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SUBROUTINE DERI22 (C,B,WORK,NORBS,FOC2,AB,MINEAR,FCI)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION C(NORBS,NORBS), B(*), WORK(NORBS,NORBS), FOC2(*),
1AB(*), FCI(*)
************************************************************************
* 1) BUILD THE 2-ELECTRON FOCK MATRIX DEPENDING ON B AS FOLLOWS :
* DP = C * SCALE*B * C' ... DP DENSITY MATRIX 'DERIVATIVE',
* FOC2 = 0.5 * TRACE ( DP * (2<J>-<K>) ) DONE IN FOCK2 & FOCK1.
* 2) HALF-TRANSFORM ONTO M.O. BASIS : DPT = FOC2 * C
* AND COMPUTE DIAGONAL BLOCKS ELEMENTS OF C' * FOC2, EXTRACTING
* IN FCI ELEMENTS OVER C.I-ACTIVE M.O ONLY.
* 3) COMPUTE SUPERVECTOR AB = (DIAG + A) * B DEFINED BY THE MATRIX :
* AB(I,J)= ( DIAG(I,J)*B(I,J)+DPT(I,J) )*SCALAR(I,J) WITH I.GT.J,
* DIAG(I,J)=(EIGS(I)-EIGS(J))/(O(J)-O(I)) >0, O OCCUPANCY NUMBERS,
* EIGS EIGENVALUES OF FOCK OPERATOR WITH EIGENVECTORS C IN A.O.
*
* INPUT
* C(NORBS,NORBS) : M.O. EIGENVECTORS (COLUMNWISE).
* B(*) : B SUPERVECTOR PACKED BY OFF-DIAGONAL BLOCKS, SCALED
* WORK(*) : WORK AREA OF SIZE N*N.
* NORBS : NUMBER OF M.O.S
* NELEC,NMOS : LAST FROZEN CORE M.O. , C.I-ACTIVE BAND LENGTH.
* IN COMMON
* DIAG,SCALAR AS DEFINED IN 'DERI0'.
* OUTPUT
* FOC2(*) : 2-ELECTRON FOCK MATRIX, PACKED CANONICAL.
* AB(*) : ANTISYMMETRIC MATRIX PACKED IN SUPERVECTOR FORM WITH
* THE CONSECUTIVE FOLLOWING BLOCKS:
* 1) OPEN-CLOSED I.E. B(IJ)=B(I,J) WITH I OPEN & J CLOSED
* AND I RUNNING FASTER THAN J,
* 2) VIRTUAL-CLOSED SAME RULE OF ORDERING,
* 3) VIRTUAL-OPEN SAME RULE OF ORDERING.
* FCI(*) : FOCK DIAGONAL BLOCKS ELEMENTS OVER C.I-ACTIVE M.O.
* FOC2 CAN BE EQUIVALENCED WITH WORK IN THE CALLING SEQUENCE.
************************************************************************
C
C NOTE: NORBS AND NORD ARE THE SAME ADDRESS. THE NAME NORBD IS NOT
C USED HERE.
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM)
1 ,NLAST(NUMATM),NORBD,NELECS,NALPHA,NBETA
2 ,NCLOSE,NOPEN,NDUMY,FRACT
3 /WMATRX/ WJ(N2ELEC),WK(N2ELEC)
COMMON /DENSTY/ PDUMY(MPACK*2), DPA(MPACK)
COMMON /FOKMAT/ FDUMY(MPACK), SCALAR(MPACK)
COMMON /NVOMAT/ DIAG(MPACK/2)
COMMON /WORK1 / FDUMY2(15*NPULAY), DP(6*NPULAY)
COMMON /CIBITS/ NMOS,LAB,NELEC,NBO(3)
DIMENSION W(N2ELEC)
EQUIVALENCE (W,WJ)
C
LINEAR=(NORBS*(NORBS+1))/2
C
C DERIVATIVE OF THE DENSITY MATRIX IN DP (PACKED,CANONICAL).
C ----------------------------------------------------------
C DP = C * B * C' .
C
C STEP 0 : UNSCALE VECTOR B.
DO 10 I=1,MINEAR
10 B(I)=B(I)*SCALAR(I)
C
C STEP 1 : WORK = C * B . DP TEMPORARY ARRAY.
L=1
IF(NBO(2).NE.0 .AND. NBO(1).NE.0) THEN
C OPEN-CLOSED
CALL MXM(C(1,NBO(1)+1),NORBS,B(L),NBO(2),WORK,NBO(1))
C CLOSED-OPEN
CALL MXMT (C,NORBS,B(L),NBO(1),WORK(1,NBO(1)+1),NBO(2))
L=L+NBO(2)*NBO(1)
ENDIF
IF(NBO(3).NE.0 .AND. NBO(1).NE.0) THEN
C VIRTUAL-CLOSED
IF(L.GT.1) THEN
CALL MXM(C(1,NOPEN+1),NORBS,B(L),NBO(3),DP,NBO(1))
DO 20 I=1,NORBS*NBO(1)
20 WORK(I,1)=WORK(I,1)+DP(I)
ELSE
CALL MXM(C(1,NOPEN+1),NORBS,B(L),NBO(3),WORK,NBO(1))
ENDIF
C CLOSED-VIRTUAL
CALL MXMT(C,NORBS,B(L),NBO(1),WORK(1,NOPEN+1),NBO(3))
L=L+NBO(3)*NBO(1)
ENDIF
IF(NBO(3).NE.0 .AND. NBO(2).NE.0) THEN
C VIRTUAL-OPEN
CALL MXM(C(1,NOPEN+1),NORBS,B(L),NBO(3),DP,NBO(2))
J=NORBS*NBO(1)
DO 30 I=1,NORBS*NBO(2)
30 WORK(J+I,1)=WORK(J+I,1)+DP(I)
C OPEN-VIRTUAL
CALL MXMT (C(1,NBO(1)+1),NORBS,B(L),NBO(2),DP,NBO(3))
J=NORBS*NOPEN
DO 40 I=1,NORBS*NBO(3)
40 WORK(J+I,1)=WORK(J+I,1)+DP(I)
ENDIF
C
C STEP 2 : DP= WORK * C' WITH DP PACKED,CANONICAL.
L=0
DO 50 I=1,NORBS
DO 50 J=1,I
L=L+1
50 DP(L)=SDOT(NORBS,WORK(I,1),NORBS,C(J,1),NORBS)
C
C 2-ELECTRON FOCK MATRIX BUILD WITH THE DENSITY MATRIX DERIVATIVE.
C ----------------------------------------------------------------
C RETURNED IN FOC2 (PACKED CANONICAL).
DO 60 I=1,LINEAR
FOC2(I)=0.D0
60 DPA(I)=0.5D0*DP(I)
CALL FOCK2 (FOC2,DP,DPA,W,WJ,WK,NUMAT,NAT,NFIRST,NMIDLE,NLAST)
CALL FOCK1 (FOC2,DP,DPA,DPA)
C
C BUILD DP AND EXTRACT FCI.
C --------------------------
C
C DP(NORBS,NEND) = FOC2(NORBS,NORBS) * C(NORBS,NEND).
NEND=MAX(NOPEN,NELEC+NMOS)
L=1
DO 70 I=1,NOPEN
CALL SUPDOT (DP(L),FOC2,C(1,I),NORBS,1)
70 L=L+NORBS
C EXTRACT FCI
L=1
NEND=0
DO 90 LOOP=1,3
NINIT=NEND+1
NEND =NEND+NBO(LOOP)
N1=MAX(NINIT,NELEC+1 )
N2=MIN(NEND ,NELEC+NMOS)
IF(N2.LT.N1) GO TO 90
DO 80 I=N1,N2
IF(I.GT.NINIT) THEN
CALL MXM (C(1,I),1,DP(NORBS*(NINIT-1)+1),NORBS,FCI(L),I-N
1INIT)
L=L+I-NINIT
ENDIF
80 CONTINUE
90 CONTINUE
DO 100 I=NELEC+1,NELEC+NMOS
FCI(L)=-DOT(C(1,I),DP(NORBS*(I-1)+1),NORBS)
100 L=L+1
C
C NEW SUPERVECTOR AB = (DIAG + C'* FOC2 * C) * B , SCALED.
C --------------------------------------------------------
C
C PART 1 : AB(I,J) = (C' * DP)(I,J) DONE BY BLOCKS.
L=1
IF(NBO(2).NE.0 .AND. NBO(1).NE.0) THEN
CALL MTXM (C(1,NBO(1)+1),NBO(2),DP,NORBS,AB(L),NBO(1))
L=L+NBO(2)*NBO(1)
ENDIF
IF(NBO(3).NE.0 .AND. NBO(1).NE.0) THEN
CALL MTXM (C(1,NOPEN+1),NBO(3),DP,NORBS,AB(L),NBO(1))
L=L+NBO(3)*NBO(1)
ENDIF
IF(NBO(3).NE.0 .AND. NBO(2).NE.0)
1CALL MTXM(C(1,NOPEN+1),NBO(3),DP(NORBS*NBO(1)+1),
2NORBS,AB(L),NBO(2))
C
C PART 2 : AB = SCALE * (D * B + AB) AND RESCALE BASIS VECTOR B.
DO 110 I=1,MINEAR
AB(I)=(DIAG(I)*B(I)+AB(I))*SCALAR(I)
110 B(I)=B(I)/SCALAR(I)
RETURN
END
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