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SUBROUTINE DIAT(NI,NJ,XI,XJ,DI)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
************************************************************************
*
* DIAT CALCULATES THE DI-ATOMIC OVERLAP INTEGRALS BETWEEN ATOMS
* CENTERED AT XI AND XJ.
*
* ON INPUT NI = ATOMIC NUMBER OF THE FIRST ATOM.
* NJ = ATOMIC NUMBER OF THE SECOND ATOM.
* XI = CARTESIAN COORDINATES OF THE FIRST ATOM.
* XJ = CARTESIAN COORDINATES OF THE SECOND ATOM.
*
* ON OUTPUT DI = DIATOMIC OVERLAP, IN A 9 * 9 MATRIX. LAYOUT OF
* ATOMIC ORBITALS IN DI IS
* 1 2 3 4 5 6 7 8 9
* S PX PY PZ D(X**2-Y**2) D(XZ) D(Z**2) D(YZ)D(XY)
*
* LIMITATIONS: IN THIS FORMULATION, NI AND NJ MUST BE LESS THAN 107
* EXPONENTS ARE ASSUMED TO BE PRESENT IN COMMON BLOCK EXPONT.
*
************************************************************************
COMMON /KEYWRD/KEYWRD
CHARACTER*241 KEYWRD
INTEGER A,PQ2,B,PQ1,AA,BB
COMMON /NUMCAL/ NUMCAL
SAVE NPQ, IVAL
LOGICAL ANALYT
COMMON /EXPONT/ EMUS(107),EMUP(107),EMUD(107)
DIMENSION DI(9,9),S(3,3,3),UL1(3),UL2(3),C(3,5,5),NPQ(107)
1 ,XI(3),XJ(3), SLIN(27), IVAL(3,5)
2, C1(3,5), C2(3,5), C3(3,5), C4(3,5), C5(3,5)
3, S1(3,3), S2(3,3), S3(3,3)
EQUIVALENCE(SLIN(1),S(1,1,1))
EQUIVALENCE (C1(1,1),C(1,1,1)), (C2(1,1),C(1,1,2)),
1 (C3(1,1),C(1,1,3)), (C4(1,1),C(1,1,4)),
2 (C5(1,1),C(1,1,5)), (S1(1,1),S(1,1,1)),
3 (S2(1,1),S(1,1,2)), (S3(1,1),S(1,1,3))
DATA NPQ/1,0, 2,2,2,2,2,2,2,0, 0,3,3,3,3,3,3,0, 0,4,4,4,4,4,4,4,
14,4,4,4,4,4,4,4,4,0, 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5
2,32*6,15*0,3,5*0/
DATA IVAL/1,0,9,1,3,8,1,4,7,1,2,6,0,0,5/
DATA ICALCN/0/
IF(ICALCN.NE.NUMCAL)THEN
ANALYT=(INDEX(KEYWRD,'ANALYT').NE.0)
ICALCN=NUMCAL
ENDIF
X1=XI(1)
X2=XJ(1)
Y1=XI(2)
Y2=XJ(2)
Z1=XI(3)
Z2=XJ(3)
PQ1=NPQ(NI)
PQ2=NPQ(NJ)
DO 20 I=1,9
DO 10 J=1,9
DI(I,J)=0.0D0
10 CONTINUE
20 CONTINUE
CALL COE(X1,Y1,Z1,X2,Y2,Z2,PQ1,PQ2,C,R)
IF(PQ1.EQ.0.OR.PQ2.EQ.0.OR.R.GE.10.D0) RETURN
IF(R.LT.0.001)THEN
RETURN
ENDIF
IA=MIN(PQ1,3)
IB=MIN(PQ2,3)
A=IA-1
B=IB-1
IF(ANALYT)THEN
CALL GOVER(NI,NJ,XI,XJ,R,DI)
C# WRITE(6,*)' OVERLAP FROM GOVER'
C# WRITE(6,'(4F15.10)')SG
RETURN
ENDIF
IF(NI.LT.18.AND.NJ.LT.18) THEN
CALL DIAT2(NI,EMUS(NI),EMUP(NI),R,NJ,EMUS(NJ),EMUP(NJ),S)
ELSE
UL1(1)=EMUS(NI)
UL2(1)=EMUS(NJ)
UL1(2)=EMUP(NI)
UL2(2)=EMUP(NJ)
UL1(3)=MAX(EMUD(NI),0.3D0)
UL2(3)=MAX(EMUD(NJ),0.3D0)
DO 30 I=1,27
30 SLIN(I)=0.0D0
NEWK=MIN(A,B)
NK1=NEWK+1
DO 40 I=1,IA
ISS=I
IB=B+1
DO 40 J=1,IB
JSS=J
DO 40 K=1,NK1
IF(K.GT.I.OR.K.GT.J) GOTO 40
KSS=K
S(I,J,K)=SS(PQ1,PQ2,ISS,JSS,KSS,UL1(I),UL2(J),R)
40 CONTINUE
ENDIF
DO 50 I=1,IA
KMIN=4-I
KMAX=2+I
DO 50 J=1,IB
IF(J.EQ.2)THEN
AA=-1
BB=1
ELSE
AA=1
IF(J.EQ.3) THEN
BB=-1
ELSE
BB=1
ENDIF
ENDIF
LMIN=4-J
LMAX=2+J
DO 50 K=KMIN,KMAX
DO 50 L=LMIN,LMAX
II=IVAL(I,K)
JJ=IVAL(J,L)
DI(II,JJ)=S1(I,J)*(C3(I,K)*C3(J,L))*AA+
1(C4(I,K)*C4(J,L)+C2(I,K)*C2(J,L))*BB*S2(I,J)+(C5(I,K)*C5(J,L)
2+C1(I,K)*C1(J,L))*S3(I,J)
50 CONTINUE
C# WRITE(6,*)' OVERLAP FROM DIAT2'
C# DO 12 I=1,4
C# 12 WRITE(6,'(4F15.10)')(DI(J,I),J=1,4)
RETURN
END
DOUBLE PRECISION FUNCTION SS(NA,NB,LA1,LB1,M1,UA,UB,R1)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
LOGICAL FIRST
DIMENSION FA(0:13),AFF(0:2,0:2,0:2),AF(0:19),BF(0:19),
1BI(0:12,0:12)
SAVE AFF, FA, BI, FIRST
DATA FIRST /.TRUE./
DATA AFF/27*0. D0/
DATA FA/1.D0,1.D0,2.D0,6.D0,24.D0,120.D0,720.D0,5040.D0,40320.D0,
1362880.D0,3628800.D0,39916800.D0,479001600.D0,6227020800.D0/
M=M1-1
LB=LB1-1
LA=LA1-1
R=R1/0.529167D0
IF(FIRST) THEN
FIRST=.FALSE.
C
C INITIALISE SOME CONSTANTS
C
C BINOMIALS
C
DO 10 I=0,12
BI(I,0)=1.D0
BI(I,I)=1.D0
10 CONTINUE
DO 20 I=0,11
I1=I-1
DO 20 J=0,I1
BI(I+1,J+1)=BI(I,J+1)+BI(I,J)
20 CONTINUE
AFF(0,0,0)=1.D0
AFF(1,0,0)=1.D0
AFF(1,1,0)=1.D0
AFF(2,0,0)=1.5D0
AFF(2,1,0)=1.73205D0
AFF(2,2,0)=1.224745D0
AFF(2,0,2)=-0.5D0
ENDIF
P=(UA+UB)*R*0.5D0
B=(UA-UB)*R*0.5D0
QUO=1/P
AF(0)=QUO*EXP(-P)
DO 30 N=1,19
AF(N)=N*QUO*AF(N-1)+AF(0)
30 CONTINUE
CALL BFN(B,BF)
SUM=0.D0
LAM1=LA-M
LBM1=LB-M
C
C START OF OVERLAP CALCULATION PROPER
C
DO 50 I=0,LAM1,2
IA=NA+I-LA
IC=LA-I-M
DO 50 J=0,LBM1,2
IB=NB+J-LB
ID=LB-J-M
SUM1=0.D0
IAB=IA+IB
DO 40 K1=0,IA
DO 40 K2=0,IB
DO 40 K3=0,IC
DO 40 K4=0,ID
DO 40 K5=0,M
IAF=IAB-K1-K2+K3+K4+2*K5
DO 40 K6=0,M
IBF=K1+K2+K3+K4+2*K6
JX=(-1)**(M+K2+K4+K5+K6)
SUM1=SUM1+BI(ID,K4)*
1BI(M,K5)*BI(IC,K3)*BI(IB,K2)*BI(IA,K1)*
2BI(M,K6)*JX*AF(IAF)*BF(IBF)
40 CONTINUE
SUM=SUM+SUM1*AFF(LA,M,I)*AFF(LB,M,J)
50 CONTINUE
SS=SUM*R**(NA+NB+1)*UA**NA*UB**NB/(2.D0**(M+1))*
1SQRT(UA*UB/(FA(NA+NA)*FA(NB+NB))*((LA+LA+1)*(LB+LB+1)))
RETURN
END
SUBROUTINE COE(X1,Y1,Z1,X2,Y2,Z2,PQ1,PQ2,C,R)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INTEGER PQ1,PQ2,PQ
DIMENSION C(75)
XY=(X2-X1)**2+(Y2-Y1)**2
R=SQRT(XY+(Z2-Z1)**2)
XY=SQRT(XY)
IF (XY.LT.1.D-10) GO TO 10
CA=(X2-X1)/XY
CB=(Z2-Z1)/R
SA=(Y2-Y1)/XY
SB=XY/R
GO TO 50
10 IF (Z2-Z1) 20,30,40
20 CA=-1.D0
CB=-1.D0
SA=0.D0
SB=0.D0
GO TO 50
30 CA=0.D0
CB=0.D0
SA=0.D0
SB=0.D0
GO TO 50
40 CA=1.D0
CB=1.D0
SA=0.D0
SB=0.D0
50 CONTINUE
DO 60 I=1,75
60 C(I)=0.D0
IF (PQ1.GT.PQ2) GO TO 70
PQ=PQ2
GO TO 80
70 PQ=PQ1
80 CONTINUE
C(37)=1.D0
IF (PQ.LT.2) GO TO 90
C(56)=CA*CB
C(41)=CA*SB
C(26)=-SA
C(53)=-SB
C(38)=CB
C(23)=0.D0
C(50)=SA*CB
C(35)=SA*SB
C(20)=CA
IF (PQ.LT.3) GO TO 90
C2A=2*CA*CA-1.D0
C2B=2*CB*CB-1.D0
S2A=2*SA*CA
S2B=2*SB*CB
C(75)=C2A*CB*CB+0.5D0*C2A*SB*SB
C(60)=0.5D0*C2A*S2B
C(45)=0.8660254037841D0*C2A*SB*SB
C(30)=-S2A*SB
C(15)=-S2A*CB
C(72)=-0.5D0*CA*S2B
C(57)=CA*C2B
C(42)=0.8660254037841D0*CA*S2B
C(27)=-SA*CB
C(12)=SA*SB
C(69)=0.5773502691894D0*SB*SB*1.5D0
C(54)=-0.8660254037841D0*S2B
C(39)=CB*CB-0.5D0*SB*SB
C(66)=-0.5D0*SA*S2B
C(51)=SA*C2B
C(36)=0.8660254037841D0*SA*S2B
C(21)=CA*CB
C(6)=-CA*SB
C(63)=S2A*CB*CB+0.5D0*S2A*SB*SB
C(48)=0.5D0*S2A*S2B
C(33)=0.8660254037841D0*S2A*SB*SB
C(18)=C2A*SB
C(3)=C2A*CB
90 CONTINUE
RETURN
END
SUBROUTINE BFN(X,BF)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION BF(13)
C**********************************************************************
C
C BINTGS FORMS THE "B" INTEGRALS FOR THE OVERLAP CALCULATION.
C
C**********************************************************************
DIMENSION FACT(17)
SAVE FACT
DATA FACT/1.D0,2.D0,6.D0,24.D0,120.D0,720.D0,5040.D0,40320.D0,
1362880.D0,3628800.D0,39916800.D0,479001600.D0,6227020800.D0,
28.71782912D10,1.307674368D12,2.092278989D13,3.556874281D14/
K=12
IO=0
ABSX = ABS(X)
IF (ABSX.GT.3.D00) GO TO 40
IF (ABSX.LE.2.D00) GO TO 10
LAST=15
GO TO 60
10 IF (ABSX.LE.1.D00) GO TO 20
LAST=12
GO TO 60
20 IF (ABSX.LE.0.5D00) GO TO 30
LAST=7
GO TO 60
30 IF (ABSX.LE.1.D-6) GOTO 90
LAST=6
GO TO 60
40 EXPX=EXP(X)
EXPMX=1.D00/EXPX
BF(1)=(EXPX-EXPMX)/X
DO 50 I=1,K
50 BF(I+1)=(I*BF(I)+(-1.D00)**I*EXPX-EXPMX)/X
GO TO 110
60 DO 80 I=IO,K
Y=0.0D00
DO 70 M=IO,LAST
XF=1.0D00
IF(M.NE.0) XF=FACT(M)
70 Y=Y+(-X)**M*(2*MOD(M+I+1,2))/(XF*(M+I+1))
80 BF(I+1)=Y
GO TO 110
90 DO 100 I=IO,K
100 BF(I+1)=(2*MOD(I+1,2))/(I+1.D0)
110 CONTINUE
RETURN
C
END
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