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SUBROUTINE DIAT2(NA,ESA,EPA,R12,NB,ESB,EPB,S)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION S(3,3,3)
C***********************************************************************
C
C OVERLP CALCULATES OVERLAPS BETWEEN ATOMIC ORBITALS FOR PAIRS OF ATOMS
C IT CAN HANDLE THE ORBITALS 1S, 2S, 3S, 2P, AND 3P.
C
C***********************************************************************
COMMON /SETC/ A(7),B(7),SA,SB,FACTOR,ISP,IPS
DIMENSION INMB(17),III(78)
SAVE INMB, III
DATA INMB/1,0,2,2,3,4,5,6,7,0,8,8,8,9,10,11,12/
C NUMBERING CORRESPONDS TO BOND TYPE MATRIX GIVEN ABOVE
C THE CODE IS
C
C III=1 FIRST - FIRST ROW ELEMENTS
C =2 FIRST - SECOND
C =3 FIRST - THIRD
C =4 SECOND - SECOND
C =5 SECOND - THIRD
C =6 THIRD - THIRD
DATA III/1,2,4, 2,4,4, 2,4,4,4, 2,4,4,4,4,
1 2,4,4,4,4,4, 2,4,4,4,4,4,4, 3,5,5,5,5,5,5,6,
2 3,5,5,5,5,5,5,6,6, 3,5,5,5,5,5,5,6,6,6, 3,5,5,5,5,5,5,6,6,6,6
3, 3,5,5,5,5,5,5,6,6,6,6,6/
C
C ASSIGNS BOND NUMBER
C
JMAX=MAX0(INMB(NA),INMB(NB))
JMIN=MIN0(INMB(NA),INMB(NB))
II=III((JMAX*(JMAX-1))/2+JMIN)
DO 10 I=1,3
DO 10 J=1,3
DO 10 K=1,3
10 S(I,J,K)=0.D0
RAB=R12/0.529167D0
GOTO (20,30,40,50,60,70), II
C
C ------------------------------------------------------------------
C *** THE ORDERING OF THE ELEMENTS WITHIN S IS
C *** S(1,1,1)=(S(B)/S(A))
C *** S(1,2,1)=(P-SIGMA(B)/S(A))
C *** S(2,1,1)=(S(B)/P-SIGMA(A))
C *** S(2,2,1)=(P-SIGMA(B)/P-SIGMA(A))
C *** S(2,2,2)=(P-PI(B)/P-PI(A))
C ------------------------------------------------------------------
C *** FIRST ROW - FIRST ROW OVERLAPS
C
20 CALL SET (ESA,ESB,NA,NB,RAB,II)
S(1,1,1)=.25D00*SQRT((SA*SB*RAB*RAB)**3)*(A(3)*B(1)-B(3)*A(1))
RETURN
C
C *** FIRST ROW - SECOND ROW OVERLAPS
C
30 CALL SET (ESA,ESB,NA,NB,RAB,II)
W=SQRT((SA**3)*(SB**5))*(RAB**4)*0.125D00
S(1,1,1) = SQRT(1.D00/3.D00)
S(1,1,1)=W*S(1,1,1)*(A(4)*B(1)-B(4)*A(1)+A(3)*B(2)-B(3)*A(2))
IF (NA.GT.1) CALL SET (EPA,ESB,NA,NB,RAB,II)
IF (NB.GT.1) CALL SET (ESA,EPB,NA,NB,RAB,II)
W=SQRT((SA**3)*(SB**5))*(RAB**4)*0.125D00
S(ISP,IPS,1)=W*(A(3)*B(1)-B(3)*A(1)+A(4)*B(2)-B(4)*A(2))
RETURN
C
C *** FIRST ROW - THIRD ROW OVERLAPS
C
40 CALL SET (ESA,ESB,NA,NB,RAB,II)
W=SQRT((SA**3)*(SB**7)/7.5D00)*(RAB**5)*0.0625D00
SROOT3 = SQRT(3.D00)
S(1,1,1)=W*(A(5)*B(1)-B(5)*A(1)+
12.D00*(A(4)*B(2)-B(4)*A(2)))/SROOT3
IF (NA.GT.1) CALL SET (EPA,ESB,NA,NB,RAB,II)
IF (NB.GT.1) CALL SET (ESA,EPB,NA,NB,RAB,II)
W=SQRT((SA**3)*(SB**7)/7.5D00)*(RAB**5)*0.0625D00
S(ISP,IPS,1)=W*(A(4)*(B(1)+B(3))-B(4)*(A(1)+A(3))+
1B(2)*(A(3)+A(5))-A(2)*(B(3)+B(5)))
RETURN
C
C *** SECOND ROW - SECOND ROW OVERLAPS
C
50 CALL SET (ESA,ESB,NA,NB,RAB,II)
W=SQRT((SA*SB)**5)*(RAB**5)*0.0625D00
RT3=1.D00/SQRT(3.D00)
S(1,1,1)=W*(A(5)*B(1)+B(5)*A(1)-2.0D00*A(3)*B(3))/3.0D00
CALL SET (ESA,EPB,NA,NB,RAB,II)
IF (NA.GT.NB) CALL SET (EPA,ESB,NA,NB,RAB,II)
W=SQRT((SA*SB)**5)*(RAB**5)*0.0625D00
D=A(4)*(B(1)-B(3))-A(2)*(B(3)-B(5))
E=B(4)*(A(1)-A(3))-B(2)*(A(3)-A(5))
S(ISP,IPS,1)=W*RT3*(D+E)
CALL SET (EPA,ESB,NA,NB,RAB,II)
IF (NA.GT.NB) CALL SET (ESA,EPB,NA,NB,RAB,II)
W=SQRT((SA*SB)**5)*(RAB**5)*0.0625D00
D=A(4)*(B(1)-B(3))-A(2)*(B(3)-B(5))
E=B(4)*(A(1)-A(3))-B(2)*(A(3)-A(5))
S(IPS,ISP,1)=-W*RT3*(E-D)
CALL SET (EPA,EPB,NA,NB,RAB,II)
W=SQRT((SA*SB)**5)*(RAB**5)*0.0625D00
S(2,2,1)=-W*(B(3)*(A(5)+A(1))-A(3)*(B(5)+B(1)))
HD = .5D00
S(2,2,2)=HD*W*(A(5)*(B(1)-B(3))-B(5)*(A(1)-A(3))
1-A(3)*B(1)+B(3)*A(1))
RETURN
C
C *** SECOND ROW - THIRD ROW OVERLAPS
C
60 CALL SET (ESA,ESB,NA,NB,RAB,II)
W=SQRT((SA**5)*(SB**7)/7.5D00)*(RAB**6)*0.03125D00
RT3 = 1.D00 / SQRT(3.D00)
TD = 2.D00
S(1,1,1)=W*(A(6)*B(1)+A(5)*B(2)-TD*(A(4)*B(3)+
1A(3)*B(4))+A(2)*B(5)+A(
21)*B(6))/3.D00
CALL SET (ESA,EPB,NA,NB,RAB,II)
IF (NA.GT.NB) CALL SET (EPA,ESB,NA,NB,RAB,II)
W=SQRT((SA**5)*(SB**7)/7.5D00)*(RAB**6)*0.03125D00
TD = 2.D00
S(ISP,IPS,1)=W*RT3*(A(6)*B(2)+A(5)*B(1)-TD*(A(4)*B(4)+A(3)*B(3))
1+A(2)*B(6)+A(1)*B(5))
CALL SET (EPA,ESB,NA,NB,RAB,II)
IF (NA.GT.NB) CALL SET (ESA,EPB,NA,NB,RAB,II)
W=SQRT((SA**5)*SB**7/7.5D00)*(RAB**6)*0.03125D00
TD = 2.D00
S(IPS,ISP,1)=-W*RT3*(A(5)*(TD*B(3)-B(1))-B(5)*(TD*A(3)-A(1))-A(2
1)*(B(6)-TD*B(4))+B(2)*(A(6)-TD*A(4)))
CALL SET (EPA,EPB,NA,NB,RAB,II)
W=SQRT((SA**5)*SB**7/7.5D00)*(RAB**6)*0.03125D00
S(2,2,1)=-W*(B(4)*(A(1)+A(5))-A(4)*(B(1)+B(5))
1+B(3)*(A(2)+A(6))-A(3)*(B(2)+B(6)))
HD = .5D00
S(2,2,2)=HD*W*(A(6)*(B(1)-B(3))-B(6)*(A(1)-
1A(3))+A(5)*(B(2)-B(4))-B(5
2)*(A(2)-A(4))-A(4)*B(1)+B(4)*A(1)-A(3)*B(2)+B(3)*A(2))
RETURN
C
C *** THIRD ROW - THIRD ROW OVERLAPS
C
70 CALL SET (ESA,ESB,NA,NB,RAB,II)
W=SQRT((SA*SB*RAB*RAB)**7)/480.D00
RT3 = 1.D00 / SQRT(3.D00)
S(1,1,1)=W*(A(7)*B(1)-3.D00*(A(5)*B(3)-A(3)*B(5))-A(1)*B(7))/3.D00
CALL SET (ESA,EPB,NA,NB,RAB,II)
IF (NA.GT.NB) CALL SET (EPA,ESB,NA,NB,RAB,II)
W=SQRT((SA*SB*RAB*RAB)**7)/480.D00
D=A(6)*(B(1)-B(3))-2.D00*A(4)*(B(3)-B(5))+A(2)*(B(5)-B(7))
E=B(6)*(A(1)-A(3))-2.D00*B(4)*(A(3)-A(5))+B(2)*(A(5)-A(7))
S(ISP,IPS,1)=W*RT3*(D-E)
CALL SET (EPA,ESB,NA,NB,RAB,II)
IF (NA.GT.NB) CALL SET (ESA,EPB,NA,NB,RAB,II)
W=SQRT((SA*SB*RAB*RAB)**7)/480.D00
D=A(6)*(B(1)-B(3))-2.D00*A(4)*(B(3)-B(5))+A(2)*(B(5)-B(7))
E=B(6)*(A(1)-A(3))-2.D00*B(4)*(A(3)-A(5))+B(2)*(A(5)-A(7))
S(IPS,ISP,1)=-W*RT3*(-D-E)
CALL SET (EPA,EPB,NA,NB,RAB,II)
W=SQRT((SA*SB*RAB*RAB)**7)/480.D00
TD = 2.D00
S(2,2,1)=-W*(A(3)*(B(7)+TD*B(3))-A(5)*(B(1)+
1TD*B(5))-B(5)*A(1)+A(7)*B(3))
HD = .5D00
S(2,2,2)=HD*W*(A(7)*(B(1)-B(3))+B(7)*(A(1)-
1A(3))+A(5)*(B(5)-B(3)-B(1)
2)+B(5)*(A(5)-A(3)-A(1))+2.D00*A(3)*B(3))
RETURN
C
END
SUBROUTINE SET (S1,S2,NA,NB,RAB,II)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
COMMON /SETC/ A(7),B(7),SA,SB,FACTOR,ISP,IPS
C***********************************************************************
C
C SET IS PART OF THE OVERLAP CALCULATION, CALLED BY OVERLP.
C IT CALLS AINTGS AND BINTGS
C
C***********************************************************************
IF (NA.GT.NB) GO TO 10
ISP=1
IPS=2
SA=S1
SB=S2
GOTO 20
10 ISP=2
IPS=1
SA=S2
SB=S1
20 J=II+2
IF (II.GT.3) J=J-1
ALPHA=0.5D00*RAB*(SA+SB)
BETA=0.5D00*RAB*(SB-SA)
JCALL=J-1
CALL AINTGS (ALPHA,JCALL)
CALL BINTGS (BETA,JCALL)
RETURN
C
END
SUBROUTINE AINTGS (X,K)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
COMMON /SETC/ A(7),B(7),SDUM(3),IDUM(2)
C***********************************************************************
C
C AINTGS FORMS THE "A" INTEGRALS FOR THE OVERLAP CALCULATION.
C
C***********************************************************************
C=EXP(-X)
A(1)=C/X
DO 10 I=1,K
A(I+1)=(A(I)*I+C)/X
10 CONTINUE
RETURN
C
END
SUBROUTINE BINTGS (X,K)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
COMMON /SETC/ A(7),B(7),SDUM(3),IDUM(2)
DIMENSION FACT(17)
C**********************************************************************
C
C BINTGS FORMS THE "B" INTEGRALS FOR THE OVERLAP CALCULATION.
C
C**********************************************************************
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/
IO=0
ABSX = ABS(X)
IF (ABSX.GT.3.D00) GO TO 40
IF (ABSX.LE.2.D00) GO TO 10
IF (K.LE.10) GO TO 40
LAST=15
GO TO 60
10 IF (ABSX.LE.1.D00) GO TO 20
IF (K.LE.7) GO TO 40
LAST=12
GO TO 60
20 IF (ABSX.LE.0.5D00) GO TO 30
IF (K.LE.5) GO TO 40
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
B(1)=(EXPX-EXPMX)/X
DO 50 I=1,K
50 B(I+1)=(I*B(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 B(I+1)=Y
GO TO 110
90 DO 100 I=IO,K
100 B(I+1)=(2*MOD(I+1,2))/(I+1.D0)
110 CONTINUE
RETURN
C
END
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