 3698 y(nal)24 b(to)g(an)g(exponential)f(weight)h(function,)g(such)f(as) h(the)g(Laguerre)g(polynomials.)-41 3819 y(Alternatively)31 b(polynomials)d(orthogonal)i(on)e(a)i Fj(\256nite)e FE(interval)h(can)h (be)f(used)f(by)-41 3939 y(mapping)g(the)g(\256nite)h(intervals)f(onto) g(an)h(in\256nite)e(interval)i(by)f(means)g(of)g(an)g(op-)-41 4059 y(portune)h(transformation)f(of)g(the)h(coordinates,)844 4158 y Fu(Z)913 4184 y Ft(1)896 4366 y Fz(0)994 4289 y FC(dr)e(f)14 b(\204r)e(\205)26 b FA(\203)1477 4158 y Fu(Z)1547 4184 y Fz(1)1530 4366 y Ft(\000)p Fz(1)1640 4289 y FC(dt)20 b(f)14 b(\204r)e(\204t)t(\205\205)2124 4224 y(dr)p 2124 4262 128 4 v 2132 4356 a(dt)2286 4289 y(:)537 b FE(\(A.3.42\))-41 4498 y(A)22 b(logarithmic)g(transformation) 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b(the)g(surface)g(of)f(the)h(sphere,)j(and)c(the)h(number)g(of)f (angular)h(points)f(as)h(a)555 817 y(function)33 b(of)g(the)h(radius)e (must)i(therefore)f(be)h(optimised)e(for)g(an)i(ef\256cient)g(im-)555 937 y(plementation)40 b(of)d(the)i(scheme.)68 b(In)38 b(general,)k(the)c(angular)h(accuracy)h(may)f(be)555 1057 y(decreased)32 b(in)e(the)h(region)f(of)g(the)h(nucleus,)g(since)f (the)h(electronic)h(density)e(and)555 1178 y(functionals)36 b(thereof)g(become)g(spherically)g(symmetric)g(as)g(the)h(radius)e(of)g (the)555 1298 y(sphere)c(tends)h(to)f(zero.)47 b(A)31 b(set)h(of)f(points)f(for)g(a)i(spherical)f(quadrature)h(can)g(be)555 1419 y(de\256ned)25 b(by)g(the)h(degree)f(L)g(of)f(the)i(angular)g (polynomial)e(that)j(can)e(be)g(integrated)555 1539 y(exactly.)38 b(Up)22 b(to)h FC(L)j FA(\203)g FE(35,)c(Lebedev)g(octahedral)j(grids)c (may)i(be)g(used.)36 b(For)22 b FC(L)k(>)g FE(35,)555 1659 y(a)31 b(product)f(formula)g(can)g(be)g(applied,)g(namely)h(the)f 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(calculated)i(observables)e(on)g(these)h(parameters)g(may)g(then)f(be)g (used)g(to)2118 5640 y(73)p eop %%Page: 74 82 74 81 bop -41 275 a Fw(Chapter)29 b(A.)f(Computer)g(code)h Fv(Crystal)p -41 315 3238 4 v -41 576 a FE(de\256ne)e(their)g(default)g (values.)38 b(This)26 b(process)h(will)f(now)h(be)g(discussed)f(in)g (detail.)-41 696 y(The)k(use)h(of)f(the)h(linear)f(scaling)h(of)f(the)h (angular)g(degree)g(L\(r\))g(discussed)e(at)j(the)-41 817 y(end)23 b(of)g(section)h(A.3)e(simpli\256es)h(the)g(parameter)i (space)f(to)g(be)f(optimised.)36 b(Given)-41 937 y(that)29 b(the)f(radial)g(integration)g(is)f(performed)g(on)h(a)g(single)f (in\256nite)g(interval)h(over)-41 1057 y(a)c(number)f(of)g(points)g(R,) g(then)h(a)g(simultaneous)g(variation)f(of)g(both)h(R)f(and)h(L)f(max) -41 1178 y(may)j(be)g(made.)37 b(Optimum)25 b(pairs)g(of)g(values)h (may)g(be)f(selected)i(to)f(minimise)e(the)-41 1298 y(error)30 b(for)g(a)g(given)g(number)f(N)h(of)g(grid)f(points)g(per)h(atom.)45 b(Since)30 b(the)h(same)f(cri-)-41 1419 y(teria)25 b(must)f(be)h (applied)e(to)i(both)f(periodic)g(\(crystals,)i(slabs)e(and)g (polymers\))h(and)-41 1539 y(non-periodic)f(systems)h(\(atoms)g(and)g (molecules\),)h(we)f(have)g(used)f(a)h(set)g(of)f(eigh-)-41 1659 y(teen)36 b(systems)f(in)f(the)i(calibration)f(including)f(closed) h(and)g(open-shell)g(atoms,)-41 1780 y(molecules,)f(polymers,)f(slabs,) g(and)g(covalent,)h(semi-ionic)d(and)i(ionic)e(crystals.)-41 1900 y(A)j(complete)h(list)f(of)g(these)h(systems)f(and)g(the)h(basis)e (sets)i(used)e(can)i(be)f(found)-41 2021 y(in)g(the)i(paper)f(of)f (Towler,)i(Zupan,)g(and)f(Caus)1826 2020 y(\301)1829 2021 y(a)1879 1986 y Fz(50)1962 2021 y FE(.)57 b(For)35 b(atoms)h(and)e(molecules)-41 2141 y(we)25 b(use)g(various)e(standard)i (sets,)h(while)e(those)h(for)f(the)h(crystalline)h(calculations)-41 2261 y(have)j(a)f(similar)f(structure)i(to)g(standard)f(molecular)h (sets)g(such)f(as)g(STO-3G)g(and)-41 2382 y(6-21G.)106 2502 y(A)33 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4898 4 121 v 900 4862 a(experiment)p 1631 4898 V 1969 4898 V 744 w(5.57)p 2534 4898 V 335 w(28.5)p 3031 4898 V 368 w(-189)p 3667 4898 V 680 4902 2990 4 v 555 5174 a(Table)20 b(A.4.5:)33 b(Effect)19 b(of)g(computational)i(parameters)g(on)e (calculated)j(properties)555 5294 y(of)28 b(NaCl.)2118 5640 y(77)p eop %%Page: 78 86 78 85 bop -41 275 a Fw(Chapter)29 b(A.)f(Computer)g(code)h Fv(Crystal)p -41 315 3238 4 v 1522 5640 a FE(78)p eop %%Page: 79 87 79 86 bop 555 1241 a Fy(Bibliography)595 1668 y Fz(1)687 1703 y FE(R.)50 b(G.)f(Parr)i(and)e(W.)h(Yang,)55 b Fj(Density)49 b(Functional)f(Theory)h(of)i(Atoms)f(and)687 1823 y(Molecules)p FE(,)28 b(\(Oxford,)g(New)g(York,)g(1989\).)595 1997 y Fz(2)687 2031 y FE(R.)c(M.)f(Dreisler)i(and)f(E.)f(K.)g(U.)h(Gross,)g Fj(Density)f(Functional)f(Theory)p FE(,)i(\(Springer-)687 2152 y(Verlag,)29 b(Berlin,)e(1990\).)595 2325 y Fz(3)687 2360 y FE(L.)h(H.)f(Thomas,)38 b(Proc.)29 b(Camb.)f(Phil.)f(Soc.)i Fx(23)p FE(,)f(542)f(\(1927\).)595 2533 y Fz(4)687 2567 y FE(E.)i(Fermi,)42 b(Rend.)29 b(Accad.,)h(Lincei)e Fx(6)p FE(,)i(602)e(\(1927\);)g(E.)h(Fermi,)42 b(Z.)29 b(Phys.)g Fx(48)p FE(,)g(73)687 2688 y(\(1928\).)595 2861 y Fz(5)687 2896 y FE(P.)f(A.)g(M.)g(Dirac,)h(Cambridge)f(Philos.)f(Soc.)i Fx(26)p FE(,)e(376)g(\(1930\).)595 3069 y Fz(6)687 3104 y FE(E.)h(P.)g(Wigner,)f(Phys.)i(Rev.)f Fx(46)p FE(,)f(1002)g (\(1934\).)595 3277 y Fz(7)687 3312 y FE(J.)h(C.)g(Slater,)h(Phys.)g (Rev.)f Fx(81)p FE(,)f(385)g(\(1951\),)595 3485 y Fz(8)687 3520 y FE(J.)h(G)844 3519 y(\302)847 3520 y(asp)1001 3519 y(\302)1004 3520 y(ar,)h(Acta)g(Phys.)g(Acad.)f(Sci.)g(Hung.)g Fx(3)p FE(,)g(263)e(\(1954\).)595 3693 y Fz(9)687 3728 y FE(P.)i(Hohenberg)g(and)h(W.)f(Kohn,)37 b(Phys.)28 b(Rev.)g Fx(136)p FE(,)g(B864)f(\(1964\).)555 3901 y Fz(10)687 3936 y FE(M.)h(Levy,)g(Proc.)g(Natl.)h(Acad.)g(Sci.)f(U.S.A.) g Fx(76)p FE(,)f(6062)g(\(1979\).)555 4109 y Fz(11)687 4144 y FE(W.)h(Kohn)g(and)g(L.)g(J.)g(Sham,)39 b(Phys.)28 b(Rev.)g Fx(140)p FE(,)g(A1133)e(\(1965\).)555 4317 y Fz(12)687 4351 y FE(U.)g(von)g(Barth)h(and)f(L.)g(Hedin,)35 b(J.)26 b(Phys.)g(C:)g(Solid)g(State)j(Phys.)d Fx(5)p FE(,)g(1629)f(\(1972\).)555 4525 y Fz(13)687 4559 y FE(S.)j(H.)g (Vosko,)f(L.)h(Wilk,)f(and)i(M.)f(Nusair,)f(Can.)h(J.)g(Phys.)g Fx(58)p FE(,)g(1200)e(\(1980\).)555 4733 y Fz(14)687 4767 y FE(J.)i(P.)g(Perdew)h(and)f(A.)h(Zunger,)e(Phys.)h(Rev.)g(B)g Fx(23)p FE(,)g(5048)f(\(1981\).)555 4941 y Fz(15)687 4975 y FE(J.)h(P.)g(Perdew)h(and)f(Y.)g(Wang,)h(Phys.)f(Rev.)g(B)g Fx(45)p FE(,)g(13244)d(\(1992\).)555 5149 y Fz(16)687 5183 y FE(D.)j(M.)g(Ceperley)h(and)f(B.)g(J.)g(Alder,)g(Phys.)g(Rev.)g (Lett.)h Fx(45)p FE(,)f(566)f(\(1980\).)555 5357 y Fz(17)687 5391 y FE(L.)h(Kleinman)g(and)g(S.)h(Lee,)f(Phys.)g(Rev.)g(B)g Fx(37)p FE(,)g(4634)e(\(1988\).)2118 5640 y(79)p eop %%Page: 80 88 80 87 bop -41 275 a Fw(Bibliography)p -41 315 3238 4 v -41 542 a Fz(18)91 576 y FE(S.-K.)28 b(Ma)h(and)f(K.)g(A.)g (Brueckner,)f(Phys.)i(Rev.)f Fx(165)p FE(,)f(18)h(\(1968\).)-41 742 y Fz(19)91 777 y FE(D.)g(C.)g(Langreth)h(and)f(M.)g(J.)g(Mehl,)g (Phys.)g(Rev.)g(B)g Fx(28)p FE(,)g(1809)e(\(1983\).)-41 943 y Fz(20)91 977 y FE(J.)i(P.)g(Perdew,)h(Phys.)f(Rev.)g(Lett.)h Fx(55)p FE(,)e(1665)g(\(1985\);)g(e.)h Fj(ibid)p FE(.)f Fx(55)p FE(,)h(2370)f(\(1985\).)-41 1143 y Fz(21)91 1178 y FE(J.)38 b(P.)h(Perdew)f(and)h(Y.)f(Wang,)j(Phys.)d(Rev.)g(B)g Fx(33)p FE(,)j(8800)36 b(\(1986\);)43 b(e.)38 b Fj(ibid)p FE(.)g Fx(40)p FE(,)91 1298 y(3399)26 b(\(1989\).)-41 1464 y Fz(22)91 1499 y FE(J.)i(P.)g(Perdew,)h(Phys.)f(Rev.)g(B)g Fx(33)p FE(,)f(8822)g(\(1986\);)g(e.)h Fj(ibid)p FE(.)f Fx(34)p FE(,)h(7406)f(\(1986\).)-41 1665 y Fz(23)91 1700 y FE(A.)h(Becke,)g(Phys.)g(Rev.)g(A)h Fx(38)p FE(,)f(3098)e(\(1988\).) -41 1866 y Fz(24)91 1900 y FE(C.)h(Lee,)i(W.)f(Yang,)g(and)g(R.)g(G.)g (Parr,)h(Phys.)f(Rev.)g(B)g Fx(37)p FE(,)g(785)f(\(1988\).)-41 2066 y Fz(25)91 2101 y FE(J.)h(P.)g(Perdew,)h(Physica)f(B,)g Fx(172)p FE(,)g(1)g(\(1991\).)-41 2267 y Fz(26)91 2301 y FE(J.)g(P.)g(Perdew,)g(J.)g(A.)g(Chevary,)g(S.)h(H.)e(Vosko,)h(K.)f (A.)h(Jackson,)h(M.)e(R.)h(Pederson,)91 2422 y(D.)39 b(J.)f(Singh,)j(and)d(C.)g(Fiolhais,)i(Phys.)f(Rev.)f(B)h Fx(46)p FE(,)h(6671)d(\(1992\);)42 b Fx(48)p FE(,)f(4978)91 2542 y(\(1993\))27 b(\(E\).)-41 2708 y Fz(27)91 2743 y FE(J.)e(P.)h(Perdew,)g(K.)f(Burke,)g(and)g(M.)h(Ernzerhof,)f(Phys.)g (Rev.)g(Lett.,)i(accepted)g(for)91 2863 y(publication,)h(\(1996\).)-41 3029 y Fz(28)91 3064 y FE(P.)h(Bagno,)g(O.)g(Jepsen,)g(and)g(O.)g (Gunnarsson,)f(Phys.Rev.B.)g(40,)g(1997)g(\(1989\);)91 3184 y(T.)g(L.)f(Cook,)g(D.)i(S.)f(Stakes,)h(Science)g Fx(267)p FE(,)f(1975)f(\(1995\).)-41 3350 y Fz(29)91 3385 y FE(W.)33 b(J.)h(Broad,)g(New)g(York)f(Times,)h(Science)h(Times,) f(B7,)f(\(Thursday,)i(April)e(4,)91 3505 y(1995\).)-41 3671 y Fz(30)91 3706 y FE(J.)28 b(Weber,)g(private)h(communication.)-41 3872 y Fz(31)91 3907 y FE(A.)f(Zupan,)g(work)f(in)h(progress.)-41 4073 y Fz(32)91 4107 y FE(D.)g(R.)g(Hartree,)39 b(Proc.)29 b(Cambridge)f(Roy.)g(Soc.)g Fx(24)p FE(,)g(89)g(\(1928\).)-41 4273 y Fz(33)91 4308 y FE(V.)g(A.)g(Fock,)g(Z.)g(Physik)f Fx(61)p FE(,)h(126)f(\(1930\).)-41 4474 y Fz(34)91 4508 y FE(W.)21 b(Kohn,)27 b(Density)22 b(Functional)f(Theory:)35 b(Fundamentals)22 b(and)f(Applications,)91 4629 y(in)e Fj(Highlights)f(of)i(Condensed)e(Matter)h(Theory)p FE(,)h(edited)g(by)f (F.Bassani,)h(F.)f(Fumi,)91 4749 y(and)28 b(M.)g(P.)g(Tosi,)f(pages)i (1\26115,)e(North-Holland,)h(1985.)-41 4915 y Fz(35)91 4950 y FE(W.)35 b(Kohn)g(and)h(P.)g(Vashishta,)63 b Fj(General)35 b(density)f(functional)h(theory)p FE(,)i(pages)91 5070 y(79\261147,)f(Plenum,)29 b(New)f(York,)f(1983.)-41 5236 y Fz(36)91 5271 y FE(D.)e(C.)f(Langreth)h(and)g(J.)f(P.)h(Perdew,)g (Solid)g(State)h(Commun.)e Fx(17)p FE(,)h(1425)e(\(1975\);)91 5391 y(Phys.)28 b(Rev.)g(B)g Fx(15)p FE(,)g(2884)e(\(1977\).)1522 5640 y(80)p eop %%Page: 81 89 81 88 bop 3223 275 a Fw(Bibliography)p 555 315 3238 4 v 555 542 a Fz(37)687 576 y FE(O.)19 b(Gunnarson)g(and)g(B.)g(I.)g (Lundquist,)h(Phys.)f(Rev.)g(B)g Fx(13)p FE(,)h(4274)d(\(1976\);)k(O.)e (Gun-)687 696 y(narson,)28 b(M.)g(Jonson,)g(and)g(B.)f(I.)i(Lundquist,) e(Phys.)h(Rev.)g(B)g Fx(20)p FE(,)g(3136)e(\(1979\).)555 871 y Fz(38)687 905 y FE(M.)i(Levy)g(and)h(J.)f(P.)g(Perdew,)g(Phys.)g (Rev.)g(A)h Fx(32)p FE(,)f(2010)e(\(1985\).)555 1079 y Fz(39)687 1114 y FE(M.)32 b(Levy,)g(Int.)h(J.)e(Quantum)i(Chem.,)f (Symp.)g Fx(S23)p FE(,)g(617)f(\(1989\);)h(Phys.)g(Rev.)g(A)687 1234 y Fx(43)p FE(,)c(4637)e(\(1991\).)555 1408 y Fz(40)687 1443 y FE(J.)h(P.)g(Perdew,)g(in)g Fw(Electronic)h(Structure)g(of)f (Solids)f('91)p FE(,)g(edited)h(by)g(P.)g(Ziesche)687 1563 y(and)h(H.)g(Eschrig)g(\(Akademie)g(Verlag,)h(Berlin,)e(1991\),)g (page)i(11.)555 1737 y Fz(41)687 1772 y FE(M.)f(Gell-Mann)h(and)g(K.)e (A.)h(Brueckner,)g(Phys.)g(Rev.)g Fx(106)p FE(,)g(364)f(\(1957\).)555 1946 y Fz(42)687 1980 y FE(G.)h(L.)g(Oliver)g(and)g(J.)g(P.)g(Perdew,)h (Phys.)f(Rev.)g(A)g Fx(32)p FE(,)g(2010)f(\(1985\).)555 2155 y Fz(43)687 2189 y FE(C.)f(Bowen,)h(G.)f(Sugiyama,)i(and)f(B.)f (J.)h(Alder,)g(Phys.)g(Rev.)f(B)h Fx(50)p FE(,)f(14838)f(\(1994\);)687 2309 y(S.)41 b(Moroni,)h(D.M.)e(Ceperley,)k(and)d(G.)f(Senatore,)45 b(Phys.)40 b(Rev.)g(Lett.)i Fx(75)p FE(,)h(689)687 2430 y(\(1995\).)555 2604 y Fz(44)687 2638 y FE(G.)28 b(Ortiz,)g(Phys.)h (Rev.)f(B)g Fx(45)p FE(,)f(11328)f(\(1992\).)555 2813 y Fz(45)687 2847 y FE(J.)i(P.)g(Perdew)h(and)f(K.Burke,)f(Int.)i(J.)f (Quantum)h(Chem.)e Fx(57)p FE(,)h(309)f(\(1996\).)555 3021 y Fz(46)687 3056 y FE(N.)21 b(Moll,)i(M.)e(Bockstedte,)i(M.)e (Fuchs,)h(E.)f(Pehlke,)i(and)e(M.)h(Schef\257er,)g(Phys.)g(Rev.)687 3176 y(B)28 b Fx(52)p FE(,)g(2550)e(\(1995\).)555 3350 y Fz(47)687 3385 y FE(P.)i(H.)g(T.)f(Philipsen)h(and)g(E.)g(J.)g (Baerends,)g(Phys.)g(Rev.)g(B)g Fx(54)p FE(,)g(5326)e(\(1996\).)555 3559 y Fz(48)687 3594 y FE(A.)g(Zupan,)h(J.)f(P.)g(Perdew,)h(K.)f (Burke,)g(and)h(M.)f(Caus)2693 3593 y(\302)2696 3594 y(a,)g Fw(Density-gradient)i(anal-)687 3714 y(ysis)e(for)h(density)f (functional)h(theory:)38 b(Application)27 b(to)g(atoms)p FE(,)g(to)h(appear)f(in)687 3834 y(Int.)i(J.)f(Quantum)h(Chem.)e Fx(S)p FE(.)555 4009 y Fz(49)687 4043 y FE(R.)f(Dovesi,)f(C.)h(Pisani,) f(C.)g(Roetti,)i(M.)f(Caus)2372 4042 y(\301)2375 4043 y(a,)g(and)g(V.)f(R.)h(Saunders,)g Fj(CRYSTAL)687 4163 y(88)i(-)g(An)h(ab)f(initio)g(all)g(electron)g(LCAO)h(Hartree-Fock)g (program)e(for)h(periodic)687 4284 y(systems)p FE(,)43 b(\(QCPE)e(Program)h(No.)e(577,)i(Quantum)g(Chemistry)e(Program)i(Ex-) 687 4404 y(change,)g(Indiana)c(University,)i(Bloomington,)g(Indiana,)h (1989\);)h(R.)c(Dovesi,)687 4524 y(V.)26 b(R.)g(Saunders,)h(and)g(C.)e (Roetti,)j Fj(Crystal)e(92)f(user)h(documentation)p FE(,)f(\(Univer-) 687 4645 y(sity)j(of)g(Torino)f(and)i(SERC)f(Daresbury)h(Laboratory,)g (1992\).)555 4819 y Fz(50)687 4854 y FE(M.)f(Towler,)g(A.)g(Zupan,)g (M.)f(Caus)1996 4853 y(\301)1999 4854 y(a,)i(Comp.)e(Phys.)h(Comm.)f Fx(98)p FE(,)h(181)f(\(1996\).)555 5028 y Fz(51)687 5062 y FE(M.)h(Kohout,)g(A.)g(Savin,)g(H.)f(Preuss,)h(J.)h(Chem.)e(Phys)i Fx(95)p FE(,)e(1928)g(\(1991\).)555 5236 y Fz(52)687 5271 y FE(H.)h(Schmider,)h(R.)g(P.)f(Sagar,)i(and)f(V.)g(H.)f(Smith,)h (Jr.,)f(J.)h(Chem.)f(Phys.)h Fx(94)p FE(,)f(8627)687 5391 y(\(1991\);)f Fj(idem)p FE(,)g(Can.)h(J.)g(Chem.)g Fx(70)p FE(,)g(506)f(\(1992\).)2118 5640 y(81)p eop %%Page: 82 90 82 89 bop -41 275 a Fw(Bibliography)p -41 315 3238 4 v -41 542 a Fz(53)91 576 y FE(G.)30 b(Herzberg,)i Fj(Spectra)e(of)h (Diatomic)f(Molecules)p FE(,)h(\(Van)h(Nostrand-Reinhold,)91 696 y(Princeton,)c(N.J.,)g(1970\).)-41 873 y Fz(54)91 907 y FE(W.)37 b(G.)h(Wyckoff,)h Fj(Crystal)e(Structures)p FE(,)i(2nd)d(ed.)i(\(Wiley,)i(New)e(York,)h(1963\),)91 1027 y(Vol.)28 b(1.)-41 1204 y Fz(55)91 1238 y FE(A.)g(D.)g(Becke,)g (J.)h(Chem.)e(Phys.)h Fx(97)p FE(,)g(9173)f(\(1992\).)-41 1414 y Fz(56)91 1449 y FE(E.)21 b(I.)g(Proynov,)i(E.)d(Ruiz,)j(A.)e (Vela,)i(and)f(D.)g(R.)f(Salahub,)i(Int.)f(J.)f(Quantum)i(Chem.)91 1569 y(S)29 b Fx(29)p FE(,)e(61)h(\(1995\).)-41 1745 y Fz(57)91 1780 y FE(V.)g(Ozolin)504 1779 y(\317)509 1780 y(s)g(and)g(M.)g(K)980 1779 y(\310)980 1780 y(orling,)f(Phys.)i (Rev.)f(B)g Fx(48)p FE(,)f(18304)f(\(1993\).)-41 1956 y Fz(58)91 1990 y FE(C.)h(Filippi,)f(D.)j(J.)f(Singh,)g(and)g(C.)f (Umrigar,)h(Phys.)g(Rev.)g(B)g Fx(50)p FE(,)g(14947)e(\(1994\).)-41 2167 y Fz(59)91 2201 y FE(N.)21 b(Moll,)h(M.)g(Bockstedte,)h(M.)e (Fuchs,)h(E.)f(Pehlke,)i(and)e(M.)g(Schef\257er,)i(Phys.)e(Rev.)91 2321 y(B)28 b Fx(52)p FE(,)g(2550)e(\(1995\).)-41 2498 y Fz(60)91 2532 y FE(J.)20 b(C.)g(Grossman,)i(L.)e(Mitas,)i(and)f(K.)f (Raghavachari,)j(Phys.)e(Rev.)f(Lett.)h Fx(75)p FE(,)h(3870)91 2653 y(\(1995\);)27 b Fx(76)p FE(,)h(1006)e(\(1996\))h(\(E\).)-41 2829 y Fz(61)91 2863 y FE(D.)h(R.)g(Hamann,)h(Phys.)f(Rev.)g(Lett.)h Fx(76)p FE(,)e(660)g(\(1996\).)-41 3039 y Fz(62)91 3074 y FE(B.)33 b(G.)g(Johnson,)i(P.)e(M.)h(W.)f(Gill,)h(and)g(J.)g(A.)f (Pople,)i(J.)f(Chem.)f(Phys.)g Fx(98)p FE(,)i(5612)91 3194 y(\(1993\).)-41 3371 y Fz(63)91 3405 y FE(D.)28 b(Porezag)i(and)e(M.)g(R.)g(Pederson,)g(J.)g(Chem.)g(Phys.)g Fx(102)p FE(,)g(9345)e(\(1995\).)-41 3581 y Fz(64)91 3616 y FE(B.)38 b(G.)h(Johnson,)h(C.)f(A.)f(Gonzales,)k(P.)d(M.)g(W.)f (Gill,)j(and)e(J.)g(A.)f(Pople,)k(Chem.)91 3736 y(Phys.)28 b(Lett.)h Fx(221)p FE(,)f(100)f(\(1994\).)-41 3912 y Fz(65)91 3947 y FE(S.)40 b(P.)h(Walch,)i(R.)e(J.)f(Duchovic,)j(C.)c(M.) h(Rohl\256ng,)k(J.)c(Chem.)g(Phys)g Fx(90)p FE(,)j(3230)91 4067 y(\(1989\).)-41 4243 y Fz(66)91 4278 y FE(S.)28 b(P.)g(Walch,)h(J.)f(J.)g(Chem.)g(Phys)h Fx(93)p FE(,)e(2384)g (\(1990\).)-41 4454 y Fz(67)91 4488 y FE(C.)d(Pisani,)g(R.)g(Dovesi,)h (and)g(C.)e(Roetti,)j Fj(Hartree-Fock)f(Ab)g(Initio)g(Treatment)e(of)91 4609 y(Crystalline)k(Systems)h FE(\(Springer-Verlag,)h(Berlin,)e (1988\);)-41 4785 y Fz(68)91 4819 y FE(CRYSTAL)38 b(95,)g(Universit) 1135 4818 y(\301)1138 4819 y(a)g(di)f(Torino)f(and)i(Daresbury)h (Laboratory)f(\(to)h(be)91 4940 y(published\).)-41 5116 y Fz(69)91 5150 y FE(G.)21 b(te)i(Velde,)g Fj(Numerical)e(integration)f (and)h(other)g(methodological)g(aspects)g(of)91 5271 y(band)f(structure)g(calculations)p FE(,)g(Disertation,)j(Vrije)d (Universiteit)g(Amsterdam)91 5391 y(\(1990\);)27 b(G.)h(te)h(Velde,)f (E.J.)f(Baerends,)h(Phys.)g(Rev.)g(B)g Fx(44)p FE(,)g(7888)f(\(1991\).) 1522 5640 y(82)p eop %%Page: 83 91 83 90 bop 3223 275 a Fw(Bibliography)p 555 315 3238 4 v 555 542 a Fz(70)687 576 y FE(M.)28 b(Caus)1038 575 y(\301)1041 576 y(a)h(and)f(A.)g(Zupan,)g(Chem.)f(Phys.)h(Lett.)h Fx(220)p FE(,)f(145)f(\(1994\).)555 745 y Fz(71)687 779 y FE(C.)21 b(W.)f(Murray,)j(G.)e(J.)g(Lamming,)h(N.)e(C.)g(Handy,)j (and)e(R.)g(D.)g(Amos,)h(Chem.)e(Phys.)687 900 y(Lett.)29 b Fx(199)p FE(,)f(551)f(\(1992\).)555 1069 y Fz(72)687 1103 y FE(P.)k(M.)h(W.)f(Gill,)g(B.)g(G.)g(Johnson,)h(J.)f(A.)g(Pople,) h(and)g(M.)f(J.)g(Frisch,)h(Chem.)e(Phys.)687 1224 y(Lett.)f Fx(197)p FE(,)f(499)f(\(1992\).)555 1393 y Fz(73)687 1427 y FE(R.)40 b(Dovesi,)i(C.)e(Pisani,)i(F.)d(Ricca,)44 b(and)c(C.)f(Roetti,)44 b(J.)c(Chem.)f(Soc.:)62 b(Faraday)687 1547 y(Transactions)29 b(II)f Fx(70)p FE(,)g(1381)f(\(1974\).)555 1716 y Fz(74)687 1751 y FE(C.)43 b(Pisani)g(and)g(R.)g(Dovesi,)k(Int.)c (J.)h(Quantum)g(Chem.)e Fx(17)p FE(,)47 b(501)42 b(\(1980\);)50 b(R.)687 1871 y(Dovesi,)31 b(C.)g(Pisani,)g(C.)f(Roetti,)i(and)f(V.)g (R.)g(Saunders,)h(Phys.)f(Rev.)g(B)f Fx(28)h FE(5781)687 1991 y(\(1983\).)555 2160 y Fz(75)687 2195 y FE(V.)38 b(R.)g(Saunders,)j(C.)c(Freyria-Fava,)42 b(R.)37 b(Dovesi,)k(L.)c (Salasco,)42 b(and)c(C.)g(Roetti,)687 2315 y(Mol.)28 b(Phys.)g Fx(77)p FE(,)g(629)f(\(1992\).)555 2484 y Fz(76)687 2519 y FE(A.)39 b(St.)g(Amant)g(and)g(D.)g(R.)f(Salahub,)k(Chem.)c (Phys.)h(Lett.)g Fx(169)p FE(,)i(387)c(\(1990\);)687 2639 y(D.)28 b(R.)g(Salahub,)h(Abst.)g(Papers)f(Am.)g(Chem.)g(Soc.)h Fx(209)p FE(,)e(6)h(\(1995\).)555 2808 y Fz(77)687 2842 y FE(See,)k(for)d(example,)j(R.)e(Kutteh,)h(E.)f(Apr)2244 2841 y(\301)2247 2842 y(a,)h(and)f(J.)g(Nichols,)g(Chem.)g(Phys.)g (Lett)687 2963 y Fx(238)p FE(,)e(173)f(\(1995\))g(and)h(references)h (therein.)555 3132 y Fz(78)687 3166 y FE(F.)f(E.)g(Harris)f(and)i(H.)e (J.)h(Monkhorst,)g(Phys.)g(Rev.)g(Lett.)h Fx(23)p FE(,)f(1026)e (\(1969\).)555 3335 y Fz(79)687 3370 y FE(A.)i(D.)h(Becke,)f(J.)g (Chem.)f(Phys.)i Fx(88)p FE(,)e(2547)g(\(1988\).)555 3539 y Fz(80)687 3573 y FE(A.)h(Savin,)g(Int.)h(J.)f(Quantum)h(Chem.,)e (Symp.)h Fx(S22)p FE(,)g(457)f(\(1988\).)555 3742 y Fz(81)687 3776 y FE(V.)k(I.)g(Lebedev,)g(Zh.)g(Vychis.)f(Mat.)i(Mat.)f(Fiz.)g Fx(16)p FE(,)g(293)f(\(1976\);)h(V.)g(I.)g(Lebedev,)687 3897 y(Sibirsk.)c(Mat.)i(Zh.)e Fx(18)h FE(132)f(\(1977\).)555 4066 y Fz(82)687 4100 y FE(W.)k(H.)g(Press,)h(B.)e(P.)h(Flannery,)i(S.) e(A.)g(Teukolsky,)g(and)h(W.)f(T.)f(Vetterling,)j Fj(Nu-)687 4221 y(merical)28 b(Recipes)g FE(\(Cambridge)g(University)f(Press,)h (1988\).)555 4390 y Fz(83)687 4424 y FE(C.)41 b(W.)g(Murray,)k(N.)d(C.) f(Handy,)j(and)e(G.)f(J.)h(Lamming,)i(Mol.)e(Phys.)f Fx(78)p FE(,)k(997)687 4544 y(\(1993\).)2118 5640 y(83)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF