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SUBROUTINE ANALYT(PSUM,PALPHA,PBETA,COORD,NAT,JJA,JJD,
1IIA,IID,ENG)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION COORD(3,*),ENG(3), PSUM(*), PALPHA(*), PBETA(*),NAT(*)
************************************************************************
* *
* CALCULATION OF ANALYTICAL DERIVATIVES *
* *
************************************************************************
C
C COMMON BLOCKS 'OWNED' BY REST OF PROGRAM.
C
COMMON /CORE / CORE(107)
1 /BETAS / BETAS(107),BETAP(107),BETAD(107)
2 /EXPONT/ ZS(107),ZP(107),ZD(107)
3 /ALPHA / ALPA(107)
COMMON /TWOEL3/ F03(107)
COMMON /NATORB/ NATORB(107)
COMMON /ALPHA3/ ALP3(153)
COMMON /IDEAS / FN1(107,10),FN2(107,10),FN3(107,10)
COMMON /WMATRX/ W(N2ELEC*2)
COMMON /NATYPE/ NZTYPE(107),MTYPE(30),LTYPE
COMMON /BETA3 / BETA3(153)
COMMON /VSIPS / VS(107),VP(107),VD(107)
COMMON /KEYWRD/ KEYWRD
C
C COMMON BLOCKS 'OWNED' BY ANT
C
COMMON /DERIVS/ DS(16),DG(22),DR(100),TDX(3),TDY(3),TDZ(3)
COMMON /EXTRA/ G(22), TXYZ(9)
C
C ON RETURN, ENG HOLDS ANALYTICAL DERIVATIVES
C
COMMON /FORCE3/ IDMY(5),I3N,IX
COMMON /NUMCAL/ NUMCAL
DIMENSION EAA(3),EAB(3),ENUC(3), BI(4), BJ(4)
CHARACTER*241 KEYWRD
SAVE AM1, MINDO3
LOGICAL AM1, MINDO3
DATA ICALCN/0/
IF (ICALCN.NE.NUMCAL) THEN
ICALCN=NUMCAL
AM1=(INDEX(KEYWRD,'AM1')+INDEX(KEYWRD,'PM3').NE.0)
MINDO3=(INDEX(KEYWRD,'MINDO').NE.0)
ENDIF
A0=0.529167D0
JD=JJD-JJA+1
JA=1
ID=IID-IIA+1+JD
IA=JD+1
DO 10 J=1,3
EAA(J)=0.0D0
EAB(J)=0.0D0
ENUC(J)=0.0D0
ENG(J)=0.0D0
10 CONTINUE
I=2
NI=NAT(I)
ISTART=NZTYPE(NI)*4-3
J=1
NJ=NAT(J)
JSTART=NZTYPE(NJ)*4-3
R2=(COORD(1,I)-COORD(1,J))**2+(COORD(2,I)-COORD(2,J))**2
1 + (COORD(3,I)-COORD(3,J))**2
RIJ=SQRT(R2)
R0=RIJ/A0
RR=R2/(A0*A0)
DO 150 IX=1,3
DEL1=COORD(IX,I)-COORD(IX,J)
TERMAA=0.0D0
TERMAB=0.0D0
ISP=0
IOL=0
C THE FIRST DERIVATIVES OF OVERLAP INTEGRALS
DO 30 K=IA,ID
KA=K-IA
KG=ISTART+KA
DO 30 L=JA,JD
LA=L-JA
LG=JSTART+LA
IOL=IOL+1
DS(IOL)=0.0D0
IF(KA.EQ.0.AND.LA.EQ.0) THEN
C (S/S) TERM
IF(ABS(DEL1).LE.1.0D-6) GO TO 30
IS=1
ELSEIF(KA.EQ.0.AND.LA.GT.0) THEN
C (S/P) TERM
IS=3
IF(IX.EQ.LA) GO TO 20
IF(ABS(DEL1).LE.1.0D-6) GO TO 30
IS=2
DEL2=COORD(LA,I)-COORD(LA,J)
ELSEIF(KA.GT.0.AND.LA.EQ.0) THEN
C (P/S) TERM
IS=5
IF(IX.EQ.KA) GO TO 20
IF(ABS(DEL1).LE.1.0D-6) GO TO 30
IS=4
DEL2=COORD(KA,I)-COORD(KA,J)
ELSE
C (P/P) TERM
IF(KA.EQ.LA) THEN
C P/P
IS=9
IF(IX.EQ.KA) GO TO 20
IF(ABS(DEL1).LE.1.0D-6) GO TO 30
C P'/P'
IS=8
DEL2=COORD(KA,I)-COORD(KA,J)
ELSEIF(IX.NE.KA.AND.IX.NE.LA) THEN
C P'/P"
IF(ABS(DEL1).LE.1.0D-6) GO TO 30
IS=7
DEL2=COORD(KA,I)-COORD(KA,J)
DEL3=COORD(LA,I)-COORD(LA,J)
ELSE
C P/P' OR P'/P
DEL2=COORD(KA+LA-IX,I)-COORD(KA+LA-IX,J)
IS=6
ENDIF
ENDIF
C
C CALCULATE OVERLAP DERIVATIVES, STORE RESULTS IN DS
C
20 CALL DERS(KG,LG,RR,DEL1,DEL2,DEL3,IS,IOL)
30 CONTINUE
IF(.NOT.MINDO3.AND.IX.EQ.1) READ (2) (G(I22),I22=1,22)
IF(.NOT.MINDO3) CALL DELRI(DG,NI,NJ,R0,DEL1)
CALL DELMOL(COORD,I,J,NI,NJ,IA,ID,JA,JD,IX,RIJ,DEL1,ISP)
C
C THE FIRST DERIVATIVE OF NUCLEAR REPULSION TERM
IF(MINDO3)THEN
II=MAX(NI,NJ)
NBOND=(II*(II-1))/2+NI+NJ-II
ALPHA=0
IF(NBOND.LT.154)THEN
ALPHA=ALP3(NBOND)
ELSE
ALPH1=100
ALPH2=100
IF(NATORB(NI).EQ.0)ALPH1=ALPA(NI)
IF(NATORB(NJ).EQ.0)ALPH2=ALPA(NJ)
ENDIF
C2=(7.1995D0/F03(NI)+7.1995D0/F03(NJ))**2
C1=DEL1/RIJ*CORE(NI)*CORE(NJ)*14.399D0
C3=DEL1/RIJ*ABS(CORE(NI)*CORE(NJ))*14.399D0
IF(NBOND.EQ.22.OR.NBOND.EQ.29)THEN
TERMNC=-C1*ALPHA*(1.D0/RIJ**2 - RIJ*(RIJ**2+C2)**(-1.5D0)
1 + 1.D0/RIJ - 1.D0/SQRT(RIJ**2+C2)) * EXP(-RIJ) -
2C1*RIJ*(RIJ**2+C2)**(-1.5D0)
ELSEIF (RIJ.LT.1.D0.AND.NATORB(NI)*NATORB(NJ).EQ.0) THEN
TERMNC=0.D0
ELSEIF(NBOND.GE.154) THEN
C
C SPECIAL CASE INVOLVING SPARKLES
C
EXP1=EXP(-MIN(ALPH1*RIJ,20.D0))
EXP2=EXP(-MIN(ALPH2*RIJ,20.D0))
PART1=-C3*(1.D0/RIJ**2 - RIJ*(RIJ**2+C2)**(-1.5D0))
1*(EXP1+EXP2)
PART2=-C3*(1.D0/RIJ -1.D0/SQRT(RIJ**2+C2))
1*(ALPH1*EXP1 + ALPH2*EXP2)
PART3=-C1*RIJ*(RIJ**2+C2)**(-1.5D0)
TERMNC=PART1+PART2+PART3
C# WRITE(6,'(4F13.6)')PART1,PART2,PART3,TERMNC
ELSE
TERMNC=-C1*(1.D0/RIJ**2 - RIJ*(RIJ**2+C2)**(-1.5D0) +
1ALPHA/RIJ - ALPHA/SQRT(RIJ**2+C2)) * EXP(-ALPHA*RIJ) -
2C1*RIJ*(RIJ**2+C2)**(-1.5D0)
ENDIF
DR1=DEL1/RIJ*14.399D0*RIJ*(RIJ**2+C2)**(-1.5D0)
ELSE
C
C CORE-CORE TERMS, MNDO AND AM1
C
C
C SPECIAL TREATMENT FOR N-H AND O-H TERMS
C
IF(RIJ.LT.1.D0.AND.NATORB(NI)*NATORB(NJ).EQ.0)THEN
TERMNC=0.D0
GOTO 50
ENDIF
C1=CORE(NI)*CORE(NJ)
IF(NI.EQ.1.AND.(NJ.EQ.7.OR.NJ.EQ.8)) THEN
F3=1.0D0+EXP(-ALPA(1)*RIJ)+RIJ*EXP(-ALPA(NJ)*RIJ)
DD=(DG(1)*F3-G(1)*(DEL1/RIJ)*(ALPA(1)*EXP(-ALPA(1)*RIJ)
1 +(ALPA(NJ)*RIJ-1.0D0)*EXP(-ALPA(NJ)*RIJ)))*C1
ELSEIF((NI.EQ.7.OR.NI.EQ.8).AND.NJ.EQ.1) THEN
F3=1.0D0+EXP(-ALPA(1)*RIJ)+RIJ*EXP(-ALPA(NI)*RIJ)
DD=(DG(1)*F3-G(1)*(DEL1/RIJ)*(ALPA(1)*EXP(-ALPA(1)*RIJ)
1 +(ALPA(NI)*RIJ-1.0D0)*EXP(-ALPA(NI)*RIJ)))*C1
ELSE
C# ELSEIF(NATORB(NI)+NATORB(NJ).EQ.0) THEN
C
C SPECIAL CASE OF TWO SPARKLES
C
PART1=DG(1)*C1
PART2=-(G(1)*(DEL1/RIJ)*(ALPA(NI)*EXP(-ALPA(NI)*RI
1J) +ALPA(NJ)*EXP(-ALPA(NJ)*RIJ)))*ABS(C1)
PART3=DG(1)*(EXP(-ALPA(NI)*RIJ)+EXP(-ALPA(NJ)*RIJ))*ABS(C
11)
DD=PART1+PART2+PART3
C# WRITE(6,'(4F13.6)')PART1,PART2,PART3,DD
C# ELSE
C
C THE GENERAL CASE
C
C# F3=1.0D0+EXP(-ALPA(NI)*RIJ)+EXP(-ALPA(NJ)*RIJ)
C# DD=(DG(1)*F3-G(1)*(DEL1/RIJ)*(ALPA(NI)*EXP(-ALPA(NI)*RI
C# 1J) +ALPA(NJ)*EXP(-ALPA(NJ)*RIJ)))*C1
ENDIF
TERMNC=DD
ENDIF
C
C **** START OF THE AM1 SPECIFIC DERIVATIVE CODE ***
C
C ANALYT=-A*(1/(R*R)+2.D0*B*(R-C)/R)*EXP(-B*(R-C)**2)
C
C ANALYTICAL DERIVATIVES
C
IF( AM1 )THEN
ANAM1=0.D0
DO 40 IG=1,10
IF(ABS(FN1(NI,IG)).GT.0.D0)
1ANAM1=ANAM1+FN1(NI,IG)*
2(1.D0/(RIJ*RIJ)+2.D0*FN2(NI,IG)*(RIJ-FN3(NI,IG))/RIJ)*
3EXP(MAX(-30.D0,-FN2(NI,IG)*(RIJ-FN3(NI,IG))**2))
IF(ABS(FN1(NJ,IG)).GT.0.D0)
1ANAM1=ANAM1+FN1(NJ,IG)*
2(1.D0/(RIJ*RIJ)+2.D0*FN2(NJ,IG)*(RIJ-FN3(NJ,IG))/RIJ)*
3EXP(MAX(-30.D0,-FN2(NJ,IG)*(RIJ-FN3(NJ,IG))**2))
40 CONTINUE
ANAM1=ANAM1*CORE(NI)*CORE(NJ)
TERMNC=TERMNC-ANAM1*DEL1/RIJ
ENDIF
C
C **** END OF THE AM1 SPECIFIC DERIVATIVE CODE ***
C
50 CONTINUE
C
C COMBINE TOGETHER THE OVERLAP DERIVATIVE PARTS
C
IF(MINDO3)THEN
II=MAX(NI,NJ)
NBOND=(II*(II-1))/2+NI+NJ-II
IF(NBOND.GT.153)GOTO 60
BI(1)=BETA3(NBOND)*VS(NI)*2.D0
BI(2)=BETA3(NBOND)*VP(NI)*2.D0
BI(3)=BI(2)
BI(4)=BI(2)
BJ(1)=BETA3(NBOND)*VS(NJ)*2.D0
BJ(2)=BETA3(NBOND)*VP(NJ)*2.D0
BJ(3)=BJ(2)
BJ(4)=BJ(2)
60 CONTINUE
ELSE
BI(1)=BETAS(NI)
BI(2)=BETAP(NI)
BI(3)=BI(2)
BI(4)=BI(2)
BJ(1)=BETAS(NJ)
BJ(2)=BETAP(NJ)
BJ(3)=BJ(2)
BJ(4)=BJ(2)
ENDIF
C
C CODE COMMON TO MINDO/3, MNDO, AND AM1
C
IOL=0
DO 70 K=IA,ID
DO 70 L=JA,JD
LK=L+K*(K-1)/2
TERMK=BI(K-IA+1)
TERML=BJ(L-JA+1)
IOL=IOL+1
TERMAB=TERMAB+(TERMK+TERML)
1*PSUM(LK)*DS(IOL)
70 CONTINUE
IF(MINDO3)THEN
C
C FIRST, CORE-ELECTRON ATTRACTION DERIVATIVES (MINDO/3)
C
C ATOM CORE I AFFECTING A.O.S ON J
DO 80 M=JA,JD
MN=(M*(M+1))/2
80 TERMAB=TERMAB+CORE(NI)*PSUM(MN)*DR1
C ATOM CORE J AFFECTING A.O.S ON I
DO 90 M=IA,ID
MN=(M*(M+1))/2
90 TERMAB=TERMAB+CORE(NJ)*PSUM(MN)*DR1
C
C NOW FOR COULOMB AND EXCHANGE TERMS (MINDO/3)
C
DO 100 I1=IA,ID
II=(I1*(I1+1))/2
DO 100 J1=JA,JD
JJ=(J1*(J1+1))/2
IJ=J1+(I1*(I1-1))/2
C
C COULOMB TERM
C
TERMAA=TERMAA-PSUM(II)*DR1*PSUM(JJ)
C
C EXCHANGE TERM
C
TERMAA=TERMAA+(PALPHA(IJ)*PALPHA(IJ)+PBETA(IJ)*PBETA(I
1J))*DR1
100 CONTINUE
ELSE
C
C FIRST, CORE-ELECTRON ATTRACTION DERIVATIVES (MNDO AND AM1)
C
C ATOM CORE I AFFECTING A.O.S ON J
ISP=0
DO 110 M=JA,JD
BB=1.D0
DO 110 N=M,JD
MN=M+N*(N-1)/2
ISP=ISP+1
TERMAB=TERMAB-BB*CORE(NI)*PSUM(MN)*DR(ISP)
110 BB=2.D0
C ATOM CORE J AFFECTING A.O.S ON I
K=MAX(JD-JA+1,1)
K=(K*(K+1))/2
ISP=-K+1
DO 120 M=IA,ID
BB=1.D0
DO 120 N=M,ID
MN=M+N*(N-1)/2
ISP=ISP+K
TERMAB=TERMAB-BB*CORE(NJ)*PSUM(MN)*DR(ISP)
120 BB=2.D0
ISP=0
C
C NOW FOR COULOMB AND EXCHANGE TERMS (MNDO AND AM1)
C
DO 140 K=IA,ID
AA=1.D0
KK=(K*(K-1))/2
DO 140 L=K,ID
LL=(L*(L-1))/2
DO 130 M=JA,JD
BB=1.D0
DO 130 N=M,JD
ISP=ISP+1
KL=K+LL
MN=M+N*(N-1)/2
C
C COULOMB TERM
C
TERMAA=TERMAA+AA*BB*PSUM(KL)*PSUM(MN)*DR(ISP)
MK=M+KK
NK=N+KK
ML=M+LL
NL=N+LL
C
C EXCHANGE TERM
C
TERMAA= TERMAA-0.5D0*AA*BB*(PALPHA(M
1K)*PALPHA(NL)+PALPHA(NK)*PALPHA(ML)+PBETA(MK)*PBETA(NL)+PBETA(NK)*
2PBETA(ML))*DR(ISP)
130 BB=2.D0
140 AA=2.D0
C END OF MNDO AND AM1 SPECIFIC CODE
ENDIF
EAA(IX)=EAA(IX)+TERMAA
EAB(IX)=EAB(IX)+TERMAB
ENUC(IX)=ENUC(IX)+TERMNC
150 CONTINUE
C# WRITE(6,*)EAA,EAB,ENUC,NAT(1),NAT(2)
160 CONTINUE
170 CONTINUE
DO 180 J=1,3
ENG(J)=EAA(J)+EAB(J)+ENUC(J)
ENG(J) = -ENG(J)*23.061D0
180 CONTINUE
RETURN
END
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