/. I. {elec, . 5d0-/-melec-'thbar, and . D=\,

/. K0d1, K. , N. Formàt, K. Kpot, . Formàtmàt1 et al., KORZ FORMAT( 5DI5 . B/ 2DI5. B, I OA2]l TÙRITE ( KOLIT, 99 ) NRITE ( KECRAN, 99 ), p.99

A. *. , *. , *. *. , and K. Hirite,

*. Bgi=bgl, . Tc, . Matl, A. Zl, . Àei et al., TK tfR rrE ( K r o s, r 02 ) KOR 2, MÀTz, zz, ADz, AEz,Tttz, Acz',ncz, rc, rx wRrrE( Kol-rr ,r02), Dr5. 8,', *r.D04* (TC- "Dl5. 8,', ) ) ^r.D03 ; | 5X,'AGr= "Dr5, p.998

B. , Z. Bgl=5x, . Tc=, T. Br5x, D. Bt et al., AD1-AEI*t .D-04^(TC-TMt ) ) *1.D03 DENZ= (ADZ-AEZ^1 .D-04* (TC -TMZ ) ) rt .DO3 HrÀ I -AGt ^DD([' ( _ BGl ^TK

E. 0. Bgz and . Sigz=, tJ AL=SIGI /STG? IF(AL.tT.1.D0)Go, p.104

, Cl.1. -X C2=X XI =Cl 't12=CZ

. Màl-'mc-)-y-c, tÀT I + c 2 ^l4A'I,2 zM0Y=c L),zI+c'2/,22 VMOy=CI,\0I +CZ*02 N=I, N2*S IGz*^ 3

L. Etal=eti+etz and I. I. D0, .S^ETAL)+1.S*ET]*( 1 . /AL-1. ) ) / ( l. -ETAL)r,^z GiZ' ( ( 1. t0.s*ETAL) +r.5,+(1. -AL)*(ETr-ETzt / (r.+ÀL) ) / ( r. -ETAL)^,r2 BETI=-6. À ( ETl^Glt**2+0.25AET2* ( 1. +AL ) ^*z*ÀL^GI2^,\2 ), pp.2-2

, 2+0. 25*ET1/AL*,\3* ( I. +AL )^^2t\GI2^,\2)

, _AL,r,r3_3.^ÀL+6.^AL^^2)* 2ETl *ETZ ^ ^ 2+ALlr x 3 ^ETZ+AL** 3,rETz^2+2. * (ÀL*^3__1. +6. *AL*3. *AL*^Z ) *ml*E112+( I. _ÀL^^3_3. ^ÀL+5. ^ÀL^*z 2^E'I2^^Z ) t3. ^S ) / ( t . _ETÀL ) ^*4 A2=(((1.-HTAL)^((3.,rAL_2._.2.^AL**3+3.*AL,r*2)^ETl+(AL,r,\3_I.+G.^ÀL_ i3'*ALt{2)^ETl'k^'2+2.*(1.-AL^^3-3.'tÀL+6.*AL**z)^ETl,ttrZ+AL^^3+2.^AI '2,\*3*trz+ ^AL^^ 3/\ETz*.*z) +3 . ^s ) / ( I . -EIAL ),r, pp.4-7

G. , =. Vf=hbar-*-kf-/-melec-xm-=3, \. /. Àpf, . Do-/-kf3-/-kf-i-/-Ùr-lte-x,-zmoy, . Màtmoy et al., KOu'r' I I 0 ), 2000.

, CÀLL SPs(KPOT)

5. Continue-2 and \. *. ,

A. Al^-'+-3 and A. ^al^u, ^U^CU+rcz-2. ),tsU)+GAMIz/tJ,\((3.^U2-6. )^CU+ 2U3-6.^U)*SU+6. )+GAI'{l, tu)*CU+(U4-1z.xvz+24. )*sU) )+CV 3U4*(BET12]'(2.^U^SU-(U2-2. )'tCU-2. )+GAl,tl2/V)'( (3,\UZ-5. )^SU-(U3-G.^U) 4CU)+cAMl-/IJz*( (4.,\U3_24.)\tJ)*SU_(U4_12.î,1J2+24.1^CtJ+24. ) )+A1/U^(CV^( SSU-U*CU) /U2+40^( 1. -CU) /ALU)+SV*( (CU+U*SU-r. ) /U2+A0^SU/ALU) ) ) ), pp.3-24

, Cl 2 =CCI 2 ".SQRT ( CI ^C2 )

. S1z=cl2, C1I ) ^ ( t. -CZZ ) -CI2^^Z ) iF

, I02 A51I=f .+(s11-1. )/Ct_ IF( C2 ) i 06 +SI2 / (Clz\Cz) ^^ . 5D0 103 IF(C2)105, pp.106-106

, AS12=SS12

C. , ySS22 ) AS22=SS22 RETURN END IF(0Q.cT.2

, 93= -A( I3, f4. Il ) ^FI (gFZ,AL( I 3, ( I3+3 ,J5-À ( 13 ,2, I I ) ^FI l

, Z,I\, ) 97 =-A( I3

I. and /. Vmoi-*, Gl +G2 ) t e rm3 2 =TERM3 2+4 . D}xpI /VMO I,\ ( G3+G4 ) u=(1.D0_2.D0^xI,rxl) t. e rm3 3 =TERM33+ I 2 . DO*pI /VMOI,\U* ( c5+G6 ) term34 =TERM34+12. DO'rpI /VMOI^U^ ( G7+GB ) iF(14, I1 )*Ff Z(eFZ,AL( I3

, 910=A, vol.33, issue.11

, 911=-À( I3,14. r1 ) *FI2(QF2,ÀL( I3,I4, It ) ) gI2=-A( ( I3+3 )TI )^FJz (QFZ,AL( ( I3+3),f4,II ) )

, D0 ) ^ ( Gg+Glo ) Lerm36=TERM36+10.DO*PIlVMOI,r ( 3. DO*U,tU-1. D0 ) ^ (GI1+G12 ) so to 25 ql-A( f3, l, I1 ) ^FBf ( qF,gQ,ÀL( I3,1, fI ) ) q2=A( ( I3+3 ) , L. rI ) ^FBJ(QF,QQ,AL( ( I3+3 )

, A, vol.131414, issue.14, pp.1-1

+. Do^pi and . Vmoi-^, GI+GZ ) berm3 2 =TFiRM3 2+4 . DO*PI /VMO I^ ( G3+G4 ) term3_1--TERM3 3-iZ. D0,rpI /VMOI* ( G5+G5 ) term34 =TERM34 -I Z . DO^PI /Vl4O I* ( G7 +GB ) rF( 14, IFB.TZ(gF,QQ,ÀL( ( I3+3 ), pp.1-1

, A( I?, Tt )*FBr2(gF.gg,ÀL( I3

, term3 5 =TER|43 5+10 . Do,tPI /Vl4OI,r 2 . DO^ ( G9+GI0 ) t,erm36 =TERM3a+l 0 . D0,\pI /V!4OI),Z. D0^ ( GI I+clZ ) TERM 3 =

, = ( terml+termZ+term3 ) /eps*Z.DO^RYD CONTINUE xnorm=(4*Pr'fzv( rt) /vMor/gg/eD tmodif d, BB D0UBLE PRECISIoN FUNCTION FBJ2 (QF,Qg,AL ) IMPLICIT DOUBLE PRECISTOUTE_H,O_Z)

, L4 L59Z653sB:t -t s3Z3B46 zà+zf:oO-' A-DEXp ( -( DARS ( gF-pQ ) _gF l

, c=QF+DABS ( QF-gg ) H_=DABS(QF-pQ)-gF FBJ 2 = 3' D'^E/ 4' D0^ ( B-A ) ^ ( 6, DAB9 I ar: aQ ) /DÀBs ( gF-Q0 )

+. , D0 / DArrs ( 0f : gg I 1DlBs r pn_ pq I ïi. pg rôî'16ï t,t r . oo 7 nr

+. +e-'do-*-e-r, QF-Qg ) ^ ( A+B ) +3 . D0*E/ B . D0

A. Al^-r-cin, *. H. Ta, and I. , , p.5

, Do*E t rc .oo t eL, DABS i gr_Qp l 5* ( ( 2. D0^ÀL_Ft*H) *À_ ( 2. D0,kÀL_c,rc) *B ) REITLTRN END DOUBLE PRECISION FUNCTION FBI2(QF,QQ,AL) iMpt,rcrr DoUBLE pRecrsroN

E. Al,

F. =e, ( al-qq I IPAPs ( QF-QQ I zoeËs r ôF-gq ) ^AL^AL ) -E

D. , A+B) ^3 . DO^AL/ QF lQrrôÂns( QF-Aô ) rôÀns ( gF_Qg )

, RETURN END DOUBLE pRECtSIoN FUNCTION FBJ(QF,Qg,AL) rMpt,rcrT DoUBLE pRECrsroN(A_H

F. Dàbs and *. Z. , QF-gg ) / z . D0^DsgRT ( pr ) * ( z . Do,rÀL-( QF-DABS ( QF_ I0Q ) )'\^ 2 ) ^DE(I I :101_ DÀÈS r gF-Qg t t i xz t +, pp.5-5

D. /. and /. Dabs_-(-qf-qq-t-tz, ( gF-oQ ) ) ^*2 t q .nô | AL') /8. D0/ÀL^* 2 . sDO RETURN END DoUBLE pRECiStON FUNCTION FBT( QF,gg,ÀL) rMpt,rcrr DoUBLE pRECrsroN(A_H,ô_zi- PI, J . 141592653 58979 323846264 3D0O L-Br = I . D0 / QF/DABS ( QF-gQ ) / 4 . ïO^DSQRT ( pr /AL ) ^ ( DE)(p ( -( QF-DABS ( QF l-gg) t).*2/4.D}lAL)-IrEXp( -(QF+DAÈSrQr--90) )**2 /4.D|IAL) )

L. , IMpLrcrr DoIIBLE pRECrsroN(A_ir,otzi-[: )j = J . 14 t592trl,3 589'7 9323846264]D00 A=DEXp i ( DAITS ( gF'-CQ ) -gF

, QF-QQ) ) À,rZi 4

, FBIi =l .r0l0FlDABSlpi aa ) /4.D0^DSQRT(pr/ÀL) ^ (À+B) -1. D0/QF 1 /DABS ( 8F Tr8 ) / QFIDABS ( 8F -QQI / 2 . DOIAL^OSQNrI PT /AL ) * ( A-B )

R. Itctijijlfj, I. , R. Ftrnç11g, *. Fbj1-(-qf-',-gq, and A. ). , rMIrLrcir DoUBLE pREcrsroN(A_H, o:zi- E r

L. and =. , D0/ÀL ) ll-fllxl( ( QF +DAnsr gr, p.6

T. , D0 :: /.ql/.iiÀn! r çn-Qg ) D0^AL :: .I^ il I I . i . D0 / 0l'1?Al! ( qF 0Ç ) {!AIs r pn_ op t ler rB, UABS ( pF_Qg t i Âu B. u0,kË* r ôie_ Hne I RET'I.]RN Hl,l) irouBl_,8 pRtrcIs i0N F.UNCTION FJ2 ( QFz ,AL ) II4I'LiCiT I]OUBLE TJRIiCISION (A -TI

P. , =. , and O. Pi-=, ( 1 . t)0 +5 . Do*DD(ei -prz /AL ) ) *ôlg*T1 pr, ÀL ) ) *DSÊRT( pr /AL7ÀL / AL | /8 . D0+0 . 25D0,+ , :rlggRr( pr ) /AL^*2;5D0*DExp( _çr.zi et) RETURN IlND DOUBLE PRECIISION FUNCTI0N FI2( gr-2,AL) II"IPLICIT DC)UBLE PRECISION . :r . ll0,/ QFtl ^DSQRT ( PI ^AL ^ALi\AL ) / QFZI,( I . D0 -DffiP ( -QFz / AL ) ) / Ql-? i -i . 5i), p.0

I. , ^DS9RT(FlI/AL) RET'UI?N li\L' t ,l t DOUBLE PRECrsIoN FLTNCTION r_I1 (QFz,AL) IMF'LTCIT' DOTIBLE PRECTSTOTtA-U,O-Z) pI

A. , /. Qfz, L. , I. Doi, E. Bi et al., ^DS9RT(prlAL) ,_iiifiiAb-z / z. noi 1 r . no_ÀEr<p? _Orz 7ei j ï-Ééqnrt prQFz,AL) IMPLICIT DOIIBLE PRECISION(A .T1,6-ZI Pr = 3 . 14 I 59 265358979 323846264 3D00 i;Jl'= I . IJO / 4DsgRT( prlAL ) / QFz 1 + i, D0 / gF.z).( 1 . D0 DD<p D0 / AL^*2 . 5DO,r ( \\, zlpg*pFz l,rnrxp ( -QFTZÀI l insgRl ( pr 2 r J-.rri QRT

L. Precisi0n, F. Fi-(-girz, A. Implicit, D. Precision-(-a-ti, O. Iiell-'lli{n et al., DSQRT(prlAL) ^DSQRT(PI /ÀL**3 ) i+ DEXP ( -Qb D0^DSgRT( pI rÂL**s ) iTEI'URN IlNil SUBROLTTINE G8, I4 1 59 26535897 9323846264 3D00 F'J= 1 . LIO /B .DO / QF}^ ( 1. DO-IJEXF):: G(Q) DE VASr-rlSTA --sINGWI rF( KDIE.EQ. 9 )G0 T0 r0 G=0. GO T0 15 i0 cÀLL GQVS(RS,AÀA,BBB) G-AI\I\'\ ( 1 . DO-DD(P ( -BBB'IK^K/KF/KF) ) 15 CONTÏNUE RETTIRN ENI

D. , IiEC r S i 0N i]uNCI.I 0N r, 1 ( ft ) II4PLICIT L)OUBLL: PRECIsION (A-H

I. K. Doutsle, A. R. , A. , A. , V. V2-)-f-1 et al., {K*vl REl'URN END F2

!. _ble, F. Rflcrsron, Û. Yt_ljcrr-double-piéôisiôiii-t-e, and . Ble,

!. Àll-vijbac-(-k, . Vi, F. Vzi, R. Turn-e-Ài-r-'\, . Litv et al.,

=. Ir3, *. Vi-rijturn-iinir-t-)-ouiile-piii, K. Ca-], and L. Vi,

F. ). Vl_v2 and \. ,

, F4

M. , C. Du, . De, and . Modif-,

*. *. ,

*. Calcul-du-pseudopotentiel-et-du-facteur-d.-e-forme-pour-un-alliaqe-j, *. ^. , U. Valence-ad, A. , I. Coef et al., DTMENSToN s ( 6'6 ), Qt'torNS (G, E), 1I.'1ERKX( 5 ) . MERKY( g ) f LMÀXÀL1C0 (2t,ALaCOCIC0R tllLl,tKORZ( I0) climension xtv04021D0 , .o6zg6D0, . og0BrDo, r. 12374D0 . . 16171D0 , .2046LD0, .2523rD0, . 30460D0 , .36Lr7D048534D0, .55147D0. .61871D0, .68493D0 , .7463LD0, pp.2-2, 2006.

7. , .. 8. 78999d0, . 74924d0, and . 73439d0,

7. 72275d0 and . 72254d0, , pp.724-732

, 72710D0 , .7287 3D0

7. 73776d0, . 73900d0, . 74016d0, . 74i24d0, and ^. *. 75300d0, 9D0,2. gDO, 33' 0D0' 3' 1D0, 3 . 2D0, 3 . 3Do, 3 -4Do, 3, gDO,1. g5D0, 22. 0D0, 2 . 1D0,2 . zDO, 2 . 3D0, 2. 4DO, 2 . 5D0,2 . 6D0,2, 7DOD0/ DATA AVS/ . 70853D0, .85509D0, . 97905D0,1.08482D0,1. I 7gg7DO ,L.26569DC DÀTA BVS, p.5, 2000.

2. *. Korl, K. Kecran, I. , K. Korz, . Format et al., NVF(, pRECI 106 F'ORIIAT( 5Dl5, ùR ITE ( KOUT, IA 2 ) KD04* (TC-' ,D15.8. ' ) ),r,I.D03, p.5

/. Denl=, W. Denz, . Kout, . To-'7-)-rinit, . Rpas et al., lZ ) ) ^ 1 . D0 3 0l=MATI

X. De, X. De-rf4, and D. Preci=-',,

I. and I. Kout,

F. , X. Volumes, A. Des-c-zps, P. Màtmo, =. C. et al., , p.5

R. =. , \. /. Do, and . Ab,

\. ^. Gotofonctron and D. De-hartree, 100I ,1002,1003 ,1004,1005, 1005 )KDIE l00t hIRITE, pp.0-6

/. Drile, , p.12

D. Forl, . De-vàshïstà-singwt, A. Xrs, Y. Call-fitid, . Xrs et al., , pp.1003-1007

1. Fori-"-iat-(-10x, D. Fonctton, and . De-t0tg0-wo0druff, ) ntv=46 call tita( nbv,xl-v,ytv,yytv) G0T0, pp.1006-1010

1. F-'ori-'iàt-(-lox, . Fonction-dielectr-]-que, . T. De-s, and L. Rf-10x,-',-q-"-rbx,-'vi-',, 18X,',Fl1"18X,',FI? " 18X 2-i I.'ONC.i iùI{L iE( KOuT, 3I0c ) li.l-oNC_J,V2,22, F'REt, D0 QX=L1 IF(KoDVQ. NE. I )G0T0 L7 DO 15 I=I,10I VZ 22 =V 2'2MÀX1 i,\+iI'IIE( KE(litÀN, Ji(i0 )i::, F.CTNC _l4^A.{i XINtri..tSiJP ii;.( LlÂjis ( ir0NC 3 ) . LT. DAilS r JO4 C, CONTIN{.JE -10:;C C0l'JTitJUE V22.=V'22t V2Z2 (v 222^i)iiEcI ) ) ), pp.4-4

, 20I2) r ,vZZI ,vZZZ ,xrïZ wr i tt_. ( kECFÀN ,20!;:. ) r ,vZZi ,v222 ,vZZ '2012 F ORt''A'i { .v

R. À. I.-"-r-'^-^-^-À-*-'r-':-\-'^-^-+à-*-*-r\-t-*-Âr\,

R. R. , R. ]. , T. , N. , D. Wr-i-tl--i et al., IUBLE PRHCISIoN F-UNCTI0N r'1 (Qq) IMPTICTT DOUBLE PRECISION(A-TI,D.ZI COMMON/AVECII--iR,aC q=qq/a0 CALL VIJBÀC ( g . Vi ,V2 ,I-I1 , Fi 2 ,1122) ir l =i"I I ^DSiN( pQ*R ) / 8Q IiETURN ENIT Il'ltJBLL;'rrRECI-.lION FUNCTION F2 ( Qq ) iMT'I, p.1006

{. Vijbac, V. I. Vj, |. Fl, and F. , i:l =F'l 2^l-)3 iN ( {j!*H ) / QrJ ,R llTIiiir\,I L-I\l t'l L)L)LIBLE FRECISIÛN I:UNCTION !-3 ( Qq ) iI'IFLIt]JT LIOUBLE T'I?ECISION(À-iI, O-Z) CC)MI.4(:,N i AVECF / II . A O ti:, titq / :-ii-; cÀLL VI.iBACI( g, ) l-1.=ir2 2 *Lli: I iJ { Qç*11 ) / gQ RETURI\ :.li

. Sl-iiirou-'iinl, , pp.2-22

, IMIr;ICIT triuBLE pi{IiCISION

. Doi, K. J. /-'blia-pfectsici, . Kf, X. Ai, . Kf et al., tF ( Q. cT. I . D06 ) GCj TO ZÇt 'j.i.DCrt, ÂLrco<zl 1A ( 6, 4, 2r,','.V ('2),wtlVi;L l{1-,Qi(2.D0^KF) il'(xi ^0. Dû ) t-1, L 3, 1.2 IF (:{l . l_.IJO ) i5, i 4,i5 Ij')i.l.DC C/j T0 I, pp.2-2

{. ^. , \. , ^. , and *. *. , À * ,\ f ,r I)O 3l fl-.1.2, II)+-L :|HRM2.0. L, pp.4-4

. ]. Tj and . =o, DOO Ler-rn-jf.:Q. l)Q[r Lernr3Z=ù

, tV-e( ( i.r+-l ), i. It )^FBJ?gn,Q0,AL( i I3-r3),I,It ) )

. _Î, pF; ap lÂl ( I3 , 14 , I1 ; t ' ' qi -_ A!1 r3 { .r ), ij.: _il i iiBq!0r.,OO,Air iil;i j, ra, r1) *F.Br1( Qr" QQlaL(12, pp.1-5

, Àir ir:i 3t, p.2

, IlBrl ( gF, pg;Ârt rr,14. ii it' sB=-A( ( r3+ 3),i.4.,_l] ) lfBJr?9r, gg,Aii aii;i i,r+,r |-i-'r'm3 i.TERl,ll1+4 . pg*pI /VMgi* t Gt+CZ ) t ;r rn, J2 =TERM3 Z+4 . D0 ÀpI /VMO I* ( G3+G4 ) i:erm33=TERM33 . iZ . DO^PIIVMOI^ ( CS+G6 ) term34 =TERM34 -I Z . D0^pI /VMOI* ( G7+GB ) IF( I4.LT.4 )GOTO 25, pp.7-10

À. *. Jr, *. {-*-À-r\-^-t-rt, ^. , and ^. R\^, G9+ç1 g I Gl1+c12 ) 1) )

, rEIiMl -4 rPI^z|gIlvygr / gg I QQ^( ctcoR( rr ) ^DD(p( _Qg^QQ / 4.Do i/AL1C0( rr ) I +c?.coF

, II ) ) /AL( I3 ,14,ït ) ^^I.5D00 in:À( il, i4, ft ).+Àr 'ir 3 II ) i ), D0 30 i3=1

*. , 5D00 /VMOI rTEitM2l Ii,'( gQ. GT. 2 . LrO,rQF ) coTo 24 ,;i=À( I3,I ,Il )rFI (eFZ,AL( 13,1, f 1) ), I1)iFJ(9F2,ÀLt irr+r)

3. Ai and I. , Il ),rF.I(QFt,ÀL( I 3, l4,tti t 'J1= À( ( It,3) ,l!:ItllFJ (gPz,AL( r i j+: j ,r+

, Tl ) ) it6-ft( ( I3 f3 ),7 !ïllnptt(QF-Z,AL( ( I3+3 ), pp.1-2

, AL( r3,i4,tti t' - q8=, pp.1-1

I. Ter-m-l and . Termji, D(i*pI/VMôI* (Gt+CZ ) t c r m J 2

, {U^ ( G5 i Ce I t. c r ni i 4 = L'.1-iRM 3

, LT. 4 ) c0T0 25 99=À( I-i, 3, iL ) *FI2(gFZ,AL( I3, 3, Il ) ) ii0.,Ai ( I3.r.3) ,1: ii I ^FJ

, ( it*_l't,T4,II t.'i'm_15=TEIiMl5r i 0, D0,kpI /VMôI^ ( 3 . D0,\U,rU_ 1 . D0 ) ^, p.12

. Lerm-rl-'=term36 and . Vmoià, D0^U^U_i.D0 ) * g'r Lu 25 L+ ))

. Ij-'-i, { ( I -l . -i , I I t ,. i:'}r i 2 ( !;' , !12 , Ài , ( L j , 3, i I ) ), pp.0-1

I. , I. ). +f-'bl-)-tef, A. Qg, and . Ij, , pp.912-916

\. /. Vl-v, D0^ ( Gl1+Gl2 ) TURMJ =TEI{M31 tTERM3 2 +TERM3 3+TERM34 + 1ERM35+TER}436 w( i1) --( t-ermi_ +t erm2+tc,rm3 ) /eps,rZ.D0ÀRyD CONTINUii NnLlrm: ( a|.e iri *ZM{t iM() i / Qp i 8e } C0NTINT-,'Fl Vl=wi, TERM36r 10 . D0ÀPI /Vl40I )+ZD0iRyIJlxNORl,liXI{ORM,\(Eps-l.Do)*Eps/(r.D0*c) t'i 2 =vi t 2 -'D0 / RYD*V2 / 2 .DjlRYD/xNORI,t/XNORM* ( Eps -I . D0 ) *Eps / ( I . D0 c )

F. ,

, Rii, vol.14, issue.11

, J l0 _li f D0UBLE PRECTSION FUNCTION FBJz(gF,Qp,AL) rMplrcrr DoUBLE pRECrsroN(À_H,ojzt

. H=llabs, QF FBr 2 = 3 . DO^E/ 4 . D0'\ ( B-A ) ^ ( 5 . pgiA! / gf {Qr{g4Bs ! QF-QQ ) /DÀBs

, QF-qQ I IDAB5 ( gF-Aq I + r. ôo r ôi r gÈ) * r

, DABS i 9r-6N ) / DABS ïQF:9Q ) * ( A+BI+3 . DO,IE/ B . DO 1/.91 lgF lpÀBs c^B+H'\A ) +3 . Do;Er âlno / QF/DABS ( QF-QQ )

À. Gf, AL,r ( c^B-H'rA ) + I . Do*E/ I 5 . DO I AL, AL7 QFIDABS îpr_pg I 5^ ( ( 2 . D0*trtr-pl,tH ) *A-( 2. D0,tAL-G^G),rB

R. End, F. Function, . Qf, . Qq, . At et al.,

, ) ) *'t2 / 4.D0 / AL) E=DSQRT ( PI /AL

=. /. Fbr2, QF-QQ ) +Lz.Do I eî, 1QF/DABS ( QF-QQ ) /DÀBS ( QF-gQ ) /DABS ( QF-QQ ) ^AL,rAL ) -E

D. Dabs,

R. Iurn, . Double-preciston-functton-ftsj, Q. Qf, A. Implicit, and . Precision,

, PI = 3 . 1 4 I 59265358979 3238462643D00 l"BJ = 1 ) )'\^2 / 4 .DO I ALt /8. DO / ^L^^2 . 5Dô 2 -DSQRT( pr ) * ( 2.D0^AL-( QF+DABS ( QF 3-QQ|)^^2 )^DE)<P( -(QF+DABS(QF-QQ) )^*2 |4.DOIALt t 8.D0/AL^^2.5D0 RETURN END DoUBLE PRECTSTON FUNCTI0N FBI(QF,QQ,AL) IMPLICIT DOUBLE PRECISION(A_H,O-ZI Pi = 3 . L4L592653589793238462643D00 FBI = I . D0 / QF/DÀBS ( QF-9Q ) / 4 . DO^DSQRT( PI /AL ) ^ ( DE)(P ( -( QF-DÀBS ( QF l-gq) )**2 /4.DO/AL)-DD(P(-(QF+DABS(QF-QQ) )^,t2 t4

, RETURN END ilOuBLE PRiç15 t0N F.r.lNCTI0N r;,IJT .r ( 0r , gg

I. and Q. ,

=. Pi,

, Q0 ) ) L kzl 4

-. Fbri-=r and . Qrr, D0^DSQRT(pr /ÀL ) ^ (À+B ) -1 . D0lQF ti !.18s(QF QQ) /QF/ DABSrôÈ-oO t rz.ooinr, tos9nrrpr/AL) ^(A_B) RE'.TURN END ITOUIJLE I-'RECiSION FITNCTION FBJt ( QF, QQ,AL ) iMI'LICIT IjOUBLE PRECISfOntre_H

L. and =. J. , 14 1592653589793 ZIAq6Z643DOO r\.LrEXP( -( DABS ( gf

, rDAijS, pE,_pô ) ) ^,t2 / 4

G. Qf+dabs, QF -Q8 ) il=LIAES(Qr'8p)-QF

I. Ftsjl=, A. Af_, and Q. , ? ( qf -Qe ) / ALi N.j ia. ôo *e* r n*î:2. 6ô ier _G,rc ) +À^ ( z . D0 ^ÀL .. -l-t^ii I ) -I . D0 ( qf gg ) /DABS ( gF_ gg, DCr,tE* ( c*B+H*A ) :r:. L..?!l-l 0l-/ Ql.,/DABS ( gi-._ôo r 7Âi, / B . D0^E* ( G*B_H^À

, I{ET'URN Ltù]_! i-rOUiJi,i:l I'RIjCISi0N FUNCTTON FJZ

I. Licit, I. Precision-(-a-i{, O. *. Al-',, and /. Qfz^, QFz I r 0' 7 5D0 / Ot'z't ( 1 . Do +5 . D0^DD(pi -grz /AL ) ) *ôsqnrt pr, QF2+r .Do / QFz^ ,: ( i .Il(r+11 . D0*.DLïp ALt ) ^DSÈRTt pr zer.7ÀLlÀL ) /8. D0+0. 2sDO* _rlsgRr( pr ) /ÀL**2 . 5D0,+DEXn t . grzT et) RETURN

I. Enij-il0uble-precis, A. Imfliclt, T. , and O. , 2643D00 }i I 2, pp.0-2, 9323846.

I. , -QF 2 /ÀL ) ) *DSQRT ( PI^AL ) / QFZ+ 0 . 25D0 / QFz^ Z ( I . D0-L-'EX[)( -QFzlAL) ) ^DS9RT( PI/ÀL) 11p1ï_rI?N ii\L', DOUBLE; PRECrsIoN F-UNCTION F'I1

I. Doi, . Ible, and . A_h, , p.14

=. Frr and . D0,

, D0^ ( 1 -D0-DD(P ( -QF}7ar, l r *nspnrrpr^ÀL | / QFz FJNI] i]OIJBT,E PRFJCISlON I.'IJNCTION I, JI, issue.2

I. Doirble-precrsion, Pr -3 . l4 I 5 926535897 9323A46264 3DO0 i:-J I = l\DSQRT(prlAL, / eFlz I + i, Il0 / 4 .Do / QF2/.( r.D0 -DD D0 / 8F2l B . D0 / AL^^2 . 5D0^ ( AL -2 -11g,tqFZ )'IDD<P ( -QFZ /Àt ) iDSQRT ( pI z iL)SQRT(pr ) /8.|'0 /QFTIAL^* j.5U0,r( 1.Dô-4.D0^DD(PÎ_pnzlÀL) )

L. Qfz, A. Implicit, and . Precision,

P. ,

J. Ijou-fjle-!-'rt and F. Trn,

I. , I. Lx-)-i, . Ible, and O. Precision-(-a-h, PI -3 . 14 I 59 2653589 7 9 tZ 3846254 3D00 F'"r = I, Do / QFz* ( t. D0-Dlxp( -QFz/AL) ) ^DSQRT(prlAL*^3 )

I. Diixt and '. , D0^DSQRT( pI /ÂL^^5 ) RE'I'URN iiND Il(J 550Ett. rX) c0'I,O 560 550 CONTINTIE iib0 D0 590 K=I, Iy) =MERKY( IX) 600 MERKY( IX) =IX SI=0. 0D0 S2=L).0D0 D0 .t2O I=1,N frO lZ0 K=I.N CIK=C|.0D0 DO 710 L=l) Sl=St+CIK / 20 S2=S2+CIK 5Z=52-S I 51-S1/FL,OAT(N) -iERR -Cr

O. Preciiiôi,

P. Kf, R. , and G. , 254829._t9ZD00 A2--.284496736D00 Àl= 1D00+p*X) T2 =.I,LT 'r4 --I2 *.T2 frliï*r;uo o -( At r.r+AZ, 453152027D00 A5=1.061405429D00 T^=1.D00

M. Prtrciston,

D. Precision, . Pï, and . Ci, jj{i . û6;LBr.iD0 31.?.t13'/'-;D0 ll,i, = ?

!. , ,r9Bb'I-r ..07 r--ii=!i. +830I1 ,l? c6-.4.1909D-11 X.IrliSRT( IiS )

G. and I. , D0 / (.5û0+cl ^zL**2+C2^ZI^t\4,rC3)<21^*6+C4*ZI^*B+C 5r, pp.0-6

, ( g. 110 xB2+.6. D0^81^Bl ) ^x*^2+ i ( 9 . D0,(i.rj t -7, D0t Bl Ats2 ) ^x^^3+8. D0iBl,\83^X*^4 ) GAI4MÀ2 .-80 ÀPT rÀLPttA^x^

G. , DC* ( l-. i_rO+81*X+BZ,\X?r^2+03^X^* 3) ^),?

G. and M. Gal,

, D0 -G0 ) -r6 . D0 i 1 s . Do^Àicr{r CIC;-l.t=. !i525i10,\ ( 1. D0 -G0 ) -.75ill0^cAMt,tA-3.2D0*AICHI j:lIÀ= ? / KF r-12 -Àf CIlT, BrcHi = . 56 2 5Il0^GAMMÀ -' . 0468 75D0^ ( I .DO+tsTA) / ( Z.D0-ETÀ) ) )

G. , DOIETA^ ( 4 _ D0-ETA*^Z ) G5.AICIII ÀE'rA*À4 + ( BTi--FiT f B. DO i 3, DO^AICHT ) ^ETA^^2.CICHI G=GZ +G4.\G5 ZAçs CONTINUE RETURN END l1: j i trg

S. R. , Phys. Rev, vol.174, p.769, 1968.

H. J. , M. T. Et, and V. W. Der, Physica ZÊ, vol.259, 1974.

C. H. Woo, W. S. Et, and M. , Electronic structure of metals. I. Energy independent model pseudopotential formalism, Journal of Physics F: Metal Physics, vol.5, issue.10, p.1836, 1975.
DOI : 10.1088/0305-4608/5/10/007

W. S. , L. S. Et, and S. C. , J. Phys, issue.22, pp.10-445, 1980.

W. S. and L. S. , J. Phys. F L0, issue.23, 198012717.

L. J. Kgl and . Videnskab, Selskab. Mat. Fys. Medd, issue.24, pp.2-3

S. R. , J. Phys. C e, issue.25

K. S. S|ngwi, T. M. Sjôlander-a, and L. R. Et, Phys. Rev. B, vol.1, issue.26, p.1044, 1970.

V. P. Et and S. K. , Phys. Rev. B, vol.0, issue.875, 1972.

T. F. Et and W. O. , Phys. Rev. B, vol.2, issue.3958, 1970.

K. S. Stncwt, T. M. Land-r, and S. A. Et, Phys. Rev, issue.29, pp.176-177

S. Iohimaru and U. K. Et, Phys. Rev, issue.30, pp.4-7385, 1981.

H. W. , Pseudopotentials in the theory of metals, 1966.

. Ed and . Benjamin,

S. R. and S. R. , J. Phys. C e J. Phys. C g, issue.32, p.1140, 1970.

D. R. Hamann, S. M. Et, and C. , Phys. Rev, vol.4, issue.1, p.494, 1979.

. J. Hafner, From Hamiltonians to Phase Diagrams (The Electronic and Statistical-Mechanical Theory of sp-Bonded Metals and Alloys), 1987.

S. C. , M. R. Et-wanc, and S. , J. Phys. Fg, p.78, 1978.

, ABRAMOWITZ M' et STEGUN l'A';Handbook of mathematical I 'functions (1972) Dover publications

E. O. Et-reissland and J. A. , 2066' (39) CRAWLEY A.F. ; Int. Met' Rev' ll (9741 32' (40) KouBAA N. et GASSER J.G. ; Analytical local screened form factor obtained from Bachelet, J. Phys. F, vol.3, issue.38, 1973.

T. E. Faber, Z. J. Phil, and . Mag, IL (1965) 153' (42\ WASEDA y. ; The Structure of non Crystalline materials Editeur : Mc Graw. Hill int' Book Compagny' (43) PERCUS, J.D. et YEVIcK G.W. ; Phys. Rev, vol.110, issue.1, 1958.

N. W. Aschroft, J. ;Phvs; Rev.MARCHN.H.Liquidmeta|s.|nst.Ser.Monogr.inNationa|Phy|oso, vol.83, issue.5, p.145, 1966.