%!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: paper.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSCommandLine: dvips paper -o paper.ps %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 1997.10.20:1058 %%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 %%BeginProcSet: special.pro TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N /vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B /@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ /CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ 10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B /@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale true def end /@MacSetUp{userdict /md known{userdict /md get type /dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{itransform lineto} }{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N /txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp {pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray} N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict maxlength dict begin /magscale true def normalscale currentpoint TR /psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts /psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR /showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict begin /SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial {CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if /showpage{}N /erasepage{}N /copypage{}N newpath }N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{ end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin} N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{ /SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X /startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (paper.dvi) @start /Fa 1 116 df115 D E /Fb 2 106 df104 D<126012F07EA21278127CA27EA2121E121FA26C7EA212077FA26C7EA212017FA2 6C7EA21378137CA27FA2131E131FA2EB0F80A2130714C0A41480130FA2EB1F00A2131E13 3EA25BA2137813F8A2485AA25B1203A2485AA25B120FA248C7FCA2121E123EA25AA21278 12F8A25A1260124A7CB71E>I E /Fc 6 122 df<123C127E12FFA4127E123C08087A8715 >58 D<010FB5D8C03FB5FCA39026003FE0C713804B1500A24B5CA2027F14016092C7FCA2 4A1403605CA201011507605CA20103150F605C91B7FC5B6002F0C7121FA2010F153F605C A2011F157F95C7FC5CA2013F5D5F5CA2017F14015F91C7FCA24914035F5B00011507B5D8 FC03B512F0A340337DB240>72 D<3903E003E0390FF81FF8391C7C3C1C0018EB703E3938 3EE0FE38303FC0EB7F800070EB00FCEA607E157000E01400EAC0FEEA40FC1200A212015B A312035BA312075BA3120F5BA3121F5B0007C8FC1F227EA023>114 DI<90 391F801F8090397FE07FE09039E0F0E0703A01C0F9C0F83903807D833807007F000E1403 000C15F0001C137E0018EC01C002FEC7FC00385B1210C7FC13015CA31303A25C16400107 14E016C0001C5B007E1401010F148000FE1403011FEB0700011B130E39F839F01C397070 F878393FE07FE0390F801F8025227EA02C>120 D<13F0D803FCEB01C0D8071EEB03E0D8 0E1F1307121C003813800030140F013F14C000701300126049131FD8E07E14801240EA00 FE49133F000115005BA25D0003147E5BA215FE5D5BA214015DEBF00314070001130F3900 F83FF0EB3FFBEB0FC3EB00075DA20007130FD81F805B003F495AA24AC7FCEB007E003E13 7C00385B381803F0381E07C0D807FFC8FCEA01F823317EA026>I E /Fd 22 122 df<007FB5FCB6FCA214FEA21805789723>45 D67 D<91B712F818FF19C0020190398000 3FF06E90C7EA0FF84AED03FCF000FE4B157FA2F13F800203EE1FC05DF10FE0A214074B16 F01907A2140F5D1AF8A2141F5DA2190F143F5D1AF0A2147F4B151FA302FF17E092C9123F A34918C04A167F1A80A2010317FF4A1700A24E5A13074A4B5A611807010F5F4A4B5A181F 61011F4C5A4A4BC7FC18FE4D5A013F4B5A4A4A5A4D5A017FED3FC005FFC8FC4AEB03FE01 FFEC1FF8B812E094C9FC16F845447AC34A>I<91B91280A30201902680000713006E90C8 FC4A163FA24B81A30203160E5DA314074B151E191CA2140F5D17075F021F020E90C7FC5D A2171E023F141C4B133CA2177C027F5CED800392B5FCA291B65AED00071601A2496E5A5C A2160101035D5CA2160301075D4A90CAFCA3130F5CA3131F5CA3133F5CA2137FA313FFB6 12E0A341447AC340>70 D<91B56C93387FFFC08298B5FC02014DEBC0006E614A5FA203DF 4C6CC7FC1A0E63912603CFE05D038F5F1A381A711407030FEEE1FCA2F101C3020FEE0383 020E60F107036F6C1507021E160E021C60191CF1380F143C023804705BA2F1E01F0278ED 01C091267003F85EF003801A3F02F0ED070002E0030E5CA24E137F130102C04B91C8FC60 6201036D6C5B02805F4D5A943803800113070200DA07005BA2050E1303495D010E606F6C 5A1907011E5D011C4B5CA27048130F133C01384B5C017892C7FC191F01F85C486C027E5D D807FE027C4A7EB500F00178013FB512C0A216705A447AC357>77 D97 D99 DII<14FE137FA3EB01FC13001301A25C A21303A25CA21307A25CA2130FA25CA2131FA25C157F90393F83FFC091388F81F091381E 00F802387F4948137C5C4A137EA2495A91C7FCA25B484814FE5E5BA2000314015E5BA200 0714035E5B1507000F5DA249130F5E001F1678031F1370491480A2003F023F13F0EE00E0 90C7FC160148023E13C01603007E1680EE070000FEEC1E0FED1F1E48EC0FF80038EC03E0 2D467AC432>104 D<143C147E14FE1301A3EB00FC14701400AE137C48B4FC3803C78038 0703C0000F13E0120E121C13071238A21278EA700F14C0131F00F0138012E0EA003F1400 A25B137EA213FE5B12015BA212035B141E0007131C13E0A2000F133CEBC038A21478EB80 7014F014E0EB81C0EA0783EBC7803803FE00EA00F8174378C11E>I<14FE137FA3EB01FC 13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C167E013F49B4FC923807 83C09138000E07ED3C1F491370ED603F017E13E0EC01C09026FE03801380913907000E00 D9FC0E90C7FC5C00015B5C495AEBF9C03803FB8001FFC9FCA214F03807F3FCEBF07F9038 E01FC06E7E000F130781EBC003A2001F150FA20180140EA2003F151E161C010013E0A248 5DA2007E1578167000FE01015B15F1489038007F800038021FC7FC2A467AC42D>107 DIIII114 DI<1470EB01F8A313035CA313075CA3130F5CA3131F5CA2007FB5 12E0B6FC15C0D8003FC7FCA25B137EA313FE5BA312015BA312035BA312075BA3120F5BA2 EC0780001F140013805C140E003F131EEB001C143C14385C6C13F0495A6C485AEB8780D8 07FEC7FCEA01F81B3F78BD20>I<137C48B414072603C780EB1F80380703C0000F7F000E 153F121C0107150012385E1278D8700F147E5C011F14FE00F05B00E05DEA003FEC0001A2 495C137E150313FE495CA215071201495CA2030F13380003167849ECC070A3031F13F0EE 80E0153F00011581037F13C06DEBEF8300000101148090397C03C787903A3E0F07C70090 391FFE01FE903903F000782D2D78AB34>I<017CEE038048B4020EEB0FC02603C780013F EB1FE0380703C0000E7F5E001C037E130F01071607123804FE130300785DEA700F4A1501 011F130100F001804914C012E0EA003FDA000314034C14805B137E0307140701FE170049 5CA2030F5C0001170E495CA260A24848495A60A2601201033F5C7F4B6C485A000002F713 036D9039E7E0078090267E01C349C7FC903A1F0781F81E903A0FFF007FF8D901FCEB0FE0 3B2D78AB41>119 D<137C48B414072603C780EB1F80380703C0000F7F000E153F001C16 00130712385E0078157EEA700F5C011F14FE00F0495B12E0EA003FEC00015E5B137E1503 01FE5C5BA2150700015D5BA2150F00035D5BA2151F5EA2153F12014BC7FC6D5B00005BEB 7C0390383E0F7EEB1FFEEB03F090C712FE5DA214015D121F397F8003F0A24A5A4848485A 5D48131F00F049C8FC0070137E007813F8383801F0381E07C06CB4C9FCEA01FC294078AB 2F>121 D E /Fe 9 58 df49 DII<1538A2157815F8A2140114031407A2140F141F141B14331473146314C31301 1483EB030313071306130C131C131813301370136013C01201EA038013005A120E120C5A 123812305A12E0B712F8A3C73803F800AB4A7E0103B512F8A325397EB82A>I<0006140C D80780133C9038F003F890B5FC5D5D158092C7FC14FC38067FE090C9FCABEB07F8EB3FFE 9038780F803907E007E090388003F0496C7E12066E7EC87EA28181A21680A4123E127F48 7EA490C71300485C12E000605C12700030495A00385C6C1303001E495A6C6C485A3907E0 3F800001B5C7FC38007FFCEB1FE0213A7CB72A>II< 12301238123E003FB612E0A316C05A168016000070C712060060140E5D151800E0143848 5C5D5DC712014A5A92C7FC5C140E140C141C5CA25CA214F0495AA21303A25C1307A2130F A3495AA3133FA5137FA96DC8FC131E233B7BB82A>III E /Ff 4 53 df<130C133C137CEA03FC12FFEAFC7C1200B3B113FE 387FFFFEA2172C7AAB23>49 DII<140EA2141E 143EA2147E14FEA2EB01BE1303143E1306130E130C131813381330136013E013C0EA0180 120313001206120E120C5A123812305A12E0B612FCA2C7EA3E00A9147F90381FFFFCA21E 2D7EAC23>I E /Fg 4 91 df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h 13 115 df<007FB912E0BA12F0A26C18E03C04789A 4D>0 D<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F000B0B789E1C>I<007FBA1280 BB12C0A26C1980CEFCB0007FBA1280BB12C0A26C1980CEFCB0007FBA1280BB12C0A26C19 80422C7BAE4D>17 D<19E0F003F0180FF03FE0F0FF80943803FE00EF0FF8EF3FE0EFFF80 DC03FEC7FCEE0FF8EE3FE0EEFF80DB03FEC8FCED1FF8ED7FE0913801FF80DA07FEC9FCEC 1FF0EC7FC04948CAFCEB07FCEB1FF0EB7FC04848CBFCEA07FCEA1FF0EA7FC048CCFCA2EA 7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FC91 3801FF809138007FE0ED1FF8ED07FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3F E0EF0FF8EF03FE943800FF80F03FE0F00FF01803F000E01900B0007FB912E0BA12F0A26C 18E03C4E78BE4D>20 D25 D<1AF0A3861A78A21A7C1A3CA21A3E1A1E1A1F747EA2747E747E87747E74 7E1B7E87757EF30FE0F303F8007FBC12FEBE1280A26CF3FE00CEEA03F8F30FE0F31F8051 C7FC1B7E63505A505A63505A505AA250C8FC1A1E1A3E1A3CA21A7C1A78A21AF862A35934 7BB264>33 D<1706170F171FA2173EA2177CA217F8A2EE01F0A2EE03E0A2EE07C0A2EE0F 80A2EE1F00A2163EA25EA25EA24B5AA24B5AA24B5AA24B5AA24BC7FCA2153EA25DA25DA2 4A5AA24A5AA24A5AA24A5AA24AC8FCA2143EA25CA25CA2495AA2495AA2495AA2495AA249 C9FCA2133EA25BA25BA2485AA2485AA2485AA2485AA248CAFCA2123EA25AA25AA25A1260 305C72C600>54 D102 D<12FEEAFFE0EA07F8EA00FEEB7F806D7E6D7E130F6D7EA26D7EB3AD6D7EA26D 7E806E7E6E7EEC0FE0EC03FC913800FFE0A2913803FC00EC0FE0EC3FC04A5A4AC7FC5C49 5AA2495AB3AD495AA2495A131F495A495A01FEC8FCEA07F8EAFFE048C9FC236479CA32> I<140C141E143EA2143C147CA214F8A214F01301A2EB03E0A214C01307A2EB0F80A21400 5BA2133EA2133C137CA2137813F8A2485AA25B1203A2485AA25B120FA248C7FCA2121E12 3EA25AA2127812F8A41278127CA27EA2121E121FA26C7EA212077FA26C7EA212017FA26C 7EA21378137CA2133C133EA27FA27F1480A2EB07C0A2130314E0A2EB01F0A2130014F8A2 147CA2143C143EA2141E140C176476CA27>I<126012F07EA21278127CA27EA2121E121F A26C7EA212077FA26C7EA212017FA26C7EA21378137CA2133C133EA27FA27F1480A2EB07 C0A2130314E0A2EB01F0A2130014F8A2147CA2143C143EA4143C147CA214F8A214F01301 A2EB03E0A214C01307A2EB0F80A214005BA2133EA2133C137CA2137813F8A2485AA25B12 03A2485AA25B120FA248C7FCA2121E123EA25AA2127812F8A25A126017647BCA27>I<12 6012F0B3B3B3B3B3A81260046474CA1C>I114 D E /Fi 4 49 df<130C131EA50060EB01800078130739FC0C0FC0007FEB3F80393F8C7F00 3807CCF83801FFE038007F80011EC7FCEB7F803801FFE03807CCF8383F8C7F397F0C3F80 00FCEB0FC039781E078000601301000090C7FCA5130C1A1D7C9E23>3 D<14C01301A3497EA3497E497EA2497EEB3DDEEB79CF3901F1C7C03903E1C3E0391FC1C1 FC397F01C07F00FCEC1F8000E01403000091C7FCB3B3A4213B7FAD23>34 DI<137813FE 1201A3120313FCA3EA07F8A313F0A2EA0FE0A313C0121F1380A3EA3F00A3123E127E127C A35AA35A0F227EA413>48 D E /Fj 3 89 df<13FF000313C0380F03E0381C00F014F800 3E13FC147CA2001E13FC120CC712F8A2EB01F0EB03E0EB0FC03801FF00A2380003E0EB00 F01478147C143E143F1230127812FCA2143E48137E0060137C003813F8381E03F0380FFF C00001130018227DA01E>51 D<49B41320010FEBC06090393F80F0E09038FC0019D801F0 130D48481307484813034848130148C7FC481400123E127E1660127C12FC1600A7007C15 60127EA2123E003F15C07E6C6CEB01806C7E6C6CEB03006C6C1306D800FC131C90383F80 7890380FFFE0010190C7FC23247CA22B>67 D88 D E /Fk 15 116 df11 D<0103B512F0131F137F90B612E03A01FC1F 80003903F00FC03807C00748486C7E121F1300123EA25AA2140700FC5C5AA2140F5D141F 92C7FC143E0078133C147C007C5B383C01E0381F07C0D807FFC8FCEA01F8241E7D9C28> 27 D<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E5A5A5A126009 157A8714>59 D<15C0140114031580A214071500A25C140EA2141E141CA2143C14381478 1470A214F05CA213015CA213035C130791C7FCA25B130EA2131E131CA2133C1338A21378 137013F05BA212015BA212035BA2120790C8FC5A120EA2121E121CA2123C1238A2127812 70A212F05AA21A437CB123>61 D<1670A216F01501A24B7EA21507150DA2151915391531 ED61FC156015C0EC0180A2EC03005C14064A7F167E5C5CA25C14E05C4948137F91B6FC5B 0106C7123FA25B131C1318491580161F5B5B120112031207000FED3FC0D8FFF8903807FF FEA22F2F7DAE35>65 D<013FB512FEEEFFC0903A00FE0007F0EE01F84AEB007E83010181 18804A140F18C00103150718E05CA21307A25CA2130FA24A140FA2131F18C04A141FA201 3F1680173F91C81300A249157EA2017E5D5F01FE14014C5A494A5A4C5A00014BC7FC163E 4914FCED03F00003EC1FC0B7C8FC15F8332D7CAC3A>68 D<013FB7FCA2D900FEC7127F17 1F4A140FA20101150717065CA21303A25C16300107147017004A136016E0130F15019138 C007C091B5FC5BECC0074A6C5AA2133FA2020090C7FCA25B92C8FC137EA213FEA25BA212 01A25BA21203B512F0A2302D7DAC2D>70 D<92387FC003913903FFF80791391FC03E0F91 397E00071FD901F8EB03BF4948EB01FED90FC013004948147E49C8FC017E157C49153C48 5A120348481538485AA2485A173048481500A2127F90CAFCA35A5AA292381FFFFCA29238 003FC0EE1F80163F1700A2127E5E167E7EA26C6C14FE000F4A5A6C7E6C6C1307D801F8EB 1E3CD8007EEBFC3890391FFFE018010390C8FC302F7CAD37>I<90273FFFFC0FB5FCA2D9 00FEC7EA3F80A24A1500A201015D177E5CA2010315FE5F5CA2010714015F5CA2010F1403 5F5C91B6FC5B9139C00007E05CA2013F140F5F91C7FCA249141F5F137EA201FE143F94C7 FC5BA200015D167E5BA2000315FEB539E03FFFF8A2382D7CAC3A>I<90383FFFFEA20100 90C8FC5C5CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA291C7 EA0180A24914031700017E5C160601FE140EA2495C163C12015E49EB01F84B5A0003141F B7FC5E292D7DAC30>76 D<913807F00691383FFE0E9138F80F9E903903E001FE90380780 0049C7127C131E49143CA2491438A313F81630A26D1400A27FEB7F8014F86DB47E15F06D 13FC01077F01007F141F02011380EC003F151F150FA215071218A3150F00381500A2151E A2007C5C007E5C007F5C397B8003E039F1F00F8026E07FFEC7FC38C00FF0272F7CAD2B> 83 D97 D<13F8121FA21201A25BA21203A25BA21207A25BA2120FEBC7E0EB9FF8EBB83C381FF01E EBE01F13C09038800F80EA3F00A2123EA2007E131FA2127CA2143F00FC14005AA2147EA2 147C14FC5C387801F01303495A383C0F806C48C7FCEA0FFCEA03F0192F7DAD1E>I<3907 C007E0391FE03FF83918F8783E393879E01E39307B801F38707F00126013FEEAE0FC12C0 5B00815C0001143E5BA20003147E157C5B15FC0007ECF8081618EBC00115F0000F153891 3803E0300180147016E0001F010113C015E390C7EAFF00000E143E251F7E9D2B>110 D115 D E /Fl 29 122 df15 D<1530A7ED33FF033F13C0ED7C0092B5FCDA03C31300DA0780C7FC4AC8FC141C 14785C495A5C495A130749C9FC131E131C133C5B5BA2485AA2485AA2485AA248CAFCA25A 121EA2123E123CA3127C1278A412F8A67EA2127C127EA2127F6C7E7F6C7E13F8EA0FFE38 07FFC06C13F86C13FF6C6C13E0011F7F010313FC9038007FFEEC1FFF14039138007F8015 3F151FA2150FA393C7FCA20102131E13076D6C5A903801E0789038007FE0EC1F802A597C C42B>I<147002F8140E0101153FA301035DA24A147EA2010715FEA24A5CA2010F1401A2 4A5CA2011F1403A24A5CA2013F1407A291C75BA249140FA2017E5DA201FE021F13181838 49ED8030A20001033F13701860EE7F005E486C16E0DB01DF13C09238039F016DD9071F13 80489039801E0F83903BF7C078078700903AE1FFE003FE903AE07F8000F8000F90CAFCA2 5BA2121FA25BA2123FA290CBFCA25AA2127EA212FEA25A123835417DAB3B>22 D<010FB712E0013F16F05B48B812E04817C02807E0060030C7FCEB800EEA0F00001E010C 13705A0038011C13605A0060011813E000E013381240C7FC5C4B5AA214F014E013011503 14C01303A3EB078082130FA2EB1F00A34980133E137EA24980A2000114015BA26C48EB00 E0342C7EAA37>25 D<1730A317701760A317E05FA316015FA3160394C8FCA35E1606A316 0E160C013E1607D9FF80ED1F802603C3C0011CEB3FC0260703E01318260601F0157F000E 173F001C1538D818030230131F0038170F0030170700701570D86007026013035CA2D8E0 0F02E0148000C049491301EA001F4A150303011500013F5C1400604901031406017E91C7 FC180E180C01FE49141C4901061418183860030E1460030C14E04D5A4D5A031C49C7FC03 18130E017E5D5F6D01385B90261F80305BD90FC0EB03C0D907F0010FC8FC903901FE707C 9039003FFFF002031380DA0060C9FC15E05DA314015DA3140392CAFCA35C1406A3140E14 0C3A597DC43F>32 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>58 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313005A 1206120E5A5A5A12600B1D78891B>II<1618163C16 7CA2167816F8A216F01501A216E01503A216C01507A21680150FA2ED1F00A2151E153EA2 153C157CA2157815F8A25D1401A24A5AA25D1407A25D140FA292C7FC5CA2141E143EA214 3C147CA25CA25C1301A25C1303A25C1307A25C130FA291C8FC5BA2133EA2133C137CA213 7813F8A25B1201A25B1203A2485AA25B120FA290C9FC5AA2121E123EA2123C127CA21278 12F8A25A126026647BCA31>I<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB 1FF0EB07FE903801FF809038007FE0EC1FF8EC03FE913800FF80ED3FE0ED0FF8ED03FF03 0013C0EE3FF0EE0FFCEE01FF9338007FC0EF1FF0EF07FCEF01FF9438007FC0F01FE0A2F0 7FC0943801FF00EF07FCEF1FF0EF7FC04C48C7FCEE0FFCEE3FF0EEFFC0030390C8FCED0F F8ED3FE0EDFF80DA03FEC9FCEC1FF8EC7FE0903801FF80D907FECAFCEB1FF0EB7FC04848 CBFCEA07FCEA1FF0EA7FC048CCFC12FC12703B3878B44C>I64 D<4CB46C1318043F01F013384BB5 12FC0307D9007E1378DB1FF090380F80F0DB7F80EB03C1DA01FEC7EA01C34A48EC00E7DA 0FF0ED7FE04A48153F4A5A02FFC9121F494817C04948160F495A130F4A17804948160749 5A137F4948170091CAFC5A485A1906485AA2485A96C7FC121F5BA2123F5BA3127F5BA448 5AA419C0A2180161127F180396C7FC6018066C6C160E601818001F17386D5E000F5F6D4B 5A6C6C4B5A00034CC8FC6C6C150E6C6C153C017F5DD93FC0EB01E0D91FF0EB0FC0D907FE 017FC9FC0101B512FCD9003F13E0020790CAFC45487CC546>67 D<91B912FCA3020001C0 C7123F6F48EC03F803FF1501190093C91278A21A385C5DA3020317305DA314074B1460A2 18E0020F4B13005DA21701021F5D4B13031707170F023F027FC8FC92B6FCA391397FC000 7E4B131EA2170E02FF140C92C7FCA2171C49031813035C611906010392C7FC4A160E190C 191C010717184A163819301970130F4A5E180161011F16034A15074E5A013F163F4EC7FC 4AEC03FF01FFED3FFEB9FCA26046447CC348>69 D<91B912F8A3020001C0C7123F6F48EC 07F003FF1503190193C9FCA21A705C5DA3020317605DA314075D18C01701020F4B13005D A21703021F92C8FC4B5BA25F023F141E4B13FE92B5FCA24A5CED8000173CA202FF141892 C7FCA217384915305CA21770010315604A91C9FCA313075CA3130F5CA3131F5CA2133FA3 13FFB612F8A345447CC33F>I<91B6D8E003B61280A3020001E0C70003EB8000DB7F806E 48C7FC03FF1503A293C85BA219075C4B5EA2190F14034B5EA2191F14074B5EA2193F140F 4B5EA2197F141F4B5EA219FF143F92B8C8FCA3DA7FC0C712014B5DA2180314FF92C85BA2 18075B4A5EA2180F13034A5EA2181F13074A5EA2183F130F4A5EA2187F131F4A5EA2013F 16FFA24A93C9FCD9FFE002037FB6D8E003B67EA351447CC351>72 D<91B500C0020FB5128082A2DA007F9239007FE00070ED1F8074C7FCDBEFF8150E15CF03 C7160C70151C1401DB83FE1518A2DB81FF1538140303001630831A704A6D7E0206176016 3F7114E0140E020C6D6C5CA2706C1301141C021801075D83190302386D7E023094C8FC16 01715B147002606DEB8006A294387FC00E14E04A023F130C18E0191C0101ED1FF04A1618 170FF0F838130391C83807FC30A2943803FE705B01060301136018FF19E0010E81010C5F 187FA2131C0118705A1338181F137801FC70C9FCEA03FFB512F884180651447CC34E>78 D<91B712FEF0FFE019F802009039C0000FFE6F48EB01FF03FF9138007F80F13FC093C8EA 1FE0A24AEE0FF0A25D1AF81403A25DA21407F11FF05DA2020FEE3FE0A24B16C0197F021F 1780F1FF004B4A5A4E5A023F4B5A4E5A4BEC3FC006FFC7FC027FEC07FC92B612F0188003 80CAFC14FFA292CBFCA25BA25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133F A25CEBFFE0B612E0A345447CC33F>80 DI100 DII<14FE137FA3EB01FC13001301A25CA21303A25CA21307A25CA2 130FA25CA2131FA25CED3FC090393F81FFF0913887C0FC91380E007E023C133ED97F7013 3F4A7F4A14805C13FF91C7FC5BA24848143F17005BA200035D167E5BA2000715FE5E5B15 01000F5DA24913035E001F1607030713064914E0150F003FEDC00E170C90C7141CEE8018 4816381730007E167017E000FE91380781C0EEC38048913801FF000038EC007C30467BC4 38>104 D<01F8D903FCEC7F80D803FED91FFF903803FFE0D8071F903B7C0FC00F81F83E 0E0F80E007E01C00FC001C9026C3C0030178137C271807C700D9F0E0137E02CE902601F1 C0133E003801DCDAFB80133F003001D892C7FCD90FF814FF0070495C0060495CA200E049 49485CD8C01F187E4A5C1200040715FE013F6091C75BA2040F14014960017E5D1903041F 5D13FE494B130762043F160E0001060F130C4992C713C0191F4CED801C00031A1849027E 1638F2003004FE167000071A60494A16E0F201C0030192380F0380000FF18700494AEC03 FED80380D90070EC00F84F2D7DAB55>109 D<01F8EB03FCD803FEEB1FFFD8071F90387C 0FC03B0E0F80E007E03A0C07C3C003001CD9C7007F001801CE1301003801DC80003013D8 EB0FF800705B00605BA200E0491303D8C01F5D5C12001607013F5D91C7FCA2160F495D13 7E161F5F13FE49143F94C7FC187000014B136049147E16FE4C13E0000317C049150104F8 1380170300071700495D170EEE781C000FED7C3849EC1FF0D80380EC07C0342D7DAB3A> I112 D<01F8EB0FC0D803FEEB7FF0D8070FEBF038000E903883C07C3A0C07C701FC 001C13CE0018EBDC03003813D8003013F8D90FF013F800709038E000E0006015005C12E0 EAC01F5C1200A2133F91C8FCA35B137EA313FE5BA312015BA312035BA312075BA3120F5B EA0380262D7DAB2C>114 DI<02 FCEB07E0903A03FF801FFC903A0F07C0781E903A1C03E0E01F903A3801F1C07FD9700013 804901FB13FF4848EBFF00495B000316FE90C71438484A130012061401000E5C120CC7FC 14035DA314075DA3140F5DA3021F143817305D1770023F1460121E003F16E0267F807FEB 01C0026F148000FF01EF1303D901CFEB070000FE903887C00E267C03835B3A3C0F01E078 3A1FFC00FFE0D803F0EB3F80302D7EAB37>120 D<133ED9FF8014E02603C3C0EB03F038 0703E0380601F0000E1507001C16E0EA180312380030150F007016C0EA60075C161FD8E0 0F158000C05BEA001F4A133F1700133F91C7FC5E49147E137EA216FE01FE5C5BA215015E 485AA215035EA200001407150F6D5C017C131F153F6D13FF90391F03CFC0903807FF8F90 3801FC0F90C7121F5EA2153F93C7FCD807C05BD81FE0137E5DA24848485A4A5A01805B39 380007C00018495A001C49C8FC6C137C380781F83803FFE0C66CC9FC2C407DAB30>I E /Fm 24 90 df<120FEA3FC0EA7FE0EAFFF0A6EA7FE0EA3FC0EA0F000C0C7A8B19>46 D65 D67 DIII<912601FFE01370021F01FC13F091B61201010315C3010F9038C00FFF90393FFE0003 D97FF81300D9FFE0147F4849143F4849141F4890C8120F485A1707485A1703485AA2007F 1601A25B94C8FC12FFA90303B612C0A2127F7F92C7387FF000A2123FA26C7EA26C7EA26C 7E6C7F6C7F6C6D14FFEB7FF8D93FFE130390390FFFE00F010390B512E301001580021F90 38FE0030020101F090C7FC3A357BB345>III75 DIII<913803FF80027F13FC49B6FC01 07010113C0903A1FF8003FF0D93FE0EB0FF8D9FFC0EB07FE48496D7E4890C76C13804980 000717C04848ED7FE0A24848ED3FF0A2003F17F8A2007F17FC49151FA300FF17FEAB007F 17FCA26D153FA2003F17F8A36C6CED7FF0A26C6CEDFFE0000717C06D5C6C17806C6D4913 006C6D495AD97FF0EB1FFCD91FF8EB3FF0903A07FF01FFC0010190B5C7FC6D6C13FC0207 13C037357BB342>II<913803FF80027F13FC49B6FC0107010113C0903A1FF8003FF0D9 3FE0EB0FF8D9FFC0EB07FE48496D7E4890C76C1380A248486E13C04848ED7FE0A2001F17 F049153F003F17F8A2007F17FC49151FA300FF17FEAB007F17FCA36D153F003F17F8A36C 6CED7FF015FE000F496C14E06C6C48903880FFC091380783C02803FF0F01E113806C9026 8E00F313006C01CEEB7FFED97FEE5CD91FFF14F00107903881FFC0010190B5EA00046D6C 150E0207148091C7381FC01EEFE07EEFFFFEA218FC82A37013F818F0827013E07013C0EF 3F0037437BB342>III<003F B812F8A4D9F003EB801FD87F80ED03FC01001501007E1600007C177CA20078173CA400F8 173E48171EA4C71600B3A9011FB612F0A437327DB13E>III I<007FB5D8E03FB51280A426007FF8C7007EC7FC6D6C14FE6E495A6D6C5C6D4A5A6D6D48 5AEDC00F6D01E05B6D4A5A6F48C8FC6D6D5A91387FFC7E023F5BEDFFF8806E5B6E5B5E6E 7F806E7F82825C824A7FDA07EF7FEC0FE703C77FDA1F837FDA3F017F4A7E027E804A6D7E 4948133F01036E7E4A8049486D7F49487F011F6E7F4A8149C76C7F017E80B500FC013FEB FFF0A43C337DB243>II E /Fn 52 123 df<91393FE00FE0903A01FFF83FF8903A07E01EF83C903A 1F800FF07E903A3F001FE0FE017E133F4914C0485A1738484890381F8000ACB812C0A33B 03F0001F8000B3A7486C497EB50083B5FCA32F357FB42D>11 DI23 D<123C127EB4FCA21380A2127F123D1201A412031300A25A1206120E120C121C5A5A1260 09177AB315>39 D<14C01301EB0380EB0F00130E5B133C5B5BA2485A485AA212075B120F 90C7FC5AA2121E123EA3123C127CA55AB0127CA5123C123EA3121E121FA27E7F12077F12 03A26C7E6C7EA213787F131C7F130FEB0380EB01C01300124A79B71E>I<12C07E127012 3C121C7E120F6C7E6C7EA26C7E6C7EA27F1378137C133C133EA2131E131FA37F1480A5EB 07C0B0EB0F80A514005BA3131E133EA2133C137C137813F85BA2485A485AA2485A48C7FC 120E5A123C12705A5A124A7CB71E>I<123C127EB4FCA21380A2127F123D1201A4120313 00A25A1206120E120C121C5A5A126009177A8715>44 DI<123C 127E12FFA4127E123C08087A8715>I48 D<13075B5B137FEA07FFB5FC13BFEAF83F1200B3B3A2497E007FB51280A3 19327AB126>I51 D<000C14C0380FC00F90B5128015005C5C14F014C0D80C18C7FC 90C8FCA9EB0FC0EB7FF8EBF07C380FC03F9038001F80EC0FC0120E000CEB07E0A2C713F0 1403A215F8A41218127E12FEA315F0140712F8006014E01270EC0FC06C131F003C14806C EB7F00380F80FE3807FFF8000113E038003F801D347CB126>53 D57 D<007FB812C0B912E0A26C17C0CCFCAC007FB812C0B912E0A26C17C033147C9C3C>61 D<15E0A34A7EA24A7EA34A7EA3EC0DFE140CA2EC187FA34A6C7EA202707FEC601FA202E0 7FECC00FA2D901807F1507A249486C7EA301066D7EA2010E80010FB5FCA249800118C77E A24981163FA2496E7EA3496E7EA20001821607487ED81FF04A7ED8FFFE49B512E0A33336 7DB53A>65 D68 DIIIII76 D78 D<90381FE00390387FFC0748B5FC3907F01FCF390F8003FF48C7FC003E 80814880A200788000F880A46C80A27E92C7FC127F13C0EA3FF013FF6C13F06C13FF6C14 C06C14F0C680013F7F01037F9038003FFF140302001380157F153FED1FC0150F12C0A215 07A37EA26CEC0F80A26C15006C5C6C143E6C147E01C05B39F1FC03F800E0B512E0011F13 8026C003FEC7FC22377CB42B>83 D<007FB712FEA390398007F001D87C00EC003E007816 1E0070160EA20060160600E01607A3481603A6C71500B3AB4A7E011FB512FCA330337DB2 37>I87 D97 DII<153FEC0FFFA3EC007F81AE EB07F0EB3FFCEBFC0F3901F003BF3907E001FF48487E48487F8148C7FCA25A127E12FEAA 127E127FA27E6C6C5BA26C6C5B6C6C4813803A03F007BFFC3900F81E3FEB3FFCD90FE013 0026357DB32B>III<151F90391FC07F809039FFF8E3C039 01F07FC73907E03F033A0FC01F83809039800F8000001F80EB00074880A66C5CEB800F00 0F5CEBC01F6C6C48C7FCEBF07C380EFFF8380C1FC0001CC9FCA3121EA2121F380FFFFEEC FFC06C14F06C14FC4880381F0001003EEB007F4880ED1F8048140FA56C141F007C15006C 143E6C5C390FC001F83903F007E0C6B51280D91FFCC7FC22337EA126>III107 DI<2703F0 1FE013FF00FF90267FF80313C0903BF1E07C0F03E0903BF3803E1C01F02807F7003F387F D803FE1470496D486C7EA2495CA2495CB3486C496C487EB53BC7FFFE3FFFF0A33C217EA0 41>I<3903F01FC000FFEB7FF09038F1E0FC9038F3807C3907F7007EEA03FE497FA25BA2 5BB3486CEB7F80B538C7FFFCA326217EA02B>II<3903F03F8000FFEBFFE09038F3C0F89038F7007ED807FE7F6C48EB 1F804914C049130F16E0ED07F0A3ED03F8A9150716F0A216E0150F16C06D131F6DEB3F80 160001FF13FC9038F381F89038F1FFE0D9F07FC7FC91C8FCAA487EB512C0A325307EA02B >I<903807F00390383FFC07EBFC0F3901F8038F3807E001000F14DF48486CB4FC497F12 3F90C77E5AA25A5AA9127FA36C6C5B121F6D5B000F5B3907E003BF3903F0073F3800F81E EB3FF8EB0FE090C7FCAAED7F8091380FFFFCA326307DA029>I<3803E07C38FFE1FF9038 E38F809038E71FC0EA07EEEA03ECA29038FC0F8049C7FCA35BB2487EB512E0A31A217FA0 1E>II<1330A51370A313F0A2 1201A212031207381FFFFEB5FCA23803F000AF1403A814073801F806A23800FC0EEB7E1C EB1FF8EB07E0182F7FAD1E>IIIII<3A7FFF807FF8A33A07F8001FC0 0003EC0F800001EC070015066C6C5BA26D131C017E1318A26D5BA2EC8070011F1360ECC0 E0010F5BA2903807E180A214F3010390C7FC14FBEB01FEA26D5AA31478A21430A25CA214 E05CA2495A1278D8FC03C8FCA21306130EEA701CEA7838EA1FF0EA0FC025307F9F29>I< 003FB512F0A2EB000F003C14E00038EB1FC00030EB3F800070137F1500006013FE495A13 035CC6485A495AA2495A495A49C7FC153013FE485A12035B48481370485A001F14604913 E0485A387F000348130F90B5FCA21C207E9F22>I E /Fo 47 123 df<0060133000F813F8387C03F0383E0FC0381F1F80380FFE006C5AEA03F0EA01C01509 6CAE27>20 D44 D48 DIII55 DII<161C163CA2167C16FCA21501821503A2ED077E150F150E151CA21538A2157015F0 15E0EC01C0A2913803807F82EC0700A2140E141E141C5CA25CA25C49B6FCA25B91388000 3F49C7EA1F80A2130E131E131C133C13385B13F05B12011203D80FF0EC3FC0D8FFFE9038 07FFFEA32F367BB539>65 D67 D<0107B612C04915F017FC903A003F8001FEEE007FEF1F8092C7EA0FC0EF07E05CEF03F0 147E170102FE15F8A25CA21301A25CA2130317035CA2130718F04A1407A2130F18E04A14 0F18C0011F151F18805CEF3F00133F177E91C85AA2494A5A4C5A017E4A5A4C5A01FE4A5A 047EC7FC49495A0001EC0FF8007FB612E0B7C8FC15F835337BB23A>I<92391FE0018092 38FFF8030207EBFE07913A1FF01F0F0091393F80079F9139FE0003DFD901F86DB4FCD907 F05C49481300495A4948147E49C8127C137E13FE485A48481578A2485AA248481570A248 5A94C7FC123F5BA3127F90CBFCA400FE91383FFFFCA25F9238003F8094C7FCA2007E5DA2 167EA2007F15FE7E5E6C6C1301A26C6C495A6D13076C6CEB0F786C6C133E3A00FF01FC30 90387FFFF0011F01C0C8FCD903FEC9FC313775B43B>71 D<010FB51280A216009038003F C05DA292C7FCA25CA2147EA214FEA25CA21301A25CA21303A25CA21307A25CA2130FA25C A2131FA25CA2133FA291C8FCA25BA2137EA213FEA25B1201B512F8A25C21337BB21E>73 D<91381FFFFE5C16FC9138003F80A31600A25D157EA315FE5DA314015DA314035DA31407 5DA3140F5DA3141F5DA3143F92C7FCA2121C007E5B00FE137EA214FE485BEAF80100E05B 495A387007E038780FC06C48C8FCEA1FFCEA07F0273579B228>I<0107B512C05BA29026 003FC0C7FC5DA292C8FCA25CA2147EA214FEA25CA21301A25CA21303A25CA21307A25CA2 130FA25C17E0011F140117C05C1603013F1580160791C7FCEE0F005B5E017E143EA201FE 5CED01FC4913030001EC1FF8007FB6FCB7FC5E2B337CB230>76 D<902607FF8090383FFF C0496D5BA2D9001F913803F8004A6C6D5A6060EC3BF0027B140360EC71F8A202F11407DA F0FC91C7FC14E0A20101017E5B170E14C0810103151EEE801CEC801FA20107ECC03C030F 1338140016E049010713781770010E14F01503011E15F0705A011C1301A2013C14FD0300 5B133816FF0178147F5F0170143FA213F070C8FC1201EA07F8267FFF807FB5140EA23A33 7BB239>78 DI<0107B612C04915F88390 3A003F8001FEEE003FEF1F8092C713C0170F5C18E0147EA214FEEF1FC05CA20101168017 3F4A1500177E010315FE5F4AEB03F8EE07E00107EC3FC091B6C7FC16F802E0C9FC130FA2 5CA2131FA25CA2133FA291CAFCA25BA2137EA213FEA25B1201387FFFF0B5FCA233337CB2 34>II<0107B512FE49ECFFC017F0903A003F8007F8EE01FCEE007E92C7127F835C 1880147EA214FEEF7F005CA2010115FE5F4A13015F01034A5AEE0FC04A495A04FEC7FC49 B512F016C09138E003E0ED01F8010F6D7E167C4A137EA2131FA25CA2013F14FEA291C7FC A24913015E137EEF01C001FE150318805B00011607277FFFF0001400B5ECFE0EEE7E1CC9 EA1FF8EE07E032357BB238>I<913901FC018091380FFF03023F13C791387E07EF903A01 F801FF0049487E4A7F495A4948133E131F91C7FC5B013E143CA3137E1638A293C7FC137F A26D7E14E014FE90381FFFC06D13F86D7F01017F6D6C7E020F7F1400153F6F7E150FA412 0EA2001E5D121CA2151F003C92C7FCA2003E143E5D127E007F5C6D485A9038C007E039F3 F80FC000F0B5C8FC38E03FFC38C00FF029377AB42B>I<0003B812C05A1880903AF800FC 003F260FC001141F0180150F01005B001EEE07001403121C003C4A5BA200380107140E12 7800705CA2020F141E00F0161CC74990C7FCA2141FA25DA2143FA292C9FCA25CA2147EA2 14FEA25CA21301A25CA21303A25CA21307A25C497E001FB512F05AA2323374B237>I<3B 3FFFF801FFFE485CA2D801FEC7EA1FC049EC0F80170049140EA2161E120349141CA2163C 1207491438A21678120F491470A216F0121F495CA21501123F90C75BA215035A007E5DA2 150712FE4892C7FCA25D150E48141E151C153C153815786C5C5D007C1301007E495A003E EB0F806C011EC8FC380FC0FC6CB45A000113E06C6CC9FC2F3570B239>I97 D<137EEA0FFE121F5B1200A35BA21201A25BA21203A25BA21207A2EBC3E0EBCFF8380FDC 3EEBF81F497E01E01380EA1FC0138015C013005AA2123EA2007E131F1580127CA2143F00 FC14005AA2147EA25CA2387801F85C495A6C485A495A6C48C7FCEA0FFCEA03F01A3578B3 23>I<14FCEB07FF90381F078090383E03C0EBFC013801F8033803F0073807E00F13C012 0F391F80070091C7FC48C8FCA35A127EA312FE5AA4007C14C0EC01E0A2EC03C06CEB0F80 EC1F006C137C380F81F03803FFC0C648C7FC1B2278A023>III<151FED7FC0EDF0E0020113F0EC03E3A2EC07C316E0ED C1C091380FC0005DA4141F92C7FCA45C143E90381FFFFEA3D9007EC7FC147CA414FC5CA5 13015CA413035CA413075CA3130FA25CA3131F91C8FCA35B133E1238EA7E3CA2EAFE7812 FC485AEA78E0EA3FC0000FC9FC244582B418>I<143FECFF80903803E1E6903807C0FF90 380F807FEB1F00133E017E133F49133EA24848137EA24848137CA215FC12074913F8A214 01A2D80FC013F0A21403120715E01407140F141F3903E03FC00001137FEBF0FF38007FCF 90381F0F801300141FA21500A25C143E1238007E137E5C00FE5B48485A387803E0387C0F 80D81FFFC7FCEA07F820317CA023>III<1538 157C15FCA315701500AB143EECFF80903801E3C090380383E0EB0701130FEB0E03131C13 3C133814071378013013C01300140FA21580A2141FA21500A25CA2143EA2147EA2147CA2 14FCA25CA21301A25CA213035C1238387E07C0A238FE0F804848C7FCEAF83EEA787CEA3F F0EA0F801E4283B118>I<133FEA07FF5A13FEEA007EA3137CA213FCA213F8A21201A213 F0A21203A213E0A21207A213C0A2120FA21380A2121FA21300A25AA2123EA2127EA2127C 1318EAFC1C133CEAF838A21378137012F013F0EAF8E01279EA3FC0EA0F00103579B314> 108 D<2703C003F8137F3C0FF00FFE01FFC03C1E783C1F07C1E03C1C7CF00F8F01F03B3C 3DE0079E0026383FC001FC7FD97F805B007001005B5E137ED8F0FC90380FC00100E05FD8 60F8148012000001021F130360491400A200034A13076049013E130FF081800007027EEC 83C0051F138049017C1403A2000F02FC1407053E130049495CEF1E0E001F01015D183C01 0049EB0FF0000E6D48EB03E03A227AA03F>I<3903C007F0390FF01FFC391E787C1E391C 7CF01F393C3DE00F26383FC01380EB7F8000781300EA707EA2D8F0FC131F00E01500EA60 F8120000015C153E5BA20003147E157C4913FCEDF8180007153C0201133801C013F0A200 0F1578EDE070018014F016E0001FECE1C015E390C7EAFF00000E143E26227AA02B>I<14 FCEB07FF90381F07C090383E03E09038FC01F0EA01F83903F000F8485A5B120F484813FC A248C7FCA214014814F8127EA2140300FE14F05AA2EC07E0A2007CEB0FC01580141FEC3F 006C137E5C381F01F0380F83E03803FF80D800FCC7FC1E2278A027>I<011E137C90387F 81FF9039F3C387C09039E3EF03E03901E1FE01D9C1FC13F0EBC3F8000313F0018314F814 E0EA07871307000313C01200010F130316F01480A2011F130716E01400A249EB0FC0A201 3EEB1F80A2017EEB3F00017F133E5D5D9038FF81F09038FDC3E09038F8FF80027EC7FC00 0190C8FCA25BA21203A25BA21207A25BB5FCA325307FA027>I<3903C00FC0390FF03FF0 391E78F078391C7DE03C393C3FC0FC00381380EB7F00007814F8D8707E13701500EAF0FC 12E0EA60F812001201A25BA21203A25BA21207A25BA2120FA25BA2121FA290C8FC120E1E 227AA020>114 DI<1303EB 0F80A3131FA21400A25BA2133EA2137EA2137C387FFFF8A2B5FC3800F800A21201A25BA2 1203A25BA21207A25BA2120FA25B1460001F13F014E01300130114C01303001E1380EB07 005BEA0F1EEA07F8EA01E015307AAE19>II<01F01338D803FC13 FCEA0F1E120E121C123C0038147CEA783E0070143CA2137ED8F07C1338EA60FCC65A1578 000114705BA215F0000314E05BA2EC01C0A2EBC003158014071500EBE00EA26C6C5A3800 F878EB7FE0EB1F801E227AA023>II<13F0D803FC1307D80F1E130F000E141F121C123C0038143FD8783E13 3E1270A2017E137ED8F07C137CEA60FCC65A15FC000114F85BA21401000314F013E0A214 0315E0EA07C0A20003130715C0EBE00F141F0001133F9038F07F8038007FEFEB1F8FEB00 1F1500A25C003E133E007E137E147C5C007C5BEA7001495A38380780D83C1FC7FCEA0FFC EA07F020317AA025>121 D<903807801C90381FE03C90383FF038017F13789038FFF8F0 3901F07CE0EBE01F3903C003C09038800780EC0F00C7121E141C143C5C5C495AEB07C049 5A011EC7FC5B5B4913704913F0000114E0485A38078001390FC003C0381FF80790383E0F 80393C1FFF00127838700FFE38F007F838E001E01E227CA01F>I E /Fp 82 127 df<1618163CA2167EA216FFA24B7FA24B6C7EA29238063FE0A24B6C7EA2 4B6C7EA292383807FC153092387003FE15609238E001FF15C002016D7F5D02036E7E92C7 FC4A6E7E1406020E6E7E140C021C6E7E141802386E7E143002706E7E146002E06E7E5C01 016F7F5C0103707E91C9FC183F010683181F4983180F49831807498318034983A249707E A24848701380A248CBEA7FC0A20006F03FE0A248F01FF0A2001FBA12F8A24819FCA24819 FEA2BCFC48477CC651>1 D<9239FFC001FC020F9038F80FFF913B3F803E3F03C0913BFC 00077E07E0D903F890390FFC0FF0494890383FF81F4948EB7FF0495A494814E049C7FCF0 0FE04991393FC0038049021F90C7FCAFB912F0A3C648C7D81FC0C7FCB3B2486CEC3FF000 7FD9FC0FB512E0A33C467EC539>11 D<4AB4FC020F13E091387F80F8903901FC001C4948 7FD907E0130F4948137F011FECFF80495A49C7FCA25B49EC7F00163E93C7FCACEE3F80B8 FCA3C648C7FC167F163FB3B0486CEC7FC0007FD9FC1FB5FCA330467EC536>I15 D<131F1480133F137FA2EBFF00485A485A5B485A485A138048C7FC123E123C5A12E01240 11126CC431>19 D<6C130100E013076C130F007C133E001F13F8380F81F03807E7E03803 FFC06C138038007E00133C1318180C74BF31>I22 D<1606A25E161C1618163816305EEC7F80903903FFF0C090380FC0FC90393E001F804913 0F01F0EB03C04848497E0003814848EB0CF84848147C1518001F157E48C7487E15701560 4802E01380007EECC01FEC0180A200FED9030013C0A21406140E140C141C14185CA25C00 7E16805CD87F01143F003F4914001303001F90C7123E0186147E000F157C01CC14FC0007 5DD803F8495A00014A5A00004A5A017E011FC7FC90387F807E9038C7FFF89038C07F8048 48C9FCA248CAFC5A1206120E120C5AA22A3F7DB431>28 D<001EEB03C0397F800FF000FF 131F01C013F8A201E013FCA3007F130F391E6003CC0000EB000CA401E0131C491318A300 0114384913300003147090C712604814E0000614C0000E130148EB038048EB070048130E 0060130C1E1D7DC431>34 D<140C141C1438147014E0EB01C01303EB0780EB0F00A2131E 5BA25B13F85B12015B1203A2485AA3485AA348C7FCA35AA2123EA2127EA4127CA312FCB3 A2127CA3127EA4123EA2123FA27EA36C7EA36C7EA36C7EA212017F12007F13787FA27F7F A2EB0780EB03C01301EB00E014701438141C140C166476CA26>40 D<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378137C133C133E131E131FA2EB0F 80A3EB07C0A3EB03E0A314F0A21301A214F8A41300A314FCB3A214F8A31301A414F0A213 03A214E0A3EB07C0A3EB0F80A3EB1F00A2131E133E133C137C13785BA2485A485AA2485A 48C7FC120E5A5A5A5A5A16647BCA26>I<16C04B7EB3AB007FBAFCBB1280A26C1900C8D8 01E0C9FCB3AB6F5A41407BB84C>43 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200 A413E013C0A312011380120313005A1206120E5A5A5A12600B1D78891B>II<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>I<14FF010713E090 381F81F890383E007C01FC133F4848EB1F8049130F4848EB07C04848EB03E0A2000F15F0 491301001F15F8A2003F15FCA390C8FC4815FEA54815FFB3A46C15FEA56D1301003F15FC A3001F15F8A26C6CEB03F0A36C6CEB07E0000315C06D130F6C6CEB1F806C6CEB3F00013E 137C90381F81F8903807FFE0010090C7FC28447CC131>48 D<143014F013011303131F13 FFB5FC13E713071200B3B3B0497E497E007FB6FCA3204278C131>II<49B4FC010F13E0013F13FC9038FE01FE3A01F0007F80D8 03C0EB3FC048C7EA1FE0120EED0FF0EA0FE0486C14F8A215077F5BA26C48130FEA03C0C8 13F0A3ED1FE0A2ED3FC01680ED7F0015FE4A5AEC03F0EC1FC0D90FFFC7FC15F090380001 FCEC007FED3F80ED1FC0ED0FE016F0ED07F816FC150316FEA2150116FFA3121EEA7F8048 7EA416FE491303A2007EC713FC00701407003015F80038140F6C15F06CEC1FE06C6CEB3F C0D803E0EB7F803A01FE01FE0039007FFFF8010F13E0010190C7FC28447CC131>II<000615C0D807C0130701FCEB7F8090B612005D5D5D15E0158026063FFCC7FC90C9 FCAE14FF010713C090381F01F090383800FC01F0137ED807C07F49EB1F8016C090C7120F 000615E0C8EA07F0A316F81503A216FCA5123E127F487EA416F890C712075A006015F0A2 0070140F003015E00038EC1FC07E001EEC3F806CEC7F006C6C13FE6C6C485A3901F807F0 39007FFFE0011F90C7FCEB07F826447BC131>II<12 1CA2EA1F8090B712C0A3481680A217005E0038C8120C0030151C00705D0060153016705E 5E4814014B5A4BC7FCC81206150E5D151815385D156015E04A5AA24A5A140792C8FC5CA2 5C141E143EA2147E147CA214FCA21301A3495AA41307A6130FAA6D5AEB01C02A457BC231 >I<14FF010713E0011F13F890387F00FE01FC133FD801F0EB1F804848EB0FC049EB07E0 0007EC03F048481301A290C713F8481400A47FA26D130116F07F6C6CEB03E013FC6C6CEB 07C09039FF800F806C9038C01F006CEBF03EECF87839007FFEF090383FFFC07F01077F6D 13F8497F90381E7FFFD97C1F1380496C13C02601E00313E048486C13F000079038007FF8 4848EB3FFC48C7120F003EEC07FE150148140016FF167F48153FA2161FA56C151E007C15 3EA2007E153C003E157C6C15F86DEB01F06C6CEB03E06C6CEB07C0D803F8EB1F80C6B4EB FF0090383FFFFC010F13F00101138028447CC131>I<14FF010713E0011F13F890387F80 FC9038FC007E48487F4848EB1F804848EB0FC0000FEC07E0485AED03F0485A16F8007F14 0190C713FCA25AA216FE1500A516FFA46C5CA36C7E5D121F7F000F5C6C6C1306150E6C6C 5B6C6C5BD8007C5B90383F01E090390FFF80FE903801FE0090C8FC150116FCA4ED03F8A2 16F0D80F801307486C14E0486C130F16C0ED1F80A249EB3F0049137E001EC75A001C495A 000F495A3907E01FE06CB51280C649C7FCEB1FF028447CC131>I<121EEA7F80A2EAFFC0 A4EA7F80A2EA1E00C7FCB3A5121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A2B78AA1B>I< 121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5121E127FEAFF80A213C0A4127F121E 1200A512011380A3120313005A1206120E120C121C5A5A12600A3E78AA1B>I<007FBAFC BB1280A26C1900CEFCB0007FBAFCBB1280A26C190041187BA44C>61 D<16C04B7EA34B7EA34B7EA34B7EA3ED19FEA3ED30FFA203707FED607FA203E07FEDC03F A2020180ED801FA2DA03007F160FA20206801607A24A6D7EA34A6D7EA34A6D7EA2027081 0260147FA202E08191B7FCA249820280C7121FA249C87F170FA20106821707A2496F7EA3 496F7EA3496F7EA201788313F8486C83D80FFF03037FB500E0027FEBFFC0A342477DC649 >65 DI< DB0FFE146092B500C013E0020314F0913A0FFC01FC0191393FC0003E02FFC7EA0F83D903 FCEC03C74948EC01E74948EC00FF4948157F4948153F4948151F49C9120F485A49160712 0348481603A248481601A248481600A2123FA2491760127FA31900485AAE6C7EA21960A2 123F7FA2001F18E07F000F18C0A26C6C160119806C6C160312016DEE07006C6C16066D6C 150E6D6C5D6D6C5D6D6C15786D6C5D6D6C4A5AD900FFEC0780DA3FC0011FC7FCDA0FFC13 FC0203B512F0020014C0DB0FFEC8FC3B487BC546>II< B912F8A3000101C0C7127F6C6C48EC07FC17011700187C183C181CA284A31806A4180704 067FA395C7FCA4160EA2161E163E16FE91B5FCA3EC8000163E161E160EA21606A319C0A3 F0018093C7FCA41803A21900A260A260A2181EA2183E187EEF01FE170748486C147FB95A A33A447CC342>IIIII< 010FB512FEA3D9000313806E130080B3B3AB123F487E487EA44A5A13801300006C495A00 705C6C13076C5C6C495A6CEB1F802603E07FC7FC3800FFFCEB1FE027467BC332>IIIIIIIII<49B413 03010FEBE007013F13F89039FE00FE0FD801F8131FD807E0EB079F49EB03DF48486DB4FC 48C8FC4881003E81127E82127C00FC81A282A37E82A27EA26C6C91C7FC7F7FEA3FF813FE 381FFFE06C13FE6CEBFFE06C14FC6C14FF6C15C0013F14F0010F80010180D9001F7F1401 9138001FFF03031380816F13C0167F163F161F17E000C0150FA31607A37EA36C16C0160F 7E17806C151F6C16006C5D6D147ED8FBC05CD8F9F0495AD8F07C495A90393FC00FE0D8E0 0FB51280010149C7FC39C0003FF02B487BC536>I<003FB912F8A3903BF0001FF8001F01 806D481303003EC7150048187C0078183CA20070181CA30060180CA5481806A5C81600B3 B3A54B7EED7FFE49B77EA33F447DC346>I86 DI89 D<001FB81280A39126800001130001FC C7FC01F04A5A01C04A5A5B90C8485A121E4C5A484B5AA200384B5A4C5AA24B90C7FC0030 4A5AA24B5AA24B5AC8485AA24B5A4B5AA24B5A5C93C8FC4A5AA24A5A4A5AA24A5A4A5AA2 4A5A14FF5D4990C9FCEF0180495A495AA2495A494814031800495AA2495A495A5F4890C8 FC485A5F485A48485D5F48485D17FE484814034848140F16FFB8FCA331447BC33C>II<01C01318000114384848137048 C712E0000EEB01C0000C1480001C13030018140000385B003013060070130E0060130CA3 00E0131C481318A400CFEB19E039FFC01FF801E013FCA3007F130FA2003F130701C013F8 390F0001E01E1D71C431>II97 DII<167FED3FFFA315018182B3EC7F80903803FFF090380FC07C 90383F000E017E1307496D5AD803F87F48487F5B000F81485AA2485AA2127FA290C8FC5A AB7E7FA2123FA26C7EA2000F5D7F6C6C5B00035C6C6C9038077F806C6C010E13C0013F01 1C13FE90380FC0F8903803FFE09026007F0013002F467DC436>III III107 DII<3901FC01FE00FF903807FFC091381E07F091383801F8000701707F 0003EBE0002601FDC07F5C01FF147F91C7FCA25BA35BB3A8486CECFF80B5D8F83F13FEA3 2F2C7DAB36>II<3901FC03FC00FF90380F FF8091383C07E091387001F83A07FDE000FE00010180137F01FFEC3F8091C7EA1FC04915 E049140F17F0160717F8160317FCA3EE01FEABEE03FCA3EE07F8A217F0160F6D15E0EE1F C06D143F17806EEB7E00D9FDC05B9039FCF003F891383C0FE091381FFF80DA03FCC7FC91 C9FCAE487EB512F8A32F3F7DAB36>I<91387F8003903903FFE00790380FE07890393F80 1C0F90387E000E496D5AD803F8EB039F0007EC01BF4914FF48487F121F5B003F81A2485A A348C8FCAB6C7EA3123F7F121F6D5C120F6D5B12076C6C5B6C6C497E6C6C130E013F131C 90380FC0F8903803FFE09038007F0091C7FCAEEEFF80033F13FEA32F3F7DAB33>I<3903 F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF3803F9C000015B13FBEC007E153C01FF13 005BA45BB3A748B4FCB512FEA3202C7DAB26>I<90383FE0183901FFFC383907E01F7839 0F0003F8001E1301481300007C1478127800F81438A21518A27EA27E6C6C13006C7E13FC 383FFFE06C13FC6C13FF6C14C06C14E0C614F0011F13F81300EC0FFC140300C0EB01FE14 00157E7E153EA27EA36C143C6C147C15786C14F86CEB01F039F38003E039F1F00F8039E0 7FFE0038C00FF01F2E7DAC26>I<1306A5130EA4131EA3133E137EA213FE12011207001F B512F0B6FCA2C648C7FCB3A4150CAA017E131C017F1318A26D133890381F8030ECC07090 3807E0E0903801FFC09038007F001E3E7EBC26>IIII< B539F007FFFCA30003D9C00113C0C6496C1300017F14FC013F5C6E13E06D7E010F495A6D 6C485A02F890C7FC903803FC060101130E6E5A903800FF186E5AEC3FF05D141F140F6E7E 81140FEC0DFCEC19FEEC38FF4A7E9138603F8002C07F0101131F49486C7E02007F01066D 7E010E1303496D7E013C80017C80D801FC1580D80FFE4913C0B5D8800F13FFA3302B7FAA 33>II<003FB612E0A29038C0003F90C713C0003CEC7F800038ECFF00 A20030495A0070495AA24A5A0060495AA24A5A4A5AA2C7485A4AC7FC5B5C495A13075C49 5A131F4A1360495A495AA249C712C0485AA2485A485A1501485A48481303A24848EB0780 4848131F00FF14FF90B6FCA2232B7DAA2B>II<01F81302D803FE13 073907FF800E48EBE01C391F1FF8F8393807FFF0D8700113E039E0007FC00040EB1F0020 0978C131>126 D E /Fq 33 123 df45 D48 DI<163FA25E5E5D5DA25D5D5D5DA25D92B5FCEC01F7EC03E7140715C7EC 0F87EC1F07143E147E147C14F8EB01F0EB03E0130714C0EB0F80EB1F00133E5BA25B485A 485A485A120F5B48C7FC123E5A12FCB91280A5C8000F90C7FCAC027FB61280A531417DC0 38>52 D<4AB47E021F13F0027F13FC49B6FC01079038807F8090390FFC001FD93FF014C0 4948137F4948EBFFE048495A5A1400485A120FA248486D13C0EE7F80EE1E00003F92C7FC A25B127FA2EC07FC91381FFF8000FF017F13E091B512F89039F9F01FFC9039FBC007FE90 39FF8003FF17804A6C13C05B6F13E0A24915F0A317F85BA4127FA5123FA217F07F121FA2 000F4A13E0A26C6C15C06D4913806C018014006C6D485A6C9038E01FFC6DB55A011F5C01 0714C0010191C7FC9038003FF02D427BC038>54 D<121E121F13FC90B712FEA45A17FC17 F817F017E017C0A2481680007EC8EA3F00007C157E5E00785D15014B5A00F84A5A484A5A 5E151FC848C7FC157E5DA24A5A14035D14074A5AA2141F5D143FA2147F5D14FFA25BA35B 92C8FCA35BA55BAA6D5A6D5A6D5A2F447AC238>I57 D65 DIIII71 DI I87 D<903801FFE0011F13FE017F6D7E 48B612E03A03FE007FF84848EB1FFC6D6D7E486C6D7EA26F7FA36F7F6C5A6C5AEA00F090 C7FCA40203B5FC91B6FC1307013F13F19038FFFC01000313E0000F1380381FFE00485A5B 127F5B12FF5BA35DA26D5B6C6C5B4B13F0D83FFE013EEBFFC03A1FFF80FC7F0007EBFFF8 6CECE01FC66CEB8007D90FFCC9FC322F7DAD36>97 D99 DII103 DI< 137C48B4FC4813804813C0A24813E0A56C13C0A26C13806C1300EA007C90C7FCAAEB7FC0 EA7FFFA512037EB3AFB6FCA518467CC520>I<90277F8007FEEC0FFCB590263FFFC09038 7FFF8092B5D8F001B512E002816E4880913D87F01FFC0FE03FF8913D8FC00FFE1F801FFC 0003D99F009026FF3E007F6C019E6D013C130F02BC5D02F86D496D7EA24A5D4A5DA34A5D B3A7B60081B60003B512FEA5572D7CAC5E>109 D<90397F8007FEB590383FFF8092B512 E0028114F8913987F03FFC91388F801F000390399F000FFE6C139E14BC02F86D7E5CA25C A35CB3A7B60083B512FEA5372D7CAC3E>II<90397FC00FF8B590B57E02C314E002CF14F89139DFC03FFC9139FF001F FE000301FCEB07FF6C496D13804A15C04A6D13E05C7013F0A2EF7FF8A4EF3FFCACEF7FF8 A318F017FFA24C13E06E15C06E5B6E4913806E4913006E495A9139DFC07FFC02CFB512F0 02C314C002C091C7FCED1FF092C9FCADB67EA536407DAC3E>I<90387F807FB53881FFE0 028313F0028F13F8ED8FFC91389F1FFE000313BE6C13BC14F8A214F0ED0FFC9138E007F8 ED01E092C7FCA35CB3A5B612E0A5272D7DAC2E>114 D<90391FFC038090B51287000314 FF120F381FF003383FC00049133F48C7121F127E00FE140FA215077EA27F01E090C7FC13 FE387FFFF014FF6C14C015F06C14FC6C800003806C15806C7E010F14C0EB003F020313E0 140000F0143FA26C141F150FA27EA26C15C06C141FA26DEB3F8001E0EB7F009038F803FE 90B55A00FC5CD8F03F13E026E007FEC7FC232F7CAD2C>II118 D121 D<001FB71280A49026FC001F130001E0495A5B49495A90C7485A48495B123E4A5B4A5B00 3C495BA24A90C7FC4A5A4A5AC7FC4A5A495B495BA2495B499038800780491300A2495A49 48130F49481400A2485B48495B485BA248495B4890C75A48485C15034848EB1FFEB7FCA4 292C7DAB32>I E end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: a4 %%BeginPaperSize: a4 /setpagedevice where { pop 1 dict dup /PageSize [ 595 842 ] put setpagedevice } { statusdict /a4tray known { statusdict begin a4tray end /a4 where { pop a4 } if } { /a4 where { pop a4 } { statusdict /setpage known { statusdict begin 595 842 0 setpage end } if } ifelse } ifelse } ifelse %%EndPaperSize %%EndSetup %%Page: 1 1 1 0 bop 309 555 a Fq(Wh)m(y)37 b(Densit)m(y-Gradien)m(t)g(Corrections)f (Impro)m(v)m(e)h(A)m(tomization)d(Energies)1447 672 y(and)k(Barrier)e (Heigh)m(ts)1075 883 y Fp(John)d(P)-8 b(.)33 b(P)m(erdew)h(and)f (Matthias)f(Ernzerhof)311 975 y Fo(Dep)l(artment)e(of)d(Physics)i(and)f (Quantum)g(The)l(ory)g(Gr)l(oup,)h(T)-6 b(ulane)27 b(University,)i(New) e(Orle)l(ans,)h(LA)g(70118)1694 1166 y Fp(Ale)-5 b(\024)-44 b(s)33 b(Zupan)447 1257 y Fo(Dep)l(artment)d(of)d(Physic)l(al)h(and)g (Or)l(ganic)g(Chemistry,)g(Jo)l(\024)-35 b(zef)28 b(Stefan)h (Institute,)f(Jamova)g(39,)g(1000)1616 1348 y(Ljubljana,)f(Slovenia) 1650 1539 y Fp(Kieron)32 b(Burk)m(e)824 1631 y Fo(Dep)l(artment)d(of)f (Chemistry,)g(R)n(utgers)h(University,)f(Camden,)f(NJ)h(08102)749 1776 y Fn(While)g(the)f(Hartree-F)-6 b(o)r(c)n(k)27 b(\(HF\))f(appro)n (ximation)h(t)n(ypically)g(underestimates)g(the)639 1867 y(strength)34 b(of)g(the)f(c)n(hemical)h(b)r(ond,)h(the)e(lo)r(cal)i (spin)f(densit)n(y)f(\(LSD\))f(appro)n(ximation)639 1959 y(o)n(v)n(erestimates)38 b(it.)70 b(Th)n(us)37 b(LSD)g(o)n(v)n(erbinds) g(atoms)g(in)g(molecules,)k(and)d(underesti-)639 2050 y(mates)27 b(the)f(heigh)n(ts)h(of)h(energy)f(barriers)h(when)e(the)h (transition)h(state)f(is)h(more)e(highly)639 2141 y(b)r(onded)f(than)g (the)h(initial)h(state.)35 b(Generalized)27 b(gradien)n(t)f(appro)n (ximations)f(\(GGA's\),)639 2233 y(whic)n(h)38 b(incorp)r(orate)h (densit)n(y-gradien)n(t)e(corrections)i(to)g(LSD,)e(impro)n(v)n(e)g (the)g(agree-)639 2324 y(men)n(t)27 b(b)r(et)n(w)n(een)h(calculated)i (and)e(measured)g(energetics.)44 b(This)29 b(has)g(b)r(een)f (previously)639 2415 y(understo)r(o)r(d)21 b(as)g(a)g(consequence)f(of) h(the)f(fact)i(that)e(gradien)n(t)h(corrections)h(fa)n(v)n(or)f(densit) n(y)639 2506 y(inhomogeneit)n(y)-6 b(,)24 b(whic)n(h)h(increases)h (when)e(a)h(b)r(ond)f(is)h(stretc)n(hed)f(or)h(brok)n(en.)33 b(W)-6 b(e)24 b(sho)n(w)639 2598 y(that)f(gradien)n(t)g(corrections)h (also)g(fa)n(v)n(or)f(high)g(densit)n(y)-6 b(,)23 b(whic)n(h)f (increases)j(when)d(a)h(b)r(ond)639 2689 y(is)31 b(compressed)f(or)g (formed,)h(but)f(that)f(the)h(inhomogeneit)n(y)g(e\013ect)g(usually)g (prev)l(ails.)639 2780 y(T)-6 b(o)24 b(quan)n(tify)f(the)g(discussion,) i(w)n(e)f(presen)n(t)f(a)h(thermo)r(dynamic-lik)n(e)d(inequalit)n(y)i (whic)n(h)639 2872 y(is)j(satis\014ed)h(when)e(gradien)n(t)h (corrections)h(fa)n(v)n(or)f(a)g(pro)r(cess.)659 3152 y Fm(I.)59 b(ENER)n(GY)30 b(FUNCTIONALS)f(AND)g(CHEMICAL)g(ENER)n (GETICS)520 3386 y Fp(Quan)m(tum)c(c)m(hemistry)g(is)g(most)f(simply)g (done)i(with)f(single-particle)d(orbitals)h Fl( )3478 3401 y Fk(\013;\033)283 3503 y Fp(whic)m(h)g(are)g(obtained)f(from)f (selfconsisten)m(t)i(single-particle)d(equations.)40 b(The)23 b(exc)m(hange-)283 3619 y(correlation)31 b(energy)i Fl(E)1154 3634 y Fj(X)n(C)1277 3619 y Fp(is)f(then)h(constructed)h (from)d(the)h(orbitals,)f(or)h(from)f(the)i(spin)283 3735 y(densities)23 b Fl(n)728 3750 y Fi(")790 3735 y Fp(and)g Fl(n)1028 3750 y Fi(#)1067 3735 y Fp(.)40 b(The)24 b(Hartree-F)-8 b(o)s(c)m(k)22 b(\(HF\))g(appro)m(ximation)e(neglects)j (correlation)283 3851 y(but)33 b(treats)g(exc)m(hange)i(exactly:)522 4094 y Fl(E)600 4053 y Fk(H)5 b(F)594 4118 y Fj(X)722 4094 y Fp([)p Fh(f)p Fl( )862 4109 y Fk(\013;\033)974 4094 y Fh(g)p Fp(])28 b(=)f Fh(\000)1269 4026 y Fp(1)p 1269 4070 49 4 v 1269 4162 a(2)1345 4011 y Fg(X)1384 4185 y Fk(\033)1482 3976 y Fg(Z)1581 4094 y Fl(d)1632 4053 y Ff(3)1671 4094 y Fl(r)1735 3976 y Fg(Z)1834 4094 y Fl(d)1885 4053 y Ff(3)1924 4094 y Fl(r)1971 4053 y Fi(0)1994 4094 y Fh(j)2039 4011 y Fg(X)2076 4185 y Fk(\013)2175 4094 y Fl( )2242 4053 y Fi(\003)2238 4118 y Fk(\013;\033)2350 4094 y Fp(\()p Fq(r)2434 4053 y Fi(0)2457 4094 y Fp(\))p Fl( )2558 4109 y Fk(\013;\033)2670 4094 y Fp(\()p Fq(r)p Fp(\))p Fh(j)2820 4053 y Ff(2)2859 4094 y Fl(=)p Fh(j)p Fq(r)2982 4053 y Fi(0)3027 4094 y Fh(\000)c Fq(r)p Fh(j)p Fl(:)238 b Fp(\(1\))283 4359 y(The)34 b(lo)s(cal)c(spin)j(densit)m(y)g (\(LSD\))f(appro)m(ximation)f([1])976 4593 y Fl(E)1054 4552 y Fk(LS)t(D)1048 4617 y Fj(X)n(C)1212 4593 y Fp([)p Fl(n)1297 4608 y Fi(")1337 4593 y Fl(;)17 b(n)1439 4608 y Fi(#)1478 4593 y Fp(])28 b(=)1637 4476 y Fg(Z)1736 4593 y Fl(d)1787 4552 y Ff(3)1827 4593 y Fl(r)35 b(n)p Fp(\()p Fq(r)p Fp(\))p Fl(\017)2125 4608 y Fj(X)n(C)2216 4593 y Fp(\()p Fl(n)2312 4608 y Fi(")2351 4593 y Fp(\()p Fq(r)p Fp(\))p Fl(;)17 b(n)2575 4608 y Fi(#)2614 4593 y Fp(\()p Fq(r)p Fp(\)\))692 b(\(2\))283 4826 y(in)m(v)m(ok)m(es)48 b Fl(\017)675 4841 y Fj(X)n(C)766 4826 y Fp(\()p Fl(n)862 4841 y Fi(")901 4826 y Fl(;)17 b(n)1003 4841 y Fi(#)1043 4826 y Fp(\),)48 b(the)e(exc)m(hange-correlation)f(energy)i(p)s(er)e (particle)f(of)h(an)h(elec-)283 4942 y(tron)37 b(gas)g(with)f(uniform)f (spin)i(densities)g Fl(n)1938 4957 y Fi(")2014 4942 y Fp(and)g Fl(n)2266 4957 y Fi(#)2342 4942 y Fp([2].)56 b(The)38 b(generalized)e(gradien)m(t)283 5059 y(appro)m(ximation)31 b(\(GGA\))g([3-8])1011 5292 y Fl(E)1089 5251 y Fk(GGA)1083 5317 y Fj(X)n(C)1256 5292 y Fp([)p Fl(n)1341 5307 y Fi(")1380 5292 y Fl(;)17 b(n)1482 5307 y Fi(#)1522 5292 y Fp(])27 b(=)1680 5175 y Fg(Z)1780 5292 y Fl(d)1831 5251 y Ff(3)1870 5292 y Fl(r)s(f)11 b Fp(\()p Fl(n)2072 5307 y Fi(")2111 5292 y Fl(;)17 b(n)2213 5307 y Fi(#)2252 5292 y Fl(;)g Fh(r)p Fl(n)2437 5307 y Fi(")2477 5292 y Fl(;)g Fh(r)p Fl(n)2662 5307 y Fi(#)2701 5292 y Fp(\))727 b(\(3\))1916 5682 y Fe(1)p eop %%Page: 2 2 2 1 bop 3549 54 a Fe(2)283 555 y Fp(mak)m(es)39 b(use)g(of)e(the)i(lo)s (cal)d(densit)m(y)i(gradien)m(t)g(as)g(w)m(ell)f(as)h(the)h(lo)s(cal)c (densit)m(y)-8 b(.)61 b(\(Except)283 672 y(where)29 b(other)e(units)g (are)g(sp)s(eci\014ed,)i(w)m(e)g(use)f(atomic)d(units)i(in)f(whic)m(h)i (\026)-50 b Fl(h)28 b Fp(=)f Fl(m)h Fp(=)g Fl(e)3306 636 y Ff(2)3373 672 y Fp(=)g(1\).)520 788 y(The)33 b(\\GGA)e(made)g (simple")g([7],)h(whic)m(h)h(w)m(e)g(emplo)m(y)e(in)h(this)f(w)m(ork,)j (arises)e(from)283 904 y(t)m(w)m(o)42 b(di\013eren)m(t)f(non-empirical) d(deriv)-5 b(ations)40 b([7,8].)68 b(All)39 b(its)i(parameters)f (\(other)h(than)283 1020 y(those)34 b(in)e(LSD\))g(are)g(fundamen)m (tal)g(constan)m(ts.)520 1137 y(Both)26 b(LSD)h(and)g(GGA)f(predict)h (realistic)e(geometries)h(and)h(vibrational)d(frequen-)283 1253 y(cies)43 b(for)g(molecules,)h(but)f(GGA)f(giv)m(es)h(a)f(b)s (etter)i(accoun)m(t)f(of)f(atomization)e(energies)283 1369 y([9,10])g(and)g(barrier)g(heigh)m(ts)g([11-15].)65 b(The)41 b(aim)d(of)i(this)g(article)e(is)i(to)g(explain)f(wh)m(y)-8 b(,)283 1485 y(using)33 b(a)f(densit)m(y-parameter)g(analysis)g(w)m(e)i (ha)m(v)m(e)f(recen)m(tly)h(dev)m(elop)s(ed)f([16,17],)f(and)h(to)283 1602 y(pro)m(vide)h(a)e(p)s(edagogical)f(discussion)i(of)g(these)h (issues.)46 b(W)-8 b(e)33 b(will)e(sho)m(w)j(ho)m(w)f(the)h(c)m(hem-) 283 1718 y(ical)f(e\013ects)i(of)e(gradien)m(t)g(corrections)h(follo)m (w)e(from)h(the)h(gradien)m(t)g(dep)s(endence)i(of)d(the)283 1834 y(functional)22 b Fl(E)810 1798 y Fk(GGA)804 1859 y Fj(X)n(C)977 1834 y Fp(.)41 b(F)-8 b(or)22 b(an)h(explanation)g(of)g (the)g(ph)m(ysical)h(origins)d(of)i(this)g(non-lo)s(calit)m(y)-8 b(,)283 1950 y(see)37 b(Ref.)51 b([18].)g(F)-8 b(or)34 b(some)h(reasons)h(wh)m(y)g(LSD)f(and)g(GGA)f(w)m(ork)i(as)g(w)m(ell)e (as)h(they)h(do,)283 2066 y(see)h(Ref.)52 b([19].)g(F)-8 b(or)34 b(metho)s(ds)h(whic)m(h)h(incorp)s(orate)f(but)g(go)g(b)s(ey)m (ond)i(GGA,)d(see)j(Refs.)283 2183 y([20])c(and)f([21].)520 2299 y(The)38 b(atomization)d(energy)k(\001)p Fl(E)1737 2314 y Fk(a)1817 2299 y Fp(is)e(the)h(extra)h(energy)f(needed)i(to)d (break)i(up)f(a)283 2415 y(molecule)32 b(in)m(to)f(separate)j(atoms.)42 b(F)-8 b(or)32 b(the)h(nitrogen)f(dimer,)1501 2588 y Fl(N)1579 2603 y Ff(2)1641 2588 y Fp(+)22 b(\001)p Fl(E)1892 2603 y Fk(a)1962 2588 y Fh(!)27 b Fp(2)p Fl(N)5 b(:)1218 b Fp(\(4\))283 2762 y(F)-8 b(or)40 b(this)g(reaction,)i(as)e(for)g (most)g(others,)j(HF)d(underbinds)h(\(\001)p Fl(E)2816 2777 y Fk(a)2898 2762 y Fp(=)f(5.0)g(eV\),)h(LSD)283 2878 y(o)m(v)m(erbinds)f(\(\001)p Fl(E)917 2893 y Fk(a)997 2878 y Fp(=)e(11.6)g(eV\),)h(and)f(GGA)g(giv)m(es)g(a)g(more)g (realistic)e(binding)h(energy)283 2994 y(\(\001)p Fl(E)474 3009 y Fk(a)557 2994 y Fp(=)j(10.5)g(eV\).)h(The)g(exp)s(erimen)m(tal)f (result)g(is)g(\001)p Fl(E)2446 3009 y Fk(a)2529 2994 y Fp(=)g(9.9)g(eV.)h(All)e(v)-5 b(alues)40 b(are)283 3110 y(tak)m(en)29 b(from)e(Ref.)42 b([7].)g(Other)28 b(reaction)f(exothermicities)f(or)i(endothermicities)e([22,23])283 3227 y(ha)m(v)m(e)34 b(also)e(b)s(een)h(studied.)520 3343 y(The)41 b(rates)f(of)f(man)m(y)h(c)m(hemical)f(reactions)h(are)g (limited)d(b)m(y)j(an)g(energy)h(barrier)283 3459 y(\001)p Fl(E)436 3474 y Fk(b)506 3459 y Fp(whic)m(h)36 b(m)m(ust)f(b)s(e)h (surmoun)m(ted)f([24].)51 b(A)35 b(w)m(ell-studied)g(case)h ([14,15,17,25])d(is)i(the)283 3575 y(h)m(ydrogen)f(abstraction)1009 3749 y Fl(H)c Fp(+)22 b Fl(H)1299 3764 y Ff(2)1360 3749 y Fp(+)g(\001)p Fl(E)1611 3764 y Fk(b)1674 3749 y Fh(!)27 b Fl(H)1882 3764 y Ff(3)1949 3749 y Fh(!)g Fl(H)2157 3764 y Ff(2)2219 3749 y Fp(+)22 b Fl(H)29 b Fp(+)22 b(\001)p Fl(E)2678 3764 y Fk(b)2713 3749 y Fl(:)726 b Fp(\(5\))283 3922 y(In)41 b(the)f(initial)c(state,)42 b(a)e(h)m(ydrogen)h(atom)d (approac)m(hes)j(a)f(h)m(ydrogen)h(molecule)d(along)283 4038 y(its)45 b(b)s(ond)g(axis)g(from)f(one)h(side,)k(with)c(energy)h (\001)p Fl(E)2287 4053 y Fk(b)2322 4038 y Fp(.)81 b(The)46 b Fl(H)24 b Fh(\001)17 b(\001)g(\001)e Fl(H)2962 4053 y Ff(2)3046 4038 y Fp(distance)46 b(will)283 4155 y(b)s(e)f(denoted)g (b)m(y)g Fl(x)p Fp(.)79 b(T)-8 b(aking)44 b Fl(x)h Fp(to)f(b)s(e)g(the) h(indep)s(enden)m(t)g(reaction)f(co)s(ordinate,)i(w)m(e)283 4271 y(determine)35 b Fl(y)t Fp(,)f(the)h Fl(H)1105 4286 y Ff(2)1179 4271 y Fp(b)s(ond)f(length)g(\()p Fl(y)h Fh(\024)c Fl(x)p Fp(\),)36 b(b)m(y)f(minimizing)30 b(the)35 b(total)e(energy)j(for)283 4387 y(eac)m(h)30 b Fl(x)p Fp(.)42 b(In)29 b(the)f(transition)f(state)i(of)e Fl(H)1767 4402 y Ff(3)1807 4387 y Fp(,)i(w)m(e)g(\014nd)g Fl(y)i Fp(=)c Fl(x)p Fp(.)43 b(When)29 b(the)f(transition)f(state)283 4503 y Fl(H)364 4518 y Ff(3)439 4503 y Fp(\014ssions,)37 b(it)d(kic)m(ks)j(out)e(a)g(h)m(ydrogen)i(atom)d(to)h(the)h(other)f (side.)53 b(The)36 b(net)g(e\013ect)g(of)283 4619 y(this)c (one-dimensional)e(pro)s(cess)j(is)f(a)f(transfer)i(of)e(n)m(uclei.)43 b(In)33 b(this)f(reaction)f([17],)h(as)g(in)283 4736 y(others)h(where)f(the)g(transition)e(state)i(is)f(more)g(highly)g(b)s (onded)h(than)f(the)h(initial)c(state,)283 4852 y(the)36 b(HF)g(barrier)e(is)h(to)s(o)g(high)f(\(\001)p Fl(E)1634 4867 y Fk(b)1704 4852 y Fp(=)i(0.8)f(eV\),)h(the)g(LSD)f(barrier)f(is)h (to)s(o)g(lo)m(w)g(\(\001)p Fl(E)3556 4867 y Fk(b)283 4968 y Fp(=)e({0.1)g(eV,)h(making)e Fl(H)1202 4983 y Ff(3)1274 4968 y Fp(b)s(ound)h(in)g(LSD\),)g(and)g(the)g(GGA)g(barrier) f(is)h(more)f(realistic)283 5084 y(\(\001)p Fl(E)474 5099 y Fk(b)552 5084 y Fp(=)43 b(0.2)g(eV\))g(in)f(comparison)g(with)h (exp)s(erimen)m(t)g(\(\001)p Fl(E)2627 5099 y Fk(b)2705 5084 y Fp(=)g(0.4)f(eV,)i(from)e(Ref.)283 5201 y([25]\).)520 5317 y(Sometimes)d(the)h(transition)f(state)h(has)h(as)f(man)m(y)g(b)s (onds)h(as)f(the)h(initial)36 b(state,)283 5433 y(e.g.,)31 b(in)f(isomerizations)d(or)j(in)m(ternal)f(rotations.)41 b(LSD)30 b(giv)m(es)g(realistic)e(barrier)h(heigh)m(ts)p eop %%Page: 3 3 3 2 bop 3549 54 a Fe(3)283 555 y Fp(for)33 b(isomerizations)d([26],)j (and)g(presumably)g(so)g(do)s(es)h(GGA.)e(LSD)g(and)h(GGA)f(predict)283 672 y(essen)m(tially)h(the)g(same)f(\(correct\))h(barriers)f(for)g(in)m (ternal)g(rotations)f([27].)520 788 y(The)26 b(transition)e(state)i (for)f(an)g(atom)f(hopping)h(on)g(a)g(metal)f(surface)i([28])f(can)h (ha)m(v)m(e)283 904 y(a)77 b Fd(lower)h Fp(co)s(ordination)36 b(n)m(um)m(b)s(er)j(than)g(the)g(initial)c(state,)40 b(and)f(then)g(GGA)e(barrier)283 1020 y(heigh)m(ts)c(are)g(lo)m(w)m(er) g(\(and)f(presumably)h(again)e(more)h(correct\))h(than)f(LSD)h (barriers.)383 1301 y Fm(I)r(I.)60 b(QUALIT)-7 b(A)g(TIVE)28 b(EXPLANA)-7 b(TIONS)29 b(F)n(OR)g(FUNCTIONAL)g(PERF)n(ORMANCE)520 1535 y Fp(All)20 b(of)i(the)g(e\013ects)h(describ)s(ed)g(in)e(the)i (preceding)f(section)g(are)h(consisten)m(t)g(with)e(one)283 1651 y(neat)k(statemen)m(t)g([11,12]:)39 b(LSD)24 b(lik)m(es)h(b)s (onds)g(to)s(o)f(m)m(uc)m(h,)i(and)f(GGA)f(corrects)i(this)e(bias.)283 1767 y(Comp)s(elling)e(further)j(evidence)g(for)f(this)g(statemen)m(t)h (can)g(b)s(e)f(found)h(in)f(a)g(comparison)f(of)283 1884 y(LSD)34 b(and)g(GGA)f(energies)i(for)e(di\013eren)m(t)i(structures)g (of)f Fl(C)2506 1899 y Fk(n)2587 1884 y Fp(clusters)g([29]:)46 b(The)35 b(few)m(er)283 2000 y(the)45 b(b)s(onds,)i(the)d(more)f(the)h (gradien)m(t)f(corrections)h(lo)m(w)m(er)g(the)g(total)e(energy)-8 b(.)78 b(GGA)283 2116 y(usually)34 b(w)m(eak)m(ens)j(and)e(stretc)m (hes)i(b)s(onds)e(relativ)m(e)f(to)g(LSD.)g(When)i(b)s(onds)f(stretc)m (h)h(or)283 2232 y(break,)d(the)f(densit)m(y)g(gradien)m(t)f(or)g (inhomogeneit)m(y)f(gro)m(ws,)i(and)g(this)f(lo)m(w)m(ers)h(the)f(GGA) 283 2349 y(energy)37 b(relativ)m(e)d(to)h(LSD.)g(Muc)m(h)h(can)g(b)s(e) f(explained)g(b)m(y)h(this)f(statemen)m(t)h([30]:)48 b(GGA)283 2465 y(fa)m(v)m(ors)34 b(densit)m(y)f(inhomogeneit)m(y)f (more)g(than)g(LSD)g(do)s(es.)520 2581 y(Ho)m(w)m(ev)m(er,)47 b(this)42 b(cannot)h(b)s(e)f(the)h(whole)f(story)-8 b(,)46 b(b)s(ecause)d(gradien)m(t)f(corrections)283 2697 y(usually)52 b(and)g(correctly)104 b Fd(shrink)h Fp(the)52 b(lengths)g(of)g(co)m(v) -5 b(alen)m(t)52 b(b)s(onds)h(to)e(h)m(ydrogen)283 2814 y([14,15,17],)46 b(coun)m(ter)f(to)e(exp)s(ectations)h(based)h(up)s(on) e(the)h(statemen)m(t)g(at)g(the)g(end)g(of)283 2930 y(the)33 b(previous)g(paragraph.)520 3046 y(Our)k(curren)m(t)h(explanation)e (can)i(b)s(e)g(summarized)e(qualitativ)m(ely)f(in)i(this)g(state-)283 3162 y(men)m(t)d([17]:)45 b(GGA)33 b(fa)m(v)m(ors)i(b)s(oth)e (inhomogeneit)m(y)f(and)i(high)f(densit)m(y)h(more)f(than)h(LSD)283 3278 y(do)s(es.)42 b(These)28 b(e\013ects)f(usually)f(comp)s(ete;)i (for)e(example,)h(inhomogeneit)m(y)d(increases)j(and)283 3395 y(densit)m(y)g(decreases)h(as)d(w)m(e)i(stretc)m(h)g(or)e(break)h (a)f(b)s(ond.)41 b(The)27 b(inhomogeneit)m(y)d(e\013ect)i(usu-)283 3511 y(ally)32 b(prev)-5 b(ails)31 b(but,)j(for)e(the)h(b)s(ond)g (length)g(of)f Fl(H)2088 3526 y Ff(2)2127 3511 y Fp(,)h(the)g(densit)m (y)h(e\013ect)g(is)e(large)g(enough)283 3627 y(to)37 b(carry)h(the)f(da)m(y)-8 b(.)58 b(The)38 b(\014nal)e(t)m(w)m(o)i (sections)g(of)e(this)h(article)f(will)e(quan)m(tify)k(and)f(test)283 3743 y(this)c(statemen)m(t.)520 3860 y(Alternativ)m(e)27 b(explanations)g([10,13])g(app)s(eal)f(to)i(the)g(selfconsisten)m(t)g (e\013ect)g(of)g(gra-)283 3976 y(dien)m(t)42 b(corrections)g(on)f(the)h (electron)g(densit)m(y)-8 b(.)71 b(F)-8 b(or)41 b(example,)i(gradien)m (t)e(corrections)283 4092 y(shrink)34 b(the)g(ionic)e(cores)i(of)f(the) h(atoms,)f(pro)s(ducing)g(a)g(stronger)h(screening)g(of)f(the)h(n)m(u-) 283 4208 y(clear)25 b(p)s(oten)m(tial)e(and)j(a)e(more)h(di\013use)g(v) -5 b(alence-electron)25 b(densit)m(y)-8 b(,)27 b(hence)g(a)d(longer)g (b)s(ond)283 4325 y(length)35 b(b)s(et)m(w)m(een)h(most)e(atoms)g(whic) m(h)h(ha)m(v)m(e)h(cores.)51 b(W)-8 b(e)35 b(do)f(not)g(disagree)h (with)f(these)283 4441 y(alternativ)m(e)47 b(explanations,)k(but)c(w)m (e)i(b)s(eliev)m(e)e(that)g(ours)h(is)f(more)f(robust,)52 b(b)s(ecause)283 4557 y(it)36 b(explains)f(wh)m(y)j(gradien)m(t)d (corrections)i(pro)s(duce)g(all)d(their)h(c)m(haracteristic)h (energetic)283 4673 y(e\013ects,)e(ev)m(en)h(when)e(applied)f(to)g(the) h(LSD)f(densit)m(y)i([13,15].)776 4954 y Fm(I)r(I)r(I.)61 b(DENSITY)29 b(P)-7 b(ARAMETERS)28 b(AND)h(THEIR)h(A)-10 b(VERA)n(GES)520 5188 y Fp(T)i(o)27 b(quan)m(tify)h(the)g(explanation)e (giv)m(en)i(at)f(the)h(end)g(of)f(the)h(preceding)g(section,)h(let)283 5304 y(us)j(de\014ne)g(the)f(lo)s(cal)d(densit)m(y)k(parameter)e Fl(r)1924 5319 y Fk(s)1960 5304 y Fp(\()p Fq(r)p Fp(\),)h(the)g(lo)s (cal)d(relativ)m(e)i(spin)h(p)s(olarization)p eop %%Page: 4 4 4 3 bop 3549 54 a Fe(4)283 555 y Fl(\020)8 b Fp(\()p Fq(r)p Fp(\),)32 b(and)h(the)g(lo)s(cal)e(inhomogeneit)m(y)h(parameter) g(or)g(reduced)j(densit)m(y)f(gradien)m(t)e Fl(s)p Fp(\()p Fq(r)p Fp(\))283 672 y(b)m(y)i(the)f(equations)1344 859 y Fl(n)28 b Fp(=)f Fl(n)1591 874 y Fi(")1653 859 y Fp(+)22 b Fl(n)1809 874 y Fi(#)1849 859 y Fl(;)1590 b Fp(\(6\))1352 1000 y Fl(\020)35 b Fp(=)27 b(\()p Fl(n)1629 1015 y Fi(")1691 1000 y Fh(\000)c Fl(n)1849 1015 y Fi(#)1888 1000 y Fp(\))p Fl(=n;)1406 b Fp(\(7\))1356 1152 y Fl(s)28 b Fp(=)f Fh(jr)p Fl(n)p Fh(j)p Fl(=)p Fp(2\(3)p Fl(\031)1974 1111 y Ff(2)2012 1152 y Fp(\))2050 1111 y Ff(1)p Fk(=)p Ff(3)2160 1152 y Fl(n)2218 1111 y Ff(4)p Fk(=)p Ff(3)2329 1152 y Fl(:)1110 b Fp(\(8\))283 1340 y(The)42 b(Seitz)f(radius)f Fl(r)1084 1355 y Fk(s)1161 1340 y Fp(is)g(the)h(radius)g(of)f(a)g(sphere)i(whic)m (h)f(on)g(a)m(v)m(erage)h(con)m(tains)e(one)283 1456 y(electron,)d(so)f Fl(r)850 1471 y Fk(s)919 1456 y Fh(!)d Fp(0)i(in)g(the)h(high-densit)m(y)f(limit;)f(v)-5 b(alence)36 b(electrons)g(t)m(ypically)e(ha)m(v)m(e)283 1572 y(1)40 b(b)s(ohr)f Fh(\024)h Fl(r)770 1587 y Fk(s)846 1572 y Fh(\024)g Fp(6)f(b)s(ohr.)64 b(The)40 b(relativ)m(e)f(spin)g(p)s (olarization)d Fl(\020)47 b Fp(v)-5 b(anishes)40 b(for)f(a)g(spin-)283 1688 y(unp)s(olarized)c(system,)j(and)f(equals)f(+)g(1)g(or)f(-1)h (where)h(all)d(the)j(electron)f(spins)g(are)g(up)283 1805 y(or)d(do)m(wn,)h(resp)s(ectiv)m(ely)-8 b(.)44 b(The)34 b(inhomogeneit)m(y)e(parameter)g Fl(s)g Fp(measures)i(ho)m(w)f(fast)g (the)283 1921 y(densit)m(y)45 b(v)-5 b(aries)43 b(on)h(the)g(scale)g (of)f(the)h(lo)s(cal)e(F)-8 b(ermi)41 b(w)m(a)m(v)m(elength;)51 b(v)-5 b(alence)44 b(electrons)283 2037 y(t)m(ypically)35 b(ha)m(v)m(e)h(0)d Fh(\024)g Fl(s)f Fh(\024)h Fp(3.)52 b(Both)35 b Fl(r)1709 2052 y Fk(s)1782 2037 y Fp(and)g Fl(s)g Fp(div)m(erge)h(in)f(the)h(lo)m(w-densit)m(y)f(tail)f(of)h(an) 283 2153 y(atom)d(or)g(molecule.)520 2270 y(In)37 b(previous)h(w)m(ork) h([16,17],)f(w)m(e)g(ha)m(v)m(e)h(studied)f(distributions)e(and)h(a)m (v)m(erages)i(of)283 2386 y(these)48 b(parameters)e(in)f(atoms,)k (molecules)c(and)h(solids,)i(and)e(ho)m(w)h(these)g(c)m(hange)g(in)283 2502 y(v)-5 b(arious)30 b(pro)s(cesses.)44 b(T)m(ypically)-8 b(,)30 b(the)h(a)m(v)m(erages)g Fh(h)p Fl(r)2155 2517 y Fk(s)2192 2502 y Fh(i)p Fp(,)f Fh(hj)p Fl(\020)8 b Fh(ji)p Fp(,)28 b(and)j Fh(h)p Fl(s)p Fh(i)e Fp(all)f(increase)i(when) 283 2618 y(w)m(e)49 b(stretc)m(h)f(or)f(break)h(a)f(b)s(ond,)k(as)c (sho)m(wn)i(in)d(Fig.)86 b(1)47 b(for)g(the)h(\014ssion)f(of)g(the)g Fl(H)3551 2633 y Ff(3)283 2734 y Fp(transition)31 b(state.)520 2851 y(Because)43 b(the)f(distributions)e(of)h(the)h(densit)m(y)g (parameters)g Fl(p)f Fp(are)g(broad,)j(their)283 2967 y(a)m(v)m(erages)k(m)m(ust)f(b)s(e)g(de\014ned)h(carefully)-8 b(.)84 b(W)-8 b(e)47 b(w)m(an)m(t)g(true)g(a)m(v)m(erages)h Fh(h)p Fl(p)p Fh(i)p Fp(,)i(whic)m(h)d(fall)283 3083 y(b)s(et)m(w)m(een)39 b(the)e(minim)m(um)c(and)k(maxim)m(um)d(v)-5 b(alues)36 b(of)g Fl(p)g Fp(presen)m(t)j(in)c(the)i(system.)56 b(But)283 3199 y(w)m(e)40 b(also)d(w)m(an)m(t)i(a)m(v)m(erages)g(that)f (will)e(giv)m(e)i(meaningful)d(estimates)j(of)g(LSD)f(and)h(GGA)283 3316 y(exc)m(hange-correlation)33 b(energies.)520 3432 y(T)-8 b(o)32 b(a)h(go)s(o)s(d)e(appro)m(ximation,)f(an)m(y)k(GGA)d (can)i(b)s(e)g(written)g(as)1140 3648 y Fl(E)1218 3607 y Fk(GGA)1212 3672 y Fj(X)n(C)1413 3648 y Fp(=)1516 3531 y Fg(Z)1616 3648 y Fl(d)1667 3607 y Ff(3)1706 3648 y Fl(r)i(n\017)1882 3663 y Fj(X)1932 3648 y Fp(\()p Fl(r)2014 3663 y Fk(s)2050 3648 y Fp(\))p Fl(F)2151 3663 y Fj(X)n(C)2242 3648 y Fp(\()p Fl(r)2324 3663 y Fk(s)2361 3648 y Fl(;)17 b(\020)8 b(;)17 b(s)p Fp(\))p Fl(;)855 b Fp(\(9\))283 3869 y(where)33 b(small)c Fh(r)p Fl(\020)38 b Fp(con)m(tributions)31 b(ha)m(v)m(e)h(b)s(een)g(neglected.)44 b(\(The)32 b(barrier)f(heigh)m (t)g(in)f(the)283 3986 y(reaction)k(of)f(Eq.)48 b(\(5\))33 b(is)g(0.15)g(eV)h(with)g(and)g(0.21)f(eV)h(without)f(these)i(con)m (tributions.\))283 4102 y(In)e(Eq.)45 b(\(9\),)1313 4361 y Fl(\017)1352 4376 y Fj(X)1401 4361 y Fp(\()p Fl(r)1483 4376 y Fk(s)1520 4361 y Fp(\))27 b(=)h Fh(\000)1806 4294 y Fp(3)p 1776 4338 108 4 v 1776 4430 a(4)p Fl(\031)1911 4240 y Fg(\022)1982 4294 y Fp(9)p Fl(\031)p 1982 4338 V 2011 4430 a Fp(4)2099 4240 y Fg(\023)2160 4256 y Ff(1)p Fk(=)p Ff(3)2313 4294 y Fp(1)p 2297 4338 81 4 v 2297 4430 a Fl(r)2341 4445 y Fk(s)3417 4361 y Fp(\(10\))283 4593 y(is)i(the)h(exc)m(hange)h(energy)f(p)s(er)g(electron)f(of)g(a)g (spin-unp)s(olarized)f(uniform)f(electron)j(gas)283 4710 y(of)36 b(densit)m(y)g(parameter)f Fl(r)1250 4725 y Fk(s)1287 4710 y Fp(.)52 b(The)37 b(enhancemen)m(t)g(factor)e(o)m(v)m(er)i (spin-unp)s(olarized)d(lo)s(cal)283 4826 y(exc)m(hange,)d Fl(F)787 4841 y Fj(X)n(C)878 4826 y Fp(\()p Fl(r)960 4841 y Fk(s)996 4826 y Fl(;)17 b(\020)8 b(;)17 b(s)p Fp(\),)28 b(is)f(displa)m(y)m(ed)h(in)g(Fig.)40 b(1)28 b(of)f(Ref.)42 b([7].)g(It)28 b(can)g(b)s(e)g(decomp)s(osed)283 4942 y(in)m(to)k(exc)m(hange)j(and)d(correlation)f(comp)s(onen)m(ts:) 1089 5129 y Fl(F)1152 5144 y Fj(X)n(C)1242 5129 y Fp(\()p Fl(r)1324 5144 y Fk(s)1361 5129 y Fl(;)17 b(\020)8 b(;)17 b(s)p Fp(\))26 b(=)i Fl(F)1777 5144 y Fj(X)1825 5129 y Fp(\()p Fl(\020)8 b(;)17 b(s)p Fp(\))k(+)h Fl(F)2224 5144 y Fj(C)2272 5129 y Fp(\()p Fl(r)2354 5144 y Fk(s)2391 5129 y Fl(;)17 b(\020)8 b(;)17 b(s)p Fp(\))803 b(\(11\))283 5317 y(where)36 b Fl(F)630 5332 y Fj(C)710 5317 y Fh(!)31 b Fp(0)j(as)h Fl(r)1090 5332 y Fk(s)1158 5317 y Fh(!)c Fp(0.)50 b(The)36 b Fl(s)p Fp(-dep)s(endence)h(of)d(Eq.)51 b(\(11\))34 b(is)g(the)h(nonlo)s(calit)m(y)e(of)283 5433 y(GGA,)f(whic)m(h)h(reduces)i(to)d(LSD)g(when)i(w)m(e)f(set)h Fl(s)27 b Fp(=)h(0:)p eop %%Page: 5 5 5 4 bop 3549 54 a Fe(5)1119 590 y Fl(E)1197 548 y Fk(LS)t(D)1191 614 y Fj(X)n(C)1383 590 y Fp(=)1486 472 y Fg(Z)1586 590 y Fl(d)1637 548 y Ff(3)1676 590 y Fl(r)35 b(n\017)1852 605 y Fj(X)1902 590 y Fp(\()p Fl(r)1984 605 y Fk(s)2020 590 y Fp(\))p Fl(F)2121 605 y Fj(X)n(C)2212 590 y Fp(\()p Fl(r)2294 605 y Fk(s)2331 590 y Fl(;)17 b(\020)8 b(;)17 b Fp(0\))p Fl(:)833 b Fp(\(12\))283 4391 y @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 4252 @rwi @setspecial %%BeginDocument: ana.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 680 794 454 1247 bl 680 794 454 1247 C NC 454 1247 m 794 Y s 488 1247 m -34 X s 471 1347 m -17 X s 488 1446 m -34 X s 471 1545 m -17 X s 488 1644 m -34 X s 471 1744 m -17 X s 488 1843 m -34 X s 471 1942 m -17 X s 488 2041 m -34 X s /xs 0 def (0.7) /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 (0.7) show gr /xs 0 def (0.75) /Times-Roman 68 stwn gsave 408 1423 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.75) show gr /xs 0 def (0.8) /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 (0.8) show gr /xs 0 def (0.85) /Times-Roman 68 stwn gsave 408 1820 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.85) show gr /xs 0 def (0.9) /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 (0.9) show gr 454 1247 m 680 X s 486 1281 m -34 Y s 567 1264 m -17 Y s 648 1264 m -17 Y s 729 1264 m -17 Y s 810 1281 m -34 Y s 891 1264 m -17 Y s 972 1264 m -17 Y s 1053 1264 m -17 Y s 1134 1281 m -34 Y s 486 1281 m -34 Y s /xs 0 def (1) /Times-Roman 68 stwn gsave 486 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 810 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 (x) /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 (x) show gr 680 794 454 1247 C 3 lw 486 2089 m 4 -29 d 2 -20 d 5 -27 d 2 -16 d 5 -27 d 4 -25 d 4 -22 d 5 -24 d 5 -24 d 3 -12 d 5 -22 d 5 -16 d 6 -22 d 6 -21 d 4 -10 d 7 -20 d 8 -20 d 1 -4 d 8 -18 d 8 -18 d 8 -14 d 10 -17 d 12 -17 d 3 -4 d 10 -13 d 12 -14 d 10 -10 d 13 -12 d 19 -13 d 15 -10 d 17 -8 d 24 -10 d 9 -4 d 20 -6 d 23 -5 d 22 -4 d 30 -5 d 51 -5 d 40 -3 d 41 -2 d 72 -2 d 76 -1 d 14 X s 2268 2268 0 0 C 479 2041 m 1 -10 d s /w 6 def /w2 {w 2 div} def /w3 {w 3 div} def 482 2020 m20 482 2020 m20 483 2009 m 2 -19 d s 485 1990 m 1 -4 d s 487 1975 m20 487 1975 m20 489 1964 m -5 Y s 489 1959 m 3 -18 d s 494 1930 m20 494 1930 m20 495 1919 m 2 -10 d s 497 1909 m 2 -13 d s 501 1885 m20 501 1885 m20 503 1874 m 2 -14 d s 505 1860 m 2 -8 d s 509 1841 m20 509 1841 m20 511 1829 m 4 -18 d s 515 1811 m 1 -4 d s 519 1796 m20 519 1796 m20 521 1785 m 1 -1 d s 522 1784 m 5 -21 d s 530 1752 m20 530 1752 m20 532 1741 m 3 -9 d s 535 1732 m 3 -13 d s 541 1708 m20 541 1708 m20 544 1698 m 2 -4 d s 546 1694 m 5 -17 d s 551 1677 m 1 -1 d s 556 1665 m20 556 1665 m20 560 1655 m 6 -14 d s 566 1641 m 3 -7 d s 574 1624 m20 574 1624 m20 579 1614 m 4 -9 d s 583 1605 m 6 -11 d s 595 1584 m20 595 1584 m20 601 1574 m 12 -16 d s 613 1558 m 2 -2 d s 622 1548 m20 622 1548 m20 630 1540 m 10 -10 d s 640 1530 m 7 -6 d s 656 1517 m20 656 1517 m20 665 1511 m 17 -10 d s 682 1501 m 3 -2 d s 695 1494 m20 695 1494 m20 705 1489 m s 705 1489 m 21 -8 d s 737 1478 m20 737 1478 m20 748 1475 m 3 -1 d s 751 1474 m 19 -4 d s 781 1468 m20 781 1468 m20 792 1466 m 18 -3 d s 810 1463 m 5 -1 d s 826 1461 m20 826 1461 m20 837 1459 m 7 -1 d s 844 1458 m 16 -1 d s 871 1456 m20 871 1456 m20 883 1455 m 4 X s 887 1455 m 18 -1 d s 916 1454 m20 916 1454 m20 928 1453 m 22 -1 d s 962 1452 m20 962 1452 m20 973 1451 m 23 X s 1007 1450 m20 1007 1450 m20 1018 1450 m 23 X s 1052 1449 m20 1052 1449 m20 1064 1449 m 23 X s 1098 1449 m20 1098 1449 m20 1109 1449 m 7 X s 1116 1449 m 16 1 d s 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 259 1922 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (y) show gr 680 794 454 1247 C 2268 2268 0 0 C 680 794 454 1247 C 2268 2268 0 0 C gsave 551 1882 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (Geometry \(\362\)) show gr 680 794 454 1247 C NC 1 lw 680 794 1361 1247 bl 680 794 1361 1247 C NC 1361 1247 m 794 Y s 1395 1247 m -34 X s 1378 1327 m -17 X s 1395 1406 m -34 X s 1378 1486 m -17 X s 1395 1565 m -34 X s 1378 1644 m -17 X s 1395 1724 m -34 X s 1378 1803 m -17 X s 1395 1882 m -34 X s 1378 1962 m -17 X s 1395 2041 m -34 X s 1395 2041 m -34 X s /xs 0 def (1.5) /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 (1.5) show gr /xs 0 def (1.6) /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 (1.6) show gr /xs 0 def (1.7) /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 (1.7) show gr /xs 0 def (1.8) /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 (1.8) show gr /xs 0 def (1.9) /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 (1.9) show gr /xs 0 def (2) /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 (2) show gr 1361 1247 m 680 X s 1393 1281 m -34 Y s 1474 1264 m -17 Y s 1555 1264 m -17 Y s 1636 1264 m -17 Y s 1717 1281 m -34 Y s 1798 1264 m -17 Y s 1879 1264 m -17 Y s 1960 1264 m -17 Y s 2041 1281 m -34 Y s 1393 1281 m -34 Y s /xs 0 def (1) /Times-Roman 68 stwn gsave 1393 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 1717 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 680 794 1361 1247 C 2268 2268 0 0 C /xs 0 def (x) /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 (x) show gr 680 794 1361 1247 C 3 lw 1377 1680 m 3 1 d 3 X 4 1 d 6 2 d 7 1 d 6 1 d 13 3 d 13 3 d 10 2 d 16 3 d 16 4 d 16 2 d 33 7 d 16 3 d 11 2 d 5 1 d 9 2 d 24 3 d 27 4 d 29 4 d 8 1 d 32 4 d 25 3 d 8 1 d 28 2 d 25 3 d 28 2 d 29 2 d 29 2 d 23 2 d 32 1 d 30 2 d 33 1 d 29 1 d 38 X s 2268 2268 0 0 C 1372 1641 m 2 X s 1374 1641 m 6 X s 1380 1641 m 13 X s 1393 1641 m 2 X s 1406 1642 m20 1406 1642 m20 1417 1642 m 23 1 d s 1451 1643 m20 1451 1643 m20 1463 1644 m 9 X s 1472 1644 m 9 1 d s 1481 1645 m 4 X s 1497 1646 m20 1497 1646 m20 1508 1647 m 6 1 d s 1514 1648 m 6 X s 1520 1648 m 3 1 d s 1523 1649 m 5 1 d s 1528 1650 m 2 1 d s 1541 1653 m20 1541 1653 m20 1552 1656 m 3 1 d s 1555 1657 m 7 1 d s 1562 1658 m 13 2 d s 1586 1661 m20 1586 1661 m20 1597 1663 m 23 3 d s 1631 1668 m20 1631 1668 m20 1642 1669 m 23 4 d s 1676 1674 m20 1676 1674 m20 1687 1676 m 11 1 d s 1698 1677 m 12 2 d s 1721 1680 m20 1721 1680 m20 1732 1682 m 10 1 d s 1742 1683 m 13 1 d s 1766 1685 m20 1766 1685 m20 1777 1687 m 11 1 d s 1788 1688 m 12 1 d s 1811 1690 m20 1811 1690 m20 1822 1691 m 17 2 d s 1839 1693 m 6 X s 1856 1694 m20 1856 1694 m20 1867 1695 m 12 1 d s 1879 1696 m 11 1 d s 1901 1698 m20 1901 1698 m20 1913 1698 m 18 2 d s 1931 1700 m 4 X s 1947 1701 m20 1947 1701 m20 1958 1701 m 23 1 d s 1992 1703 m20 1992 1703 m20 2003 1703 m 7 1 d s 2010 1704 m 16 X s 2037 1705 m20 2037 1705 m20 680 794 1361 1247 C 2268 2268 0 0 C 680 794 1361 1247 C 2268 2268 0 0 C gsave 1166 1946 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (\074r) 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 (\076) show gr 680 794 1361 1247 C NC 1 lw 680 794 454 227 bl 680 794 454 227 C NC 454 227 m 794 Y s 488 315 m -34 X s 471 359 m -17 X s 471 403 m -17 X s 471 447 m -17 X s 488 491 m -34 X s 471 535 m -17 X s 471 580 m -17 X s 471 624 m -17 X s 488 668 m -34 X s 471 712 m -17 X s 471 756 m -17 X s 471 800 m -17 X s 488 844 m -34 X s 471 888 m -17 X s 471 932 m -17 X s 471 977 m -17 X s 488 1021 m -34 X s 488 315 m -34 X s 471 271 m -17 X s /xs 0 def (0.88) /Times-Roman 68 stwn gsave 408 292 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.88) show gr /xs 0 def (0.9) /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 (0.9) show gr /xs 0 def (0.92) /Times-Roman 68 stwn gsave 408 645 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.92) show gr /xs 0 def (0.94) /Times-Roman 68 stwn gsave 408 822 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.94) show gr /xs 0 def (0.96) /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 (0.96) show gr 454 227 m 680 X s 486 261 m -34 Y s 567 244 m -17 Y s 648 244 m -17 Y s 729 244 m -17 Y s 810 261 m -34 Y s 891 244 m -17 Y s 972 244 m -17 Y s 1053 244 m -17 Y s 1134 261 m -34 Y s 486 261 m -34 Y s /xs 0 def (1) /Times-Roman 68 stwn gsave 486 159 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 810 159 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 (x) /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 (x) show gr 680 794 454 227 C 3 lw 470 229 m 3 1 d 3 1 d 4 2 d 6 4 d 6 6 d 7 7 d 10 13 d 3 4 d 13 20 d 10 16 d 16 29 d 16 29 d 16 31 d 33 60 d 26 49 d 6 10 d 18 30 d 14 22 d 22 33 d 20 27 d 23 29 d 23 26 d 22 24 d 20 19 d 22 20 d 24 20 d 28 20 d 7 5 d 24 16 d 30 16 d 27 13 d 32 15 d 31 11 d 33 11 d 29 7 d 31 5 d 6 1 d s 2268 2268 0 0 C 465 300 m 2 X s 467 300 m 6 2 d s 473 302 m 6 3 d s 479 305 m 5 5 d s 492 318 m20 492 318 m20 499 327 m 1 2 d s 500 329 m 10 16 d s 510 345 m 1 2 d s 517 356 m20 517 356 m20 523 366 m 4 7 d s 527 373 m 7 13 d s 539 396 m20 539 396 m20 545 406 m 10 20 d s 560 436 m20 560 436 m20 565 446 m 11 20 d s 581 476 m20 581 476 m20 586 487 m 11 20 d s 602 517 m20 602 517 m20 607 527 m 9 15 d s 616 542 m 2 5 d s 623 557 m20 623 557 m20 628 567 m 3 6 d s 631 573 m 7 14 d s 643 597 m20 643 597 m20 649 607 m 10 16 d s 659 623 m 2 4 d s 667 636 m20 667 636 m20 674 645 m 13 19 d s 694 673 m20 694 673 m20 701 682 m 6 8 d s 707 690 m 8 9 d s 722 708 m20 722 708 m20 729 717 m 15 17 d s 752 742 m20 752 742 m20 760 750 m 11 12 d s 771 762 m 5 4 d s 785 774 m20 785 774 m20 793 781 m 5 5 d s 798 786 m 12 10 d s 819 804 m20 819 804 m20 828 811 m 3 3 d s 831 814 m 15 10 d s 855 831 m20 855 831 m20 865 837 m 13 8 d s 878 845 m 6 4 d s 894 854 m20 894 854 m20 904 860 m 1 1 d s 905 861 m 19 9 d s 934 875 m20 934 875 m20 944 880 m 21 9 d s 975 894 m20 975 894 m20 986 898 m 18 7 d s 1004 905 m 3 1 d s 1018 910 m20 1018 910 m20 1029 913 m 6 3 d s 1035 916 m 15 4 d s 1061 923 m20 1061 923 m20 1072 925 m 22 5 d s 1106 932 m20 1106 932 m20 1117 934 m 17 2 d s 680 794 454 227 C 2268 2268 0 0 C 680 794 454 227 C 2268 2268 0 0 C gsave 259 902 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (\074s\076) show gr 680 794 454 227 C NC 1 lw 680 794 1361 227 bl 680 794 1361 227 C NC 1361 227 m 794 Y s 1395 315 m -34 X s 1378 425 m -17 X s 1395 535 m -34 X s 1378 646 m -17 X s 1395 756 m -34 X s 1378 866 m -17 X s 1395 976 m -34 X s 1395 315 m -34 X s 1395 976 m -34 X s /xs 0 def (0.4) /Times-Roman 68 stwn gsave 1315 292 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.4) show gr /xs 0 def (0.45) /Times-Roman 68 stwn gsave 1315 513 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.45) show gr /xs 0 def (0.5) /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 (0.5) show gr /xs 0 def (0.55) /Times-Roman 68 stwn gsave 1315 954 t 0 r xs neg 0 t 0 0 m /Times-Roman findfont 68 sf 0 0 m (0.55) show gr 1361 227 m 680 X s 1393 261 m -34 Y s 1474 244 m -17 Y s 1555 244 m -17 Y s 1636 244 m -17 Y s 1717 261 m -34 Y s 1798 244 m -17 Y s 1879 244 m -17 Y s 1960 244 m -17 Y s 2041 261 m -34 Y s 1393 261 m -34 Y s /xs 0 def (1) /Times-Roman 68 stwn gsave 1393 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 1717 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 680 794 1361 227 C 2268 2268 0 0 C /xs 0 def (x) /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 (x) show gr 680 794 1361 227 C 3 lw 1377 286 m 3 1 d 3 1 d 4 3 d 5 6 d 1 1 d 7 10 d 6 12 d 8 17 d 5 12 d 10 25 d 3 9 d 10 26 d 16 47 d 16 47 d 16 46 d 16 42 d 17 43 d 19 48 d 10 22 d 3 7 d 10 19 d 11 20 d 12 19 d 13 20 d 14 20 d 16 19 d 18 20 d 3 4 d 15 14 d 17 14 d 24 16 d 9 6 d 19 11 d 23 10 d 34 13 d 5 2 d 27 8 d 46 10 d 8 1 d 44 8 d 43 5 d 43 3 d 32 1 d s 2268 2268 0 0 C 1372 370 m 2 X s 1374 370 m 4 2 d s 1378 372 m 2 2 d s 1380 374 m 4 4 d s 1384 378 m 4 7 d s 1394 395 m20 1394 395 m20 1399 405 m 5 11 d s 1404 416 m 3 10 d s 1411 436 m20 1411 436 m20 1415 447 m 4 12 d s 1419 459 m 3 10 d s 1426 480 m20 1426 480 m20 1429 490 m 7 22 d s 1440 523 m20 1440 523 m20 1443 533 m 8 22 d s 1454 566 m20 1454 566 m20 1458 576 m 7 22 d s 1469 609 m20 1469 609 m20 1472 619 m 3 7 d s 1475 626 m 5 15 d s 1484 651 m20 1484 651 m20 1488 662 m 2 7 d s 1490 669 m 6 14 d s 1500 694 m20 1500 694 m20 1505 704 m 9 21 d s 1519 735 m20 1519 735 m20 1523 745 m 10 21 d s 1538 776 m20 1538 776 m20 1543 786 m 6 12 d s 1549 798 m 4 8 d s 1559 816 m20 1559 816 m20 1566 825 m 5 8 d s 1571 833 m 9 10 d s 1587 852 m20 1587 852 m20 1595 860 m 1 X s 1596 860 m 13 14 d s 1609 874 m 2 2 d s 1620 883 m20 1620 883 m20 1629 890 m 7 6 d s 1636 896 m 11 8 d s 1657 910 m20 1657 910 m20 1666 915 m 1 1 d s 1667 916 m 20 10 d s 1697 930 m20 1697 930 m20 1707 935 m 10 4 d s 1717 939 m 11 4 d s 1739 947 m20 1739 947 m20 1750 950 m 12 4 d s 1762 954 m 10 2 d s 1783 959 m20 1783 959 m20 1794 961 m 22 3 d s 1816 964 m s 1828 966 m20 1828 966 m20 1839 967 m 22 3 d s 1873 972 m20 1873 972 m20 1884 973 m 22 3 d s 1918 977 m20 1918 977 m20 1929 978 m 23 2 d s 1963 981 m20 1963 981 m20 1974 982 m 23 X s 2008 983 m20 2008 983 m20 2020 983 m 21 X s 680 794 1361 227 C 2268 2268 0 0 C 680 794 1361 227 C 2268 2268 0 0 C gsave 1166 866 t 0 r 0 0 m /Times-Roman findfont 86 sf 0 0 m (\074|) show currentpoint pop 0 t /Symbol findfont 86 sf 0 0 m (z) show currentpoint pop 0 t /Times-Roman findfont 86 sf 0 0 m (|\076) show gr 680 794 1361 227 C gr gr showpage end %%EndDocument @endspecial 360 4569 a Fn(FIG.)24 b(1.)39 b(Geometry)20 b(and)h(densit)n(y-parameter)f(a)n(v)n(erages)i(for)f(the)g(fragmen)n (tation)h(of)f Fc(H)2944 4577 y Fj(3)2999 4569 y Fn(transition)h(state) g(of)283 4661 y(Eq.)34 b(\(5\).)g Fc(x)23 b Fn(is)g(the)g(longer)i(of)f (the)f(t)n(w)n(o)g(b)r(ond)g(lengths,)h(and)f(increases)i(from)e Fc(x)e Fn(=)g Fc(y)j Fn(=)d(0)p Fc(:)p Fn(95)3011 4648 y(\027)3011 4661 y(A)i(\(LSD\))f(or)i(0)p Fc(:)p Fn(935)283 4739 y(\027)283 4752 y(A)k(\(GGA\))g(at)h(the)f(transition)h(state)g (to)g(in\014nit)n(y)e(in)h(the)g(disso)r(ciated)i(limit.)43 b(The)28 b(a)n(v)n(erages)i(de\014ned)d(in)h(Eqs.)283 4843 y(\(13\)-\(15\))23 b(ha)n(v)n(e)e(b)r(een)g(ev)l(aluated)g (selfconsisten)n(tly)i(in)f(LSD)f(\(solid)h(curv)n(e\))f(and)g(GGA)h (\(dashed)f(curv)n(es\).)33 b(Note)283 4935 y(that)26 b(gradien)n(t)g(corrections)h(increase)g(the)e(inhomogeneit)n(y)g (parameter)g Fb(h)p Fc(s)p Fb(i)g Fn(and)h(reduce)f Fb(h)p Fc(r)3021 4943 y Fa(s)3054 4935 y Fb(i)p Fn(,)h(as)g(exp)r(ected.)520 5151 y Fp(T)-8 b(o)23 b(de\014ne)h(our)f(densit)m(y-parameter)g(a)m(v)m (erages,)j(w)m(e)e(use)g(the)f(exc)m(hange-only)h(limit:)877 5378 y Fl(\017)916 5393 y Fj(X)966 5378 y Fp(\()p Fh(h)p Fl(r)1087 5393 y Fk(s)1123 5378 y Fh(i)p Fp(\))j(=)1331 5261 y Fg(Z)1431 5378 y Fl(d)1482 5337 y Ff(3)1521 5378 y Fl(r)35 b(n\017)1697 5393 y Fj(X)1746 5378 y Fp(\()p Fl(r)1828 5393 y Fk(s)1865 5378 y Fp(\))p Fl(=)1969 5261 y Fg(Z)2068 5378 y Fl(d)2119 5337 y Ff(3)2158 5378 y Fl(r)g(n;)1095 b Fp(\(13\))p eop %%Page: 6 6 6 5 bop 3549 54 a Fe(6)736 590 y Fl(F)799 605 y Fj(X)848 590 y Fp(\()p Fh(hj)p Fl(\020)8 b Fh(ji)p Fl(;)17 b Fp(0\))25 b(=)1331 472 y Fg(Z)1431 590 y Fl(d)1482 548 y Ff(3)1521 590 y Fl(r)35 b(n\017)1697 605 y Fj(X)1746 590 y Fp(\()p Fl(r)1828 605 y Fk(s)1865 590 y Fp(\))p Fl(F)1966 605 y Fj(X)2015 590 y Fp(\()p Fl(\020)8 b(;)17 b Fp(0\))p Fl(=)2301 472 y Fg(Z)2398 590 y Fl(d)2449 548 y Ff(3)2488 590 y Fl(r)36 b(n\017)2665 605 y Fj(X)2714 590 y Fp(\()p Fl(r)2796 605 y Fk(s)2833 590 y Fp(\))p Fl(;)519 b Fp(\(14\))796 807 y Fl(F)859 822 y Fj(X)908 807 y Fp(\(0)p Fl(;)17 b Fh(h)p Fl(s)p Fh(i)p Fp(\))26 b(=)1331 690 y Fg(Z)1431 807 y Fl(d)1482 766 y Ff(3)1521 807 y Fl(r)35 b(n\017)1697 822 y Fj(X)1746 807 y Fp(\()p Fl(r)1828 822 y Fk(s)1865 807 y Fp(\))p Fl(F)1966 822 y Fj(X)2015 807 y Fp(\(0)p Fl(;)17 b(s)p Fp(\))p Fl(=)2296 690 y Fg(Z)2394 807 y Fl(d)2445 766 y Ff(3)2484 807 y Fl(r)35 b(n\017)2660 822 y Fj(X)2710 807 y Fp(\()p Fl(r)2792 822 y Fk(s)2829 807 y Fp(\))p Fl(:)523 b Fp(\(15\))283 1024 y(The)24 b(a)m(v)m(erages)f Fh(h)p Fl(r)934 1039 y Fk(s)971 1024 y Fh(i)p Fp(,)h Fh(hj)p Fl(\020)8 b Fh(ji)p Fp(,)22 b(and)h Fh(h)p Fl(s)p Fh(i)e Fp(are)i(found)f(as)g(n)m(umerical)f(ro)s(ots)h (of)g(these)h(equations.)283 1140 y(If)31 b(the)g(statemen)m(t)g(that)f (\\gradien)m(t)g(corrections)g(fa)m(v)m(or)h(densit)m(y)g(inhomogeneit) m(y")e(w)m(ere)283 1256 y(the)42 b(whole)e(story)-8 b(,)44 b(w)m(e)d(w)m(ould)g(exp)s(ect)h(that)f(gradien)m(t)f(corrections)h(w)m (ould)g(fa)m(v)m(or)g(an)m(y)283 1372 y(ph)m(ysical)33 b(pro)s(cess)h(in)e(whic)m(h)1660 1555 y Fl(d)p Fh(h)p Fl(s)p Fh(i)26 b Fl(>)i Fp(0)p Fl(:)1376 b Fp(\(16\))283 1737 y(As)34 b(w)m(e)f(will)d(see)k(in)e(the)h(next)g(section,)g(Eq.)45 b(\(16\))32 b(is)64 b Fd(not)j Fp(the)34 b(righ)m(t)d(condition.)385 2014 y Fm(IV.)59 b(QUANTIT)-7 b(A)g(TIVE)27 b(EXPLANA)-7 b(TION)29 b(OF)h(FUNCTIONAL)f(PERF)n(ORMANCE)520 2245 y Fp(The)43 b(a)m(v)m(erages)h(de\014ned)g(in)e(Eqs.)74 b(\(13\))42 b(-)g(\(15\))g(can)h(b)s(e)g(used)g(to)f(estimate)g(the)283 2361 y(GGA)32 b(and)h(LSD)f(exc)m(hange-correlation)g(energies)h(as) 1018 2543 y Fl(E)1096 2502 y Fk(GGA)1090 2568 y Fj(X)n(C)1291 2543 y Fh(\031)28 b Fl(N)10 b(\017)1523 2558 y Fj(X)1573 2543 y Fp(\()p Fh(h)p Fl(r)1694 2558 y Fk(s)1730 2543 y Fh(i)p Fp(\))p Fl(F)1870 2558 y Fj(X)n(C)1961 2543 y Fp(\()p Fh(h)p Fl(r)2082 2558 y Fk(s)2118 2543 y Fh(i)p Fl(;)17 b Fh(hj)p Fl(\020)8 b Fh(ji)p Fl(;)17 b Fh(h)p Fl(s)p Fh(i)p Fp(\))p Fl(;)798 b Fp(\(17\))1027 2684 y Fl(E)1105 2643 y Fk(LS)t(D)1099 2709 y Fj(X)n(C)1291 2684 y Fh(\031)28 b Fl(N)10 b(\017)1523 2699 y Fj(X)1573 2684 y Fp(\()p Fh(h)p Fl(r)1694 2699 y Fk(s)1730 2684 y Fh(i)p Fp(\))p Fl(F)1870 2699 y Fj(X)n(C)1961 2684 y Fp(\()p Fh(h)p Fl(r)2082 2699 y Fk(s)2118 2684 y Fh(i)p Fl(;)17 b Fh(hj)p Fl(\020)8 b Fh(ji)p Fl(;)17 b Fp(0\))p Fl(;)873 b Fp(\(18\))283 2867 y(where)38 b Fl(N)48 b Fp(is)36 b(the)h(n)m(um)m(b)s(er)g(of)f(electrons.)56 b(Eqs.)h(\(17\))36 b(and)h(\(18\))f(b)s(ecome)h(exact)g(when)283 2983 y(spin-unp)s(olarized)i(exc)m(hange)j(dominates)d(all)f(other)i (e\013ects,)j(or)d(when)h(the)g(distribu-)283 3099 y(tions)d(of)f(the)h (densit)m(y)h(v)-5 b(ariables)36 b(are)i(v)m(ery)i(narro)m(w.)59 b(Ho)m(w)m(ev)m(er,)41 b(these)e(equations)f(are)283 3215 y(surprisingly)27 b(accurate)i(for)e(real)g(atoms,)h(molecules,)g (and)g(solids)f([17].)42 b(F)-8 b(or)27 b(v)m(ery)i(hea)m(vy)283 3332 y(atoms,)48 b(one)d(migh)m(t)e(w)m(an)m(t)i(to)g(eliminate)d(the)j (core-electron)g(con)m(tributions)f(to)g(\(17\))283 3448 y(and)31 b(\(18\),)f(but)h(w)m(e)g(ha)m(v)m(e)h(not)e(found)g(this)g (to)g(b)s(e)g(necessary)j(in)d(our)g(studies)h(for)e(atomic)283 3564 y(n)m(um)m(b)s(ers)34 b(up)f(to)f(17.)520 3680 y(No)m(w)h(the)g (e\013ect)g(of)f(gradien)m(t)g(corrections)h(up)s(on)g(the)g(energy)g (p)s(er)g(electron)g(is)711 3862 y(\001)28 b Fh(\021)h Fp(\()p Fl(E)1042 3821 y Fk(GGA)1036 3887 y Fj(X)n(C)1231 3862 y Fh(\000)22 b Fl(E)1408 3821 y Fk(LS)t(D)1402 3887 y Fj(X)n(C)1567 3862 y Fp(\))p Fl(=)-5 b(N)820 4004 y Fh(\031)29 b Fl(\017)965 4019 y Fj(X)1014 4004 y Fp(\()p Fh(h)p Fl(r)1135 4019 y Fk(s)1171 4004 y Fh(i)p Fp(\)[)p Fl(F)1338 4019 y Fj(X)n(C)1429 4004 y Fp(\()p Fh(h)p Fl(r)1550 4019 y Fk(s)1586 4004 y Fh(i)p Fl(;)17 b Fh(hj)p Fl(\020)8 b Fh(ji)p Fl(;)17 b Fh(h)p Fl(s)p Fh(i)p Fp(\))i Fh(\000)j Fl(F)2241 4019 y Fj(X)n(C)2332 4004 y Fp(\()p Fh(h)p Fl(r)2453 4019 y Fk(s)2489 4004 y Fh(i)p Fl(;)17 b Fh(hj)p Fl(\020)8 b Fh(ji)p Fl(;)17 b Fp(0\)])p Fl(:)475 b Fp(\(19\))283 4186 y(The)30 b(exact)g(ev)-5 b(aluation)26 b(of)i(\001)h(is)f(simpler)g(and)g(more)g(accurate)h(than)g(ev)-5 b(aluation)27 b(of)h(the)283 4302 y(last)23 b(line)e(of)i(Eq.)41 b(\(19\),)24 b(but)f(the)g(latter)f(expression)i(p)s(ermits)e(us)i(to)e (mak)m(e)h(a)g(quan)m(titativ)m(e)283 4418 y(test)34 b(of)e(our)g(qualitativ)m(e)f(explanations.)520 4535 y(Consider)f(a)g(ph)m(ysical)g(pro)s(cess)h(in)e(whic)m(h)i(eac)m(h)g (densit)m(y-parameter)f(a)m(v)m(erage)h Fh(h)p Fl(p)p Fh(i)283 4651 y Fp(c)m(hanges)44 b(to)e Fh(h)p Fl(p)p Fh(i)29 b Fp(+)f Fl(d)p Fh(h)p Fl(p)p Fh(i)42 b Fp(at)g(\014xed)h Fl(N)10 b Fp(.)74 b(This)42 b(pro)s(cess)i(will)c(b)s(e)i(fa)m(v)m (ored)i(b)m(y)f(gradien)m(t)283 4767 y(corrections)33 b(if)f(and)g(only)g(if)1694 4949 y Fl(d)p Fp(\001)c Fl(<)g Fp(0)1410 b(\(20\))283 5132 y(i.e.,)33 b(\(for)f Fl(@)5 b Fp(\001)p Fl(=@)g Fh(h)p Fl(s)p Fh(i)29 b Fl(<)e Fp(0)33 b(\))1316 5306 y Fl(d)p Fh(h)p Fl(s)p Fh(i)p 1316 5350 175 4 v 1341 5441 a(h)p Fl(s)p Fh(i)1528 5373 y Fl(>)27 b(P)1718 5306 y(d)p Fh(h)p Fl(r)1852 5321 y Fk(s)1888 5306 y Fh(i)p 1718 5350 209 4 v 1719 5441 a Fp(2)p Fh(h)p Fl(r)1851 5456 y Fk(s)1887 5441 y Fh(i)1959 5373 y Fp(+)22 b Fl(Qd)p Fh(hj)p Fl(\020)8 b Fh(ji)p Fl(;)1020 b Fp(\(21\))p eop %%Page: 7 7 7 6 bop 3549 54 a Fe(7)283 555 y Fp(where)1337 789 y Fl(P)41 b Fp(=)28 b Fh(\000)1632 722 y Fp(2)p Fh(h)p Fl(r)1764 737 y Fk(s)1800 722 y Fh(i)p 1632 766 208 4 v 1674 857 a(h)p Fl(s)p Fh(i)1859 722 y Fl(@)5 b Fp(\001)p Fl(=@)g Fh(h)p Fl(r)2184 737 y Fk(s)2222 722 y Fh(i)p 1859 766 403 4 v 1876 857 a Fl(@)g Fp(\001)p Fl(=@)g Fh(h)p Fl(s)p Fh(i)2271 789 y Fl(;)1119 b Fp(\(22\))1336 1057 y Fl(Q)28 b Fp(=)g Fh(\000)1669 990 y Fp(1)p 1632 1034 124 4 v 1632 1126 a Fh(h)p Fl(s)p Fh(i)1775 990 y Fl(@)5 b Fp(\001)p Fl(=@)g Fh(hj)p Fl(\020)j Fh(ji)p 1775 1034 427 4 v 1805 1126 a Fl(@)d Fp(\001)p Fl(=@)g Fh(h)p Fl(s)p Fh(i)2212 1057 y Fl(:)1178 b Fp(\(23\))283 1317 y(W)-8 b(e)27 b(ha)m(v)m(e)h(tested)f(\([17,18]\))f(the)h (inequalit)m(y)e(\(21\))h(for)f(ab)s(out)h(20)g(atomization)d(pro)s (cesses)283 1433 y(and)h(a)e(smaller)f(n)m(um)m(b)s(er)j(of)e(b)s(ond)h (stretc)m(hings)h(and)g(transition)d(-)h(state)i(fragmen)m(tations.)283 1549 y(W)-8 b(e)38 b(\014nd)g(that)g(the)g(inequalit)m(y)e(\(21\))h (holds)g(whenev)m(er)j(gradien)m(t)d(corrections)h(fa)m(v)m(or)g(a)283 1665 y(pro)s(cess.)520 1782 y(A)32 b(simple)f(mo)s(del)g(in)h(whic)m(h) h Fl(P)41 b Fp(=)28 b(1)k(and)h Fl(Q)28 b Fp(=)f(0)33 b(is)1144 1981 y Fl(F)1207 1996 y Fj(X)n(C)1298 1981 y Fp(\()p Fl(r)1380 1996 y Fk(s)1416 1981 y Fl(;)17 b(\020)8 b(;)17 b(s)p Fp(\))26 b(=)i Fl(F)1832 1996 y Fj(X)n(C)1923 1981 y Fp(\()p Fl(r)2005 1996 y Fk(s)2041 1981 y Fl(;)17 b(\020)8 b(;)17 b Fp(0\))k(+)h Fl(\026s)2491 1940 y Ff(2)2530 1981 y Fl(;)860 b Fp(\(24\))283 2180 y(where)33 b Fl(\026)e Fp(is)g(an)m(y)h(p)s(ositiv)m(e)e(constan)m(t.)44 b(Although)31 b(the)g(true)h(GGA)e(nonlo)s(calit)m(y)f(is)i(more)283 2296 y(complicated)h(than)i(Eq.)46 b(\(24\),)33 b(it)f(also)h(yields)g ([17])g Fl(P)42 b Fh(\031)29 b Fp(1)k(and)h Fl(Q)29 b Fh(\031)h Fp(0.)45 b(Th)m(us)35 b(w)m(e)f(can)283 2413 y(simplify)d(Eq.)44 b(\(21\))32 b(for)g(qualitativ)m(e)f(purp)s(oses)j (to)1570 2604 y Fl(d)p Fh(h)p Fl(s)p Fh(i)p 1570 2648 175 4 v 1595 2739 a(h)p Fl(s)p Fh(i)1781 2671 y Fl(>)1895 2604 y(d)p Fh(h)p Fl(r)2029 2619 y Fk(s)2065 2604 y Fh(i)p 1895 2648 209 4 v 1896 2739 a Fp(2)p Fh(h)p Fl(r)2028 2754 y Fk(s)2064 2739 y Fh(i)2114 2671 y Fl(;)1276 b Fp(\(25\))283 2930 y(whic)m(h)39 b(clearly)e(di\013ers)h(from)f(the)h (naiv)m(e)g(condition)f(\(16\))g(when)i Fl(d)p Fh(h)p Fl(r)2889 2945 y Fk(s)2925 2930 y Fh(i)e(6)p Fp(=)g(0.)59 b(In)38 b(b)s(ond)283 3047 y(stretc)m(hing,)28 b(for)d(example,)i(b)s (oth)e(the)h(left-)e(and)i(righ)m(t-hand)e(sides)i(of)f(\(25\))g(are)h (t)m(ypically)283 3163 y(p)s(ositiv)m(e.)48 b(The)35 b(left-)e(hand)h(side)g(is)g(usually)f(bigger,)h(but)g(in)f Fl(H)2669 3178 y Ff(2)2742 3163 y Fp(and)i Fl(H)3015 3178 y Ff(3)3088 3163 y Fp(it)e(is)h(smaller)283 3279 y(than)k(the)f(righ)m(t-hand)f(side.)57 b(Th)m(us)39 b(gradien)m(t)d(corrections)i(stretc)m(h)g(most)e(b)s(onds,)j(but)283 3395 y(con)m(tract)44 b(the)f Fl(H)935 3410 y Ff(2)1017 3395 y Fp(and)g Fl(H)1298 3410 y Ff(3)1380 3395 y Fp(b)s(onds,)j(and)c (a\013ect)h(atomization)d(energies)j(and)g(barrier)283 3511 y(heigh)m(ts)33 b(as)g(describ)s(ed)g(in)f(the)h(\014rst)g (section)g(of)f(this)g(article.)520 3628 y(Our)e(inequalities)e(\(21\)) i(and)g(\(25\),)g(whic)m(h)h(follo)m(w)d(from)h(the)i(fact)f(that)g (the)g(GGA)283 3744 y(enhancemen)m(t)e(factor)e Fl(F)1201 3759 y Fj(X)n(C)1292 3744 y Fp(\()p Fl(r)1374 3759 y Fk(s)1410 3744 y Fl(;)17 b(\020)8 b(;)17 b(s)p Fp(\))25 b(increases)i(with)f Fl(s)p Fp(,)h(tell)e(us)i(when)g(a)f(pro)s(cess)h (will)d(b)s(e)283 3860 y(fa)m(v)m(ored)33 b(b)m(y)g(gradien)m(t)f (corrections.)43 b(Ho)m(w)33 b(strongly)e(it)g(will)f(b)s(e)i(fa)m(v)m (ored)h(then)g(dep)s(ends)283 3976 y(up)s(on)45 b(ho)m(w)f(strongly)g Fl(F)1208 3991 y Fj(X)n(C)1299 3976 y Fp(\()p Fl(r)1381 3991 y Fk(s)1417 3976 y Fl(;)17 b(\020)8 b(;)17 b(s)p Fp(\))43 b(increases)i(with)e Fl(s)p Fp(.)78 b(Fig.)f(1)43 b(of)h(Ref.)78 b([7])44 b(sho)m(ws)283 4093 y(that)36 b(the)h(exc)m(hange-only)g(\()p Fl(r)1387 4108 y Fk(s)1458 4093 y Fp(=)c(0\))j(enhancemen)m(t)i(factor)e(has)g(an)g(esp)s(ecially) f(strong)283 4209 y(increase)e(with)f Fl(s)p Fp(,)h(whic)m(h)g(partly)f (explains)g(wh)m(y)h(the)g(HF)f(appro)m(ximation)f(underbinds)283 4325 y(atoms)j(in)f(molecules.)47 b(F)-8 b(or)33 b(example,)h(consider) g(the)h(atomization)c(of)i Fl(N)10 b(H)3127 4340 y Ff(3)3167 4325 y Fp(,)35 b(in)e(whic)m(h)283 4441 y(the)45 b(exc)m (hange-correlation)f(energy)h(increases)g(b)m(y)h(8.9)e(eV.)g(The)i (corresp)s(onding)e(in-)283 4558 y(creases)e(in)e(the)g(exc)m(hange)i (energy)f(are)f(7.0)g(\(LSD\),)g(5.9)f(\(GGA\),)g(and)i(4.7)e(\(HF\))h (eV)283 4674 y([31].)j(Th)m(us,)33 b(neglecting)d(the)h(nonlo)s(calit)m (y)e(of)h(exc)m(hange)j(has)e(an)g(e\013ect)h(somewhat)f(lik)m(e)283 4790 y(including)g(correlation.)520 4906 y(The)g(inequalities)e(\(21\)) h(and)g(\(25\))g(also)g(explain)f(the)i(e\013ects)h(of)e(gradien)m(t)g (correc-)283 5022 y(tions)j(up)s(on)g(structural)f(transformations)f (in)h(solids)g([32])h(and)g(up)s(on)f(surface)i(energies)283 5139 y([17].)p eop %%Page: 8 8 8 7 bop 3549 54 a Fe(8)1381 555 y Fm(V.)29 b(A)n(CKNO)n(WLEDGMENTS)520 789 y Fp(J.P)-8 b(.P)g(.)34 b(and)f(M.E.)h(ac)m(kno)m(wledge)g(the)f (supp)s(ort)h(of)e(the)i(National)c(Science)k(F)-8 b(oun-)283 905 y(dation)40 b(under)h(Gran)m(t)f(No.)67 b(DMR)40 b(95-21353.)66 b(A.Z.)40 b(ac)m(kno)m(wledges)i(the)f(supp)s(ort)g(of) 283 1022 y(the)33 b(Slo)m(v)m(enian)g(Ministry)f(for)g(Science)h(and)g (T)-8 b(ec)m(hnology)g(.)1544 1301 y Fm(VI.)59 b(REFERENCES)317 1599 y Fp([1])32 b(W.)h(Kohn)g(and)f(L.J.)h(Sham,)f(Ph)m(ys.)45 b(Rev.)f(140,)32 b(A1133)g(\(1965\).)317 1781 y([2])g(J.P)-8 b(.)33 b(P)m(erdew)i(and)d(Y.)h(W)-8 b(ang,)33 b(Ph)m(ys.)45 b(Rev.)f(B45,)32 b(13244)g(\(1992\).)317 1962 y([3])g(D.C.)h(Langreth)f (and)h(M.)g(J.)g(Mehl,)g(Ph)m(ys.)45 b(Rev.)f(B28,)32 b(1809)g(\(1983\).)317 2144 y([4])40 b(J.P)-8 b(.)41 b(P)m(erdew)i(and)d(Y.)h(W)-8 b(ang,)42 b(Ph)m(ys.)69 b(Rev.)f(B33,)43 b(8800)c(\(1986\);)44 b(40,)e(3399)d(\(E\))491 2260 y(\(1989\).)317 2441 y([5])32 b(J.P)-8 b(.)33 b(P)m(erdew,)i(Ph)m (ys.)45 b(Rev.)f(B33,)32 b(8822)g(\(1986\);)g(34,)g(7406)f(\(E\))i (\(1986\).)317 2623 y([6])f(A.D.)g(Bec)m(k)m(e,)j(Ph)m(ys.)46 b(Rev.)e(A38,)32 b(3098)g(\(1988\).)317 2804 y([7])42 b(J.P)-8 b(.)43 b(P)m(erdew,)k(K.)c(Burk)m(e,)j(and)d(M.)g(Ernzerhof,)j (Ph)m(ys.)75 b(Rev.)f(Lett.)g(77,)44 b(3865)491 2921 y(\(1996\);)32 b(78,)g(1396)f(\(E\))i(\(1997\).)317 3102 y([8])f(J.P)-8 b(.)33 b(P)m(erdew,)i(K.)d(Burk)m(e,)i(and)f(Y.)g(W)-8 b(ang,)32 b(Ph)m(ys.)45 b(Rev.)f(B)33 b(54,)f(16533)g(\(1996\).)317 3284 y([9])40 b(L.A.)g(Curtiss,)j(K.)e(Ragha)m(v)-5 b(ac)m(hari,)41 b(P)-8 b(.C.)41 b(Redfern,)i(and)e(J.A.)f(P)m(ople,)j(J.)d(Chem.)491 3400 y(Ph)m(ys.)45 b(106,)32 b(1063)g(\(1997\),)f(and)i(references)i (therein.)317 3581 y([10])f(D.C.)g(P)m(atton,)h(D.V.)f(P)m(orezag,)h (and)g(M.)f(R.)g(P)m(ederson,)j(Ph)m(ys.)50 b(Rev.)f(B55,)34 b(7454)491 3698 y(\(1997\).)317 3879 y([11])e(L.)g(F)-8 b(an)33 b(and)f(T.)h(Ziegler,)e(J.)i(Am.)43 b(Chem.)g(So)s(c.)h(114,)32 b(10890)f(\(1992\).)317 4061 y([12])h(L.)g(Deng,)h(T.)g(Ziegler,)e(and) i(L.)f(F)-8 b(an,)32 b(J.)h(Chem.)44 b(Ph)m(ys.)h(99,)32 b(3823)g(\(1993\).)317 4242 y([13])37 b(B.)i(Hammer,)f(K.)g(W.)g (Jacobsen,)j(and)d(J.K.)g(N\034rsk)m(o)m(v,)j(Ph)m(ys.)61 b(Rev.)g(Lett.)f(70,)491 4358 y(3971)32 b(\(1993\).)317 4540 y([14])27 b(B.G.)f(Johnson,)j(C.A.)f(Gonzales,)g(P)-8 b(.M.W.)28 b(Gill,)e(and)h(J.A.)g(P)m(ople,)i(Chem.)42 b(Ph)m(ys.)491 4656 y(Lett.)i(221,)32 b(100)f(\(1994\).)317 4838 y([15])h(D.)g(P)m(orezag)h(and)g(M.R.)g(P)m(ederson,)h(J.)f(Chem.) 44 b(Ph)m(ys.)h(102,)32 b(9345)g(\(1995\).)317 5019 y([16])26 b(A.)h(Zupan,)h(J.P)-8 b(.)28 b(P)m(erdew,)i(K.)c(Burk)m(e,)k(and)d(M.) g(Caus\023)-49 b(a,)28 b(In)m(t.)43 b(J.)27 b(Quan)m(tum)f(Chem.)491 5135 y(61,)32 b(835)g(\(1997\).)317 5317 y([17])38 b(A.)h(Zupan,)h(K.)f (Burk)m(e,)j(M.)d(Ernzerhof,)i(and)e(J.)g(P)-8 b(.)39 b(P)m(erdew,)j(J.)d(Chem.)63 b(Ph)m(ys.)491 5433 y Fq(106)p Fp(,)33 b(10184)e(\(1997\).)p eop %%Page: 9 9 9 8 bop 3549 54 a Fe(9)317 555 y Fp([18])31 b(J.P)-8 b(.)31 b(P)m(erdew,)j(M.)e(Ernzerhof,)g(A.)g(Zupan,)f(and)h(K.)f(Burk)m (e,)i(J.)e(Chem.)43 b(Ph)m(ys.,)34 b(to)491 672 y(app)s(ear.)317 854 y([19])e(K.)g(Burk)m(e,)i(M.)f(Ernzerhof,)h(and)f(J.P)-8 b(.)33 b(P)m(erdew,)h(unpublished.)317 1037 y([20])44 b(M.)h(Ernzerhof,)j(Chem.)80 b(Ph)m(ys.)g(Lett.)g(263,)47 b(499)c(\(1996\);)50 b(J.P)-8 b(.)45 b(P)m(erdew,)k(M.)491 1153 y(Ernzerhof,)41 b(and)e(K.)f(Burk)m(e,)k(J.)d(Chem.)61 b(Ph)m(ys.)j(105,)39 b(9982)f(\(1996\);)j(K.)d(Burk)m(e,)491 1269 y(M.)33 b(Ernzerhof,)h(and)e(J.P)-8 b(.)33 b(P)m(erdew,)i(Chem.)44 b(Ph)m(ys.)h(Lett.)f(265,)31 b(115)h(\(1997\).)317 1452 y([21])f(M.)i(Noland,)e(E.L.)i(Coiti)s(~)-52 b(n)o(o,)32 b(and)g(D.G.)f(T)-8 b(ruhlar,)32 b(J.)g(Ph)m(ys.)45 b(Chem.)f(A101,)31 b(1193)491 1568 y(\(1997\).)317 1751 y([22])h(R.)g(Neumann)h(and)g (N.C.)g(Handy)-8 b(,)33 b(Chem.)44 b(Ph)m(ys.)h(Lett.)f(246,)32 b(381)g(\(1995\).)317 1934 y([23])k(J.M.)g(Martell,)g(J.D.)g(Go)s (ddard,)g(and)h(L.A.)f(Eriksson,)i(J.)e(Ph)m(ys.)56 b(Chem.)f(A101,)491 2050 y(1927)32 b(\(1997\).)317 2233 y([24])g(P)-8 b(.J.)33 b(F)-8 b(eib)s(elman)30 b(and)j(J.)g(Harris,)e(Nature)i(372,)f(135)g (\(1994\).)317 2415 y([25])g(W.R.)h(Sc)m(h)m(ultz)g(and)g(D.J.)f(LeRo)m (y)-8 b(,)33 b(J.)g(Chem.)44 b(Ph)m(ys.)h(42,)32 b(3869)g(\(1965\).)317 2598 y([26])62 b(J.M.)h(Seminaro,)68 b(M.)63 b(Gro)s(dzic)m(ki,)68 b(and)63 b(P)-8 b(.)62 b(P)m(olitzer,)69 b(in)124 b Fd(Density)62 b(F)-7 b(unc-)491 2714 y(tional)38 b(Metho)-5 b(ds)39 b(in)f(Chemistry)g Fp(,)g(edited)e(b)m(y)i(J.)f(Labano)m(wski)g(and)f (J.)h(Andzelm)491 2830 y(\(Springer-V)-8 b(erlag,)31 b(Berlin,)g(1990\).)317 3013 y([27])h(A.)h(Borrmann)e(and)i(R.O.)f (Jones,)i(Chem.)44 b(Ph)m(ys.)h(Lett.)f(252,)32 b(1)g(\(1996\).)317 3196 y([28])g(B.D.)g(Y)-8 b(u)33 b(and)g(M.)g(Sc)m(he\017er,)h(Ph)m (ys.)45 b(Rev.)g(Lett.)e(77,)32 b(1095)g(\(1996\).)317 3378 y([29])g(R.O.)g(Jones)i(and)e(G.)h(Seifert,)f(Ph)m(ys.)45 b(Rev.)f(Lett.)87 b Fq(79)p Fp(,)33 b(443)f(\(1997\).)317 3561 y([30])41 b(J.P)-8 b(.)42 b(P)m(erdew,)k(J.A.)41 b(Chev)-5 b(ary)d(,)45 b(S.H.)d(V)-8 b(osk)m(o,)45 b(K.A.)c(Jac)m (kson,)46 b(M.R.)c(P)m(ederson,)491 3677 y(D.J.)35 b(Singh,)h(and)f(C.) h(Fiolhais,)d(Ph)m(ys.)54 b(Rev.)e(B46,)36 b(6671)e(\(1992\);)i(48,)g (4978)e(\(E\))491 3793 y(\(1993\).)317 3976 y([31])f(M.)h(Ernzerhof,)g (J.P)-8 b(.)34 b(P)m(erdew,)i(and)d(K.)g(Burk)m(e,)i(In)m(t.)47 b(J.)33 b(Quan)m(tum)g(Chem.)92 b Fq(64)p Fp(,)491 4092 y(285)32 b(\(1997\).)317 4275 y([32])g(A.)h(Zupan,)f(P)-8 b(.)33 b(Blaha,)f(K.)g(Sc)m(h)m(w)m(arz,)j(and)e(J.P)-8 b(.)33 b(P)m(erdew,)h(unpublished.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF