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C Copyright (c) 2003-2010 University of Florida
C
C This program is free software; you can redistribute it and/or modify
C it under the terms of the GNU General Public License as published by
C the Free Software Foundation; either version 2 of the License, or
C (at your option) any later version.
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C The GNU General Public License is included in this distribution
C in the file COPYRIGHT.
SUBROUTINE ERD__2D_COEFFICIENTS
+
+ ( MIJ,MKL,MIJKL,
+ NGQP,MGQIJKL,
+ ATOMAB,ATOMCD,
+ P,Q,
+ PX,PY,PZ,QX,QY,QZ,
+ PAX,PAY,PAZ,QCX,QCY,QCZ,
+ PINVHF,QINVHF,PQPINV,
+ RTS,
+ CASE2D,
+
+ B00,B01,B10,
+ C00X,C00Y,C00Z,
+ D00X,D00Y,D00Z )
+
C------------------------------------------------------------------------
C OPERATION : ERD__2D_COEFFICIENTS
C MODULE : ELECTRON REPULSION INTEGRALS DIRECT
C MODULE-ID : ERD
C SUBROUTINES : none
C DESCRIPTION : This operation evaluates the VRR coefficients for
C the 2D integrals for the present set of NGQP roots
C corresponding to all i,j,k,l exponent quadruplets.
C
C Not all coefficients are needed in case there are
C s- or p-shells present on either P or Q side. Also
C observe that the cartesian distance components PAX,
C PAY and PAZ are all equal to zero in case the two
C atomic centers A and B coincide, in which case they
C need not to be addressed inside the algorithm.
C Likewise for QCX,QCY and QCZ, if centers C and D
C coincide.
C
C
C Input:
C
C MIJ(KL) = current # of ij (kl) primitive
C index pairs corresponding to
C the csh pairs A,B (C,D)
C MIJKL = current # of ijkl primitive
C index quadruplets (= MIJ*MKL)
C NGQP = # of gaussian quadrature points
C (roots)
C MGQIJKL = # of roots times # of ijkl
C quadruplets (= NGQP*MIJKL)
C ATOMAB(CD) = is true, if centers A and B
C (C and D) coincide
C P(Q) = current MIJ (MKL) exponent sums
C for csh A and B (C and D)
C Px(Qx) = current MIJ (MKL) coordinates
C x=X,Y,Z for gaussian product
C centers P=A+B (Q=C+D)
C PAx(QCx) = current MIJ (MKL) coordinate
C x=X,Y,Z differences P-A (Q-C)
C between centers P and A (Q and C)
C P(Q)INVHF = current MIJ (MKL) values of
C 1/(2*P(Q)), where P and Q are
C the corresponding exponent sums
C for csh A and B (C and D)
C PQPINV = current MIJKL values of 1/(P+Q)
C RTS = current MGQIJKL values of all
C quadrature roots
C CASE2D = integer value within the range
C from 1 to 9, indicating which
C 2D coefficient evaluation case
C is present to trigger specific
C simplified sections of the code
C
C Output:
C
C Bxx = the coordinate independent
C B-coefficients (xx=00,01,10)
C C00x = the C-coefficients (individual
C cartesian components x=X,Y,Z) for
C shell expansion on center P
C D00x = the D-coefficients (individual
C cartesian components x=X,Y,Z) for
C shell expansion on center Q
C
C
C AUTHOR : Norbert Flocke
C------------------------------------------------------------------------
C
C
C ...include files and declare variables.
C
C
IMPLICIT NONE
LOGICAL ATOMAB,ATOMCD
INTEGER CASE2D
INTEGER IJ,KL
INTEGER M,N
INTEGER MIJ,MKL,MIJKL
INTEGER NG,NGQP,MGQIJKL
DOUBLE PRECISION PIJ,PXIJ,PYIJ,PZIJ,PAXIJ,PAYIJ,PAZIJ
DOUBLE PRECISION PQX,PQY,PQZ
DOUBLE PRECISION PSCALE,QSCALE
DOUBLE PRECISION QCXKL,QCYKL,QCZKL
DOUBLE PRECISION ROOT,PROOT,QROOT
DOUBLE PRECISION TWOP,TWOQ,TWOPQ
DOUBLE PRECISION HALF,ONE
DOUBLE PRECISION P (1:MIJ)
DOUBLE PRECISION PX (1:MIJ)
DOUBLE PRECISION PY (1:MIJ)
DOUBLE PRECISION PZ (1:MIJ)
DOUBLE PRECISION PAX (1:MIJ)
DOUBLE PRECISION PAY (1:MIJ)
DOUBLE PRECISION PAZ (1:MIJ)
DOUBLE PRECISION PINVHF (1:MIJ)
DOUBLE PRECISION Q (1:MKL)
DOUBLE PRECISION QX (1:MKL)
DOUBLE PRECISION QY (1:MKL)
DOUBLE PRECISION QZ (1:MKL)
DOUBLE PRECISION QCX (1:MKL)
DOUBLE PRECISION QCY (1:MKL)
DOUBLE PRECISION QCZ (1:MKL)
DOUBLE PRECISION QINVHF (1:MKL)
DOUBLE PRECISION PQPINV (1:MIJKL)
DOUBLE PRECISION B00 (1:MGQIJKL)
DOUBLE PRECISION B01 (1:MGQIJKL)
DOUBLE PRECISION B10 (1:MGQIJKL)
DOUBLE PRECISION C00X (1:MGQIJKL)
DOUBLE PRECISION C00Y (1:MGQIJKL)
DOUBLE PRECISION C00Z (1:MGQIJKL)
DOUBLE PRECISION D00X (1:MGQIJKL)
DOUBLE PRECISION D00Y (1:MGQIJKL)
DOUBLE PRECISION D00Z (1:MGQIJKL)
DOUBLE PRECISION RTS (1:MGQIJKL)
PARAMETER (HALF = 0.5D0)
PARAMETER (ONE = 1.D0)
C
C
C------------------------------------------------------------------------
C
C
C ...jump according to the 9 different cases that can arise:
C
C P-shell = s- ,p- or higher angular momentum
C Q-shell = s- ,p- or higher angular momentum
C
C each leading to simplifications in the VRR formulas.
C The case present has been evaluated outside this
C routine and is transmitted via argument.
C
C
GOTO (1,2,5,3,4,7,6,8,9) CASE2D
C
C
C ...the case P = s-shell and Q = s-shell.
C (no coefficients here)
C
C
1 RETURN
C
C
C ...the case P = p-shell and Q = s-shell.
C (no B00,B01,B10,D00)
C
C
2 IF (ATOMAB) THEN
M = 0
N = 0
DO 200 IJ = 1,MIJ
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 210 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
QSCALE = - Q (KL) * PQPINV (M)
DO 215 NG = 1,NGQP
N = N + 1
QROOT = QSCALE * RTS (N)
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
215 CONTINUE
210 CONTINUE
200 CONTINUE
ELSE
M = 0
N = 0
DO 220 IJ = 1,MIJ
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
DO 230 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
QSCALE = Q (KL) * PQPINV (M)
DO 235 NG = 1,NGQP
N = N + 1
QROOT = QSCALE * RTS (N)
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
235 CONTINUE
230 CONTINUE
220 CONTINUE
END IF
RETURN
C
C
C ...the case P = s-shell and Q = p-shell.
C (no B00,B01,B10,C00)
C
C
3 IF (ATOMCD) THEN
M = 0
N = 0
DO 300 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 310 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
PSCALE = PIJ * PQPINV (M)
DO 315 NG = 1,NGQP
N = N + 1
PROOT = PSCALE * RTS (N)
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
315 CONTINUE
310 CONTINUE
300 CONTINUE
ELSE
M = 0
N = 0
DO 320 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 330 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
PSCALE = PIJ * PQPINV (M)
DO 335 NG = 1,NGQP
N = N + 1
PROOT = PSCALE * RTS (N)
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
335 CONTINUE
330 CONTINUE
320 CONTINUE
END IF
RETURN
C
C
C ...the case P = p-shell and Q = p-shell.
C (no B01,B10)
C
C
4 IF (ATOMAB.AND.ATOMCD) THEN
M = 0
N = 0
DO 400 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 410 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 415 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = - QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
415 CONTINUE
410 CONTINUE
400 CONTINUE
ELSE IF (ATOMAB) THEN
M = 0
N = 0
DO 420 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 430 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 435 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = - QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
435 CONTINUE
430 CONTINUE
420 CONTINUE
ELSE IF (ATOMCD) THEN
M = 0
N = 0
DO 440 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
DO 450 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 455 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
455 CONTINUE
450 CONTINUE
440 CONTINUE
ELSE
M = 0
N = 0
DO 460 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
DO 470 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 475 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
475 CONTINUE
470 CONTINUE
460 CONTINUE
END IF
RETURN
C
C
C ...the case P > p-shell and Q = s-shell.
C (no B00,B01,D00)
C
C
5 IF (ATOMAB) THEN
M = 0
N = 0
DO 500 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
TWOP = PINVHF (IJ)
DO 510 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
QSCALE = ONE - PIJ * PQPINV (M)
DO 515 NG = 1,NGQP
N = N + 1
QROOT = - QSCALE * RTS (N)
B10 (N)= (ONE + QROOT) * TWOP
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
515 CONTINUE
510 CONTINUE
500 CONTINUE
ELSE
M = 0
N = 0
DO 520 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
TWOP = PINVHF (IJ)
DO 530 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
QSCALE = ONE - PIJ * PQPINV (M)
DO 535 NG = 1,NGQP
N = N + 1
QROOT = QSCALE * RTS (N)
B10 (N)= (ONE - QROOT) * TWOP
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
535 CONTINUE
530 CONTINUE
520 CONTINUE
END IF
RETURN
C
C
C ...the case P = s-shell and Q > p-shell.
C (no B00,B10,C00)
C
C
6 IF (ATOMCD) THEN
M = 0
N = 0
DO 600 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 610 KL = 1,MKL
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
PSCALE = PIJ * PQPINV (M)
DO 615 NG = 1,NGQP
N = N + 1
PROOT = PSCALE * RTS (N)
B01 (N) = (ONE - PROOT) * TWOQ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
615 CONTINUE
610 CONTINUE
600 CONTINUE
ELSE
M = 0
N = 0
DO 620 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 630 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
PSCALE = PIJ * PQPINV (M)
DO 635 NG = 1,NGQP
N = N + 1
PROOT = PSCALE * RTS (N)
B01 (N) = (ONE - PROOT) * TWOQ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
635 CONTINUE
630 CONTINUE
620 CONTINUE
END IF
RETURN
C
C
C ...the case P > p-shell and Q = p-shell.
C (no B01)
C
C
7 IF (ATOMAB.AND.ATOMCD) THEN
M = 0
N = 0
DO 700 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
TWOP = PINVHF (IJ)
DO 710 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 715 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = - QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B10 (N) = (ONE + QROOT) * TWOP
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
715 CONTINUE
710 CONTINUE
700 CONTINUE
ELSE IF (ATOMAB) THEN
M = 0
N = 0
DO 720 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
TWOP = PINVHF (IJ)
DO 730 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 735 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = - QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B10 (N) = (ONE + QROOT) * TWOP
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
735 CONTINUE
730 CONTINUE
720 CONTINUE
ELSE IF (ATOMCD) THEN
M = 0
N = 0
DO 740 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
TWOP = PINVHF (IJ)
DO 750 KL = 1,MKL
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 755 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B10 (N) = (ONE - QROOT) * TWOP
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
755 CONTINUE
750 CONTINUE
740 CONTINUE
ELSE
M = 0
N = 0
DO 760 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
TWOP = PINVHF (IJ)
DO 770 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 775 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B10 (N) = (ONE - QROOT) * TWOP
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
775 CONTINUE
770 CONTINUE
760 CONTINUE
END IF
RETURN
C
C
C ...the case P = p-shell and Q > p-shell.
C (no B10)
C
C
8 IF (ATOMAB.AND.ATOMCD) THEN
M = 0
N = 0
DO 800 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 810 KL = 1,MKL
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 815 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = - QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B01 (N) = (ONE - PROOT) * TWOQ
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
815 CONTINUE
810 CONTINUE
800 CONTINUE
ELSE IF (ATOMAB) THEN
M = 0
N = 0
DO 820 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
DO 830 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 835 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = - QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B01 (N) = (ONE - PROOT) * TWOQ
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
835 CONTINUE
830 CONTINUE
820 CONTINUE
ELSE IF (ATOMCD) THEN
M = 0
N = 0
DO 840 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
DO 850 KL = 1,MKL
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 855 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B01 (N) = (ONE - PROOT) * TWOQ
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
855 CONTINUE
850 CONTINUE
840 CONTINUE
ELSE
M = 0
N = 0
DO 860 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
DO 870 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 875 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B01 (N) = (ONE - PROOT) * TWOQ
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
875 CONTINUE
870 CONTINUE
860 CONTINUE
END IF
RETURN
C
C
C ...the case P > p-shell and Q > p-shell.
C
C
9 IF (ATOMAB.AND.ATOMCD) THEN
M = 0
N = 0
DO 900 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
TWOP = PINVHF (IJ)
DO 910 KL = 1,MKL
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 915 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = - QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B01 (N) = (ONE - PROOT) * TWOQ
B10 (N) = (ONE + QROOT) * TWOP
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
915 CONTINUE
910 CONTINUE
900 CONTINUE
ELSE IF (ATOMAB) THEN
M = 0
N = 0
DO 920 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
TWOP = PINVHF (IJ)
DO 930 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 935 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = - QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B01 (N) = (ONE - PROOT) * TWOQ
B10 (N) = (ONE + QROOT) * TWOP
C00X (N) = QROOT * PQX
C00Y (N) = QROOT * PQY
C00Z (N) = QROOT * PQZ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
935 CONTINUE
930 CONTINUE
920 CONTINUE
ELSE IF (ATOMCD) THEN
M = 0
N = 0
DO 940 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
TWOP = PINVHF (IJ)
DO 950 KL = 1,MKL
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 955 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B01 (N) = (ONE - PROOT) * TWOQ
B10 (N) = (ONE - QROOT) * TWOP
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
D00X (N) = PROOT * PQX
D00Y (N) = PROOT * PQY
D00Z (N) = PROOT * PQZ
955 CONTINUE
950 CONTINUE
940 CONTINUE
ELSE
M = 0
N = 0
DO 960 IJ = 1,MIJ
PIJ = P (IJ)
PXIJ = PX (IJ)
PYIJ = PY (IJ)
PZIJ = PZ (IJ)
PAXIJ = PAX (IJ)
PAYIJ = PAY (IJ)
PAZIJ = PAZ (IJ)
TWOP = PINVHF (IJ)
DO 970 KL = 1,MKL
QCXKL = QCX (KL)
QCYKL = QCY (KL)
QCZKL = QCZ (KL)
TWOQ = QINVHF (KL)
PQX = PXIJ - QX (KL)
PQY = PYIJ - QY (KL)
PQZ = PZIJ - QZ (KL)
M = M + 1
TWOPQ = HALF * PQPINV (M)
PSCALE = PIJ * PQPINV (M)
QSCALE = ONE - PSCALE
DO 975 NG = 1,NGQP
N = N + 1
ROOT = RTS (N)
PROOT = PSCALE * ROOT
QROOT = QSCALE * ROOT
B00 (N) = ROOT * TWOPQ
B01 (N) = (ONE - PROOT) * TWOQ
B10 (N) = (ONE - QROOT) * TWOP
C00X (N) = PAXIJ - QROOT * PQX
C00Y (N) = PAYIJ - QROOT * PQY
C00Z (N) = PAZIJ - QROOT * PQZ
D00X (N) = QCXKL + PROOT * PQX
D00Y (N) = QCYKL + PROOT * PQY
D00Z (N) = QCZKL + PROOT * PQZ
975 CONTINUE
970 CONTINUE
960 CONTINUE
END IF
C
C
C ...ready!
C
C
RETURN
END
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