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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__CSGTO
+
+ ( IMAX,ZMAX,
+ NALPHA,NCOEFF,NCSUM,
+ NCGTO1,NCGTO2,NCGTO3,NCGTO4,
+ NPGTO1,NPGTO2,NPGTO3,NPGTO4,
+ SHELL1,SHELL2,SHELL3,SHELL4,
+ X1,Y1,Z1,X2,Y2,Z2,X3,Y3,Z3,X4,Y4,Z4,
+ ALPHA,CC,CCBEG,CCEND,
+ FTABLE,MGRID,NGRID,TMAX,TSTEP,TVSTEP,
+ L1CACHE,TILE,NCTROW,
+ SPHERIC,SCREEN,
+ ICORE,
+
+ NBATCH,
+ NFIRST,
+ ZCORE )
+
C------------------------------------------------------------------------
C OPERATION : ERD__CSGTO
C MODULE : ELECTRON REPULSION INTEGRALS DIRECT
C MODULE-ID : ERD
C SUBROUTINES : ERD__SET_ABCD
C ERD__SET_IJ_KL_PAIRS
C ERD__E0F0_DEF_BLOCKS
C ERD__PREPARE_CTR
C ERD__E0F0_PCGTO_BLOCK
C ERD__CTR_4INDEX_BLOCK
C ERD__CTR_RS_EXPAND
C ERD__CTR_TU_EXPAND
C ERD__CTR_4INDEX_REORDER
C ERD__TRANSPOSE_BATCH
C ERD__XYZ_TO_RY_ABCD
C ERD__CARTESIAN_NORMS
C ERD__HRR_MATRIX
C ERD__HRR_TRANSFORM
C ERD__SPHERICAL_TRANSFORM
C ERD__NORMALIZE_CARTESIAN
C ERD__MOVE_RY
C DESCRIPTION : This operation calculates a batch of contracted
C electron repulsion integrals on up to four different
C centers between spherical or cartesian gaussian type
C shells.
C
C
C Input (x = 1,2,3 and 4):
C
C IMAX,ZMAX = maximum integer,flp memory
C NALPHA = total # of exponents
C NCOEFF = total # of contraction coeffs
C NCSUM = total # of contractions
C NCGTOx = # of contractions for csh x
C NPGTOx = # of primitives per contraction
C for csh x
C SHELLx = the shell type for csh x
C Xy,Yy,Zy = the x,y,z-coordinates for centers
C y = 1,2,3 and 4
C ALPHA = primitive exponents for csh
C 1,2,3,4 in that order
C CC = full set (including zeros) of
C contraction coefficients for csh
C 1,2,3,4 in that order, for each
C csh individually such that an
C (I,J) element corresponds to the
C I-th primitive and J-th contraction
C CC(BEG)END = (lowest)highest nonzero primitive
C index for contractions for csh
C 1,2,3,4 in that order. They are
C different from (1)NPGTOx only for
C segmented contractions
C FTABLE = Fm (T) table for interpolation
C in low T region
C MGRID = maximum m in Fm (T) table
C NGRID = # of T's for which Fm (T) table
C was set up
C TMAX = maximum T in Fm (T) table
C TSTEP = difference between two consecutive
C T's in Fm (T) table
C TVSTEP = Inverse of TSTEP
C L1CACHE = Size of level 1 cache in units of
C 8 Byte
C TILE = Number of rows and columns in
C units of 8 Byte of level 1 cache
C square tile array used for
C performing optimum matrix
C transpositions
C NCTROW = minimum # of rows that are
C accepted for blocked contractions
C SPHERIC = is true, if spherical integrals
C are wanted, false if cartesian
C ones are wanted
C SCREEN = is true, if screening will be
C done at primitive integral level
C ICORE = integer scratch space
C ZCORE (part) = flp scratch space
C
C Output:
C
C NBATCH = # of integrals in batch
C NFIRST = first address location inside the
C ZCORE array containing the first
C integral
C ZCORE = full batch of contracted (12|34)
C integrals over cartesian or
C spherical gaussians starting at
C ZCORE (NFIRST)
C
C
C
C --- NOTES ABOUT THE OVERALL INTEGRAL PREFACTOR ---
C
C The overal integral prefactor is defined here as
C follows. Consider the normalization factors for a
C primitive cartesian GTO and for a spherical GTO
C belonging to the angular momentum L = l+m+n:
C
C
C lmn l m n 2
C GTO (x,y,z) = N (l,m,n,a) * x y z * exp (-ar )
C a
C
C
C LM L LM 2
C GTO (r,t,p) = N (L,a) * r * Y (t,p) * exp (-ar )
C a
C
C
C where a = alpha exponent, t = theta and p = phi and
C N (l,m,n,a) and N (L,a) denote the respective
C cartesian and spherical normalization factors such
C that:
C
C
C lmn lmn
C integral {GTO (x,y,z) * GTO (x,y,z) dx dy dz} = 1
C a a
C
C
C LM LM
C integral {GTO (r,t,p) * GTO (r,t,p) dr dt dp} = 1
C a a
C
C
C The normalization constants have then the following
C values, assuming the spherical harmonics are
C normalized:
C
C _____________________________________
C / 2^(2L+1+1/2) * a^((2L+3)/2)
C N (l,m,n,a) = / ----------------------------------------
C \/ (2l-1)!!(2m-1)!!(2n-1)!! * pi * sqrt (pi)
C
C
C ____________________________
C / 2^(2L+3+1/2) * a^((2L+3)/2)
C N (L,a) = / -----------------------------
C \/ (2L+1)!! * sqrt (pi)
C
C
C Note, that the extra pi under the square root in
C N (l,m,n,a) belongs to the normalization of the
C spherical harmonic functions and therefore does not
C appear in the expression for N (L,a). The common
C L-,l-,m-,n- and a-independent part of the cartesian
C norm is a scalar quantity needed for all integrals
C no matter what L-,l-,m-,n- and a-values they have:
C
C _____________
C / 2^(1+1/2)
C N (0,0,0,0) = / --------------
C \/ pi * sqrt (pi)
C
C
C Also every ERI integral has a factor of 2*pi**(5/2)
C associated with it, hence the overall common factor
C for all integrals will be N(0,0,0,0)**4 times
C 2*pi**(5/2), which is equal to:
C
C
C PREFACT = 16 / sqrt(pi)
C
C
C and is set as a parameter inside the present routine.
C The alpha exponent dependent part of the norms:
C
C ______________
C \/ a^((2L+3)/2)
C
C will be calculated separately (see below) and their
C inclusion in evaluating the primitive cartesian
C [E0|F0] integrals will be essential for numerical
C stability during contraction.
C
C
C AUTHOR : Norbert Flocke
C------------------------------------------------------------------------
C
C
C ...include files and declare variables.
C
C
IMPLICIT NONE
LOGICAL ATOMIC,ATOMAB,ATOMCD
LOGICAL BLOCKED
LOGICAL EMPTY
LOGICAL EQUALAB,EQUALCD
LOGICAL MEMORY
LOGICAL REORDER
LOGICAL SCREEN
LOGICAL SPHERIC
LOGICAL SWAP12,SWAP34,SWAPRS,SWAPTU
LOGICAL TR1234
INTEGER IHNROW,IHROW,IHSCR
INTEGER IMAX,ZMAX
INTEGER IN,OUT
INTEGER INDEXA,INDEXB,INDEXC,INDEXD
INTEGER INDEXR,INDEXS,INDEXT,INDEXU
INTEGER IPRIMA,IPRIMB,IPRIMC,IPRIMD
INTEGER IPUSED,IPSAVE,IPPAIR
INTEGER ISNROWA,ISNROWB,ISNROWC,ISNROWD
INTEGER ISROWA,ISROWB,ISROWC,ISROWD
INTEGER IUSED,ZUSED
INTEGER L1CACHE,TILE,NCTROW
INTEGER LCC1,LCC2,LCC3,LCC4
INTEGER LCCA,LCCB,LCCC,LCCD
INTEGER LCCSEGA,LCCSEGB,LCCSEGC,LCCSEGD
INTEGER LEXP1,LEXP2,LEXP3,LEXP4
INTEGER LEXPA,LEXPB,LEXPC,LEXPD
INTEGER MIJ,MKL,MIJKL,MGQIJKL
INTEGER MGRID,NGRID
INTEGER MOVE,NOTMOVE
INTEGER MXPRIM,MNPRIM
INTEGER MXSHELL,MXSIZE
INTEGER NABCOOR,NCDCOOR
INTEGER NALPHA,NCOEFF,NCSUM
INTEGER NBATCH,NFIRST
INTEGER NCGTO1,NCGTO2,NCGTO3,NCGTO4
INTEGER NCGTOA,NCGTOB,NCGTOC,NCGTOD,NCGTOAB,NCGTOCD
INTEGER NCGTOR,NCGTOS,NCGTOT,NCGTOU
INTEGER NCOLHRR,NROWHRR,NROTHRR,NXYZHRR
INTEGER NCTR
INTEGER NGQP,NMOM,NGQSCR
INTEGER NIJ,NKL
INTEGER NIJBLK,NKLBLK,NIJBEG,NKLBEG,NIJEND,NKLEND
INTEGER NINT2D
INTEGER NPGTO1,NPGTO2,NPGTO3,NPGTO4
INTEGER NPGTOA,NPGTOB,NPGTOC,NPGTOD,NPGTOAB,NPGTOCD
INTEGER NPSIZE,NCSIZE,NWSIZE
INTEGER NROTA,NROTB,NROTC,NROTD
INTEGER NROWA,NROWB,NROWC,NROWD
INTEGER NRYA,NRYB,NRYC,NRYD
INTEGER NXYZA,NXYZB,NXYZC,NXYZD
INTEGER NXYZP,NXYZQ,NXYZT,NXYZET,NXYZFT
INTEGER POS1,POS2
INTEGER SHELL1,SHELL2,SHELL3,SHELL4
INTEGER SHELLA,SHELLB,SHELLC,SHELLD
INTEGER SHELLP,SHELLQ,SHELLT
INTEGER TEMP
INTEGER ZCBATCH,ZPBATCH,ZWORK,
+ ZNORMA,ZNORMB,ZNORMC,ZNORMD,
+ ZBASE,ZCNORM,
+ ZRHOAB,ZRHOCD,
+ ZP,ZPX,ZPY,ZPZ,ZPAX,ZPAY,ZPAZ,ZPINVHF,ZSCPK2,
+ ZQ,ZQX,ZQY,ZQZ,ZQCX,ZQCY,ZQCZ,ZQINVHF,ZSCQK2,
+ ZRTS,ZWTS,ZGQSCR,ZTVAL,ZPQPINV,ZSCPQK4,
+ ZB00,ZB01,ZB10,
+ ZC00X,ZC00Y,ZC00Z,ZD00X,ZD00Y,ZD00Z,
+ ZINT2DX,ZINT2DY,ZINT2DZ,
+ ZSROTA,ZSROTB,ZSROTC,ZSROTD,
+ ZHROT
INTEGER CCBEG (1:NCSUM)
INTEGER CCEND (1:NCSUM)
INTEGER ICORE (1:IMAX)
INTEGER IXOFF (1:4)
DOUBLE PRECISION ABX,ABY,ABZ,CDX,CDY,CDZ
DOUBLE PRECISION PREFACT
DOUBLE PRECISION RNABSQ,RNCDSQ
DOUBLE PRECISION SPNORM
DOUBLE PRECISION TMAX,TSTEP,TVSTEP
DOUBLE PRECISION X1,Y1,Z1,X2,Y2,Z2,X3,Y3,Z3,X4,Y4,Z4
DOUBLE PRECISION XA,YA,ZA,XB,YB,ZB,XC,YC,ZC,XD,YD,ZD
DOUBLE PRECISION ALPHA (1:NALPHA)
DOUBLE PRECISION CC (1:NCOEFF)
DOUBLE PRECISION ZCORE (1:ZMAX)
DOUBLE PRECISION FTABLE (0:MGRID,0:NGRID)
PARAMETER (PREFACT = 9.027033336764101D0)
C
C
C------------------------------------------------------------------------
C
C
C ...fix the A,B,C,D labels from the 1,2,3,4 ones.
C Calculate the relevant data for the A,B,C,D batch of
C integrals.
C
C
LEXP1 = 1
LEXP2 = LEXP1 + NPGTO1
LEXP3 = LEXP2 + NPGTO2
LEXP4 = LEXP3 + NPGTO3
LCC1 = 1
LCC2 = LCC1 + NPGTO1 * NCGTO1
LCC3 = LCC2 + NPGTO2 * NCGTO2
LCC4 = LCC3 + NPGTO3 * NCGTO3
CALL ERD__SET_ABCD
+
+ ( NCGTO1,NCGTO2,NCGTO3,NCGTO4,
+ NPGTO1,NPGTO2,NPGTO3,NPGTO4,
+ SHELL1,SHELL2,SHELL3,SHELL4,
+ X1,Y1,Z1,X2,Y2,Z2,X3,Y3,Z3,X4,Y4,Z4,
+ ALPHA (LEXP1),ALPHA (LEXP2),
+ ALPHA (LEXP3),ALPHA (LEXP4),
+ CC (LCC1),CC (LCC2),CC (LCC3),CC (LCC4),
+ SPHERIC,
+
+ NCGTOA,NCGTOB,NCGTOC,NCGTOD,
+ NPGTOA,NPGTOB,NPGTOC,NPGTOD,
+ SHELLA,SHELLB,SHELLC,SHELLD,
+ SHELLP,SHELLQ,SHELLT,
+ MXSHELL,
+ XA,YA,ZA,XB,YB,ZB,XC,YC,ZC,XD,YD,ZD,
+ ATOMIC,ATOMAB,ATOMCD,
+ EQUALAB,EQUALCD,
+ ABX,ABY,ABZ,CDX,CDY,CDZ,
+ NABCOOR,NCDCOOR,
+ RNABSQ,RNCDSQ,
+ SPNORM,
+ NXYZA,NXYZB,NXYZC,NXYZD,
+ NXYZET,NXYZFT,NXYZP,NXYZQ,
+ NRYA,NRYB,NRYC,NRYD,
+ INDEXA,INDEXB,INDEXC,INDEXD,
+ SWAP12,SWAP34,SWAPRS,SWAPTU,TR1234,
+ LEXPA,LEXPB,LEXPC,LEXPD,
+ LCCA,LCCB,LCCC,LCCD,
+ LCCSEGA,LCCSEGB,LCCSEGC,LCCSEGD,
+ NXYZHRR,NCOLHRR,NROTHRR,
+ EMPTY )
+
+
C WRITE (*,*) ' Finished set abcd '
C WRITE (*,*) ' Index A,B,C,D = ',INDEXA,INDEXB,INDEXC,INDEXD
C WRITE (*,*) ' EQUALAB = ',EQUALAB
C WRITE (*,*) ' EQUALCD = ',EQUALCD
IF (EMPTY) THEN
NBATCH = 0
RETURN
END IF
C
C
C ...enter the cartesian contracted (e0|f0) batch
C generation. Set the ij and kl primitive exponent
C pairs and the corresponding exponential prefactors.
C
C
IF (EQUALAB) THEN
NPGTOAB = (NPGTOA*(NPGTOA+1))/2
NCGTOAB = (NCGTOA*(NCGTOA+1))/2
ELSE
NPGTOAB = NPGTOA * NPGTOB
NCGTOAB = NCGTOA * NCGTOB
END IF
IF (EQUALCD) THEN
NPGTOCD = (NPGTOC*(NPGTOC+1))/2
NCGTOCD = (NCGTOC*(NCGTOC+1))/2
ELSE
NPGTOCD = NPGTOC * NPGTOD
NCGTOCD = NCGTOC * NCGTOD
END IF
NCTR = NCGTOAB * NCGTOCD
NXYZT = NXYZET * NXYZFT
IPRIMA = 1
IPRIMB = IPRIMA + NPGTOAB
IPRIMC = IPRIMB + NPGTOAB
IPRIMD = IPRIMC + NPGTOCD
CALL ERD__SET_IJ_KL_PAIRS
+
+ ( NPGTOA,NPGTOB,NPGTOC,NPGTOD,
+ NPGTOAB,NPGTOCD,
+ ATOMAB,ATOMCD,
+ EQUALAB,EQUALCD,
+ SWAPRS,SWAPTU,
+ XA,YA,ZA,XB,YB,ZB,XC,YC,ZC,XD,YD,ZD,
+ RNABSQ,RNCDSQ,
+ PREFACT,
+ ALPHA (LEXPA),ALPHA (LEXPB),
+ ALPHA (LEXPC),ALPHA (LEXPD),
+ FTABLE,MGRID,NGRID,TMAX,TSTEP,TVSTEP,
+ SCREEN,
+
+ EMPTY,
+ NIJ,NKL,
+ ICORE (IPRIMA),ICORE (IPRIMB),
+ ICORE (IPRIMC),ICORE (IPRIMD),
+ ZCORE (1) )
+
+
IF (EMPTY) THEN
NBATCH = 0
RETURN
END IF
C
C
C ...decide on the primitive [e0|f0] block size and
C return array sizes and pointers for the primitive
C [e0|f0] generation. Perform also some preparation
C steps for contraction.
C
C
NGQP = 1 + SHELLT / 2
NMOM = 2 * NGQP - 1
NGQSCR = 5 * NMOM + 2 * NGQP - 2
MEMORY = .FALSE.
CALL ERD__E0F0_DEF_BLOCKS
+
+ ( ZMAX,
+ NPGTOA,NPGTOB,NPGTOC,NPGTOD,
+ SHELLP,SHELLQ,
+ NIJ,NKL,
+ NCGTOAB,NCGTOCD,NCTR,
+ NGQP,NGQSCR,
+ NXYZT,
+ L1CACHE,NCTROW,
+ MEMORY,
+
+ NIJBLK,NKLBLK,
+ NPSIZE,NCSIZE,NWSIZE,
+ NINT2D,
+ MXPRIM,MNPRIM,
+ ZCBATCH,ZPBATCH,ZWORK,
+ ZNORMA,ZNORMB,ZNORMC,ZNORMD,
+ ZRHOAB,ZRHOCD,
+ ZP,ZPX,ZPY,ZPZ,ZPAX,ZPAY,ZPAZ,ZPINVHF,ZSCPK2,
+ ZQ,ZQX,ZQY,ZQZ,ZQCX,ZQCY,ZQCZ,ZQINVHF,ZSCQK2,
+ ZRTS,ZWTS,ZGQSCR,ZTVAL,ZPQPINV,ZSCPQK4,
+ ZB00,ZB01,ZB10,
+ ZC00X,ZC00Y,ZC00Z,ZD00X,ZD00Y,ZD00Z,
+ ZINT2DX,ZINT2DY,ZINT2DZ )
+
+
BLOCKED = (NIJBLK.LT.NIJ) .OR. (NKLBLK.LT.NKL)
CALL ERD__PREPARE_CTR
+
+ ( NCSIZE,
+ NIJ,NKL,
+ NPGTOA,NPGTOB,NPGTOC,NPGTOD,
+ SHELLA,SHELLB,SHELLC,SHELLD,
+ ALPHA (LEXPA),ALPHA (LEXPB),
+ ALPHA (LEXPC),ALPHA (LEXPD),
+ PREFACT,SPNORM,
+ EQUALAB,EQUALCD,
+ BLOCKED,
+ ZCORE (1),
+
+ ZCORE (ZNORMA),ZCORE (ZNORMB),
+ ZCORE (ZNORMC),ZCORE (ZNORMD),
+ ZCORE (ZRHOAB),ZCORE (ZRHOCD),
+ ZCORE (ZCBATCH) )
+
+
IPUSED = IPRIMD + NPGTOCD
IPSAVE = IPUSED + MNPRIM
IPPAIR = IPSAVE + MXPRIM
C
C
C ...evaluate unnormalized rescaled [e0|f0] in blocks
C over ij and kl pairs and add to final contracted
C (e0|f0). The keyword REORDER indicates, if the
C primitive [e0|f0] blocks need to be transposed
C before being contracted.
C
C
REORDER = .TRUE.
DO 1000 NIJBEG = 1,NIJ,NIJBLK
NIJEND = MIN0 (NIJBEG+NIJBLK-1,NIJ)
MIJ = NIJEND - NIJBEG + 1
DO 1100 NKLBEG = 1,NKL,NKLBLK
NKLEND = MIN0 (NKLBEG+NKLBLK-1,NKL)
MKL = NKLEND - NKLBEG + 1
MIJKL = MIJ * MKL
MGQIJKL = NGQP * MIJKL
CALL ERD__E0F0_PCGTO_BLOCK
+
+ ( NPSIZE,NINT2D,
+ ATOMIC,ATOMAB,ATOMCD,
+ MIJ,MKL,MIJKL,
+ NIJ,NIJBEG,NIJEND,NKL,NKLBEG,NKLEND,
+ NGQP,NMOM,NGQSCR,MGQIJKL,
+ NPGTOA,NPGTOB,NPGTOC,NPGTOD,
+ NXYZET,NXYZFT,NXYZP,NXYZQ,
+ SHELLA,SHELLP,SHELLC,SHELLQ,
+ XA,YA,ZA,XB,YB,ZB,XC,YC,ZC,XD,YD,ZD,
+ ABX,ABY,ABZ,CDX,CDY,CDZ,
+ ALPHA (LEXPA),ALPHA (LEXPB),
+ ALPHA (LEXPC),ALPHA (LEXPD),
+ FTABLE,MGRID,NGRID,TMAX,TSTEP,TVSTEP,
+ ICORE (IPRIMA+NIJBEG-1),
+ ICORE (IPRIMB+NIJBEG-1),
+ ICORE (IPRIMC+NKLBEG-1),
+ ICORE (IPRIMD+NKLBEG-1),
+ ZCORE (ZNORMA),ZCORE (ZNORMB),
+ ZCORE (ZNORMC),ZCORE (ZNORMD),
+ ZCORE (ZRHOAB),ZCORE (ZRHOCD),
+ ZCORE (ZP),
+ ZCORE (ZPX),ZCORE (ZPY),ZCORE (ZPZ),
+ ZCORE (ZPAX),ZCORE (ZPAY),ZCORE (ZPAZ),
+ ZCORE (ZPINVHF),ZCORE (ZSCPK2),
+ ZCORE (ZQ),
+ ZCORE (ZQX),ZCORE (ZQY),ZCORE (ZQZ),
+ ZCORE (ZQCX),ZCORE (ZQCY),ZCORE (ZQCZ),
+ ZCORE (ZQINVHF),ZCORE (ZSCQK2),
+ ZCORE (ZRTS),ZCORE (ZWTS),ZCORE (ZGQSCR),
+ ZCORE (ZTVAL),ZCORE (ZPQPINV),
+ ZCORE (ZSCPQK4),
+ ZCORE (ZB00),ZCORE (ZB01),ZCORE (ZB10),
+ ZCORE (ZC00X),ZCORE (ZC00Y),ZCORE (ZC00Z),
+ ZCORE (ZD00X),ZCORE (ZD00Y),ZCORE (ZD00Z),
+ ZCORE (ZINT2DX),
+ ZCORE (ZINT2DY),
+ ZCORE (ZINT2DZ),
+
+ ZCORE (ZPBATCH) )
+
+
C WRITE (*,*) ' Finished e0f0 pcgto block '
CALL ERD__CTR_4INDEX_BLOCK
+
+ ( NPSIZE,NCSIZE,NWSIZE,
+ NXYZT,MIJKL,
+ MIJ,MKL,NCGTOAB,NCGTOCD,
+ NPGTOA,NPGTOB,NPGTOC,NPGTOD,
+ NCGTOA,NCGTOB,NCGTOC,NCGTOD,
+ MXPRIM,MNPRIM,
+ CC (LCCA),CC (LCCB),CC (LCCC),CC (LCCD),
+ CCBEG (LCCSEGA),CCBEG (LCCSEGB),
+ CCBEG (LCCSEGC),CCBEG (LCCSEGD),
+ CCEND (LCCSEGA),CCEND (LCCSEGB),
+ CCEND (LCCSEGC),CCEND (LCCSEGD),
+ ICORE (IPRIMA+NIJBEG-1),
+ ICORE (IPRIMB+NIJBEG-1),
+ ICORE (IPRIMC+NKLBEG-1),
+ ICORE (IPRIMD+NKLBEG-1),
+ L1CACHE,TILE,NCTROW,
+ EQUALAB,EQUALCD,
+ SWAPRS,SWAPTU,
+ REORDER,
+ BLOCKED,
+ ICORE (IPUSED),
+ ICORE (IPSAVE),
+ ICORE (IPPAIR),
+ ZCORE (ZPBATCH),
+ ZCORE (ZWORK),
+
+ ZCORE (ZCBATCH) )
+
+
C WRITE (*,*) ' Finished 4 index ctr block '
1100 CONTINUE
1000 CONTINUE
C
C
C ...the unnormalized cartesian (e0|f0) contracted batch is
C ready. Expand the contraction indices (if necessary):
C
C batch (nxyzt,r>=s,t>=u) --> batch (nxyzt,r,s,t,u)
C
C and reorder the contraction index part (if necessary):
C
C batch (nxyzt,r,s,t,u) --> batch (nxyzt,1,2,3,4)
C
C The array IXOFF (x) indicates the total # of indices
C to the left of x without including the nxyzt-part.
C For the left most IXOFF value it is convenient to
C set it equal to 1 instead of 0. Note, that the IXOFF
C array indicates the true # of indices to the left
C after! the batch has been transposed (see below) and
C can be used as initial values when moving the
C ry-components later on during the HRR and cartesian ->
C spherical transformation procedure.
C
C For efficient application of the HRR contraction
C scheme we need the batch elements ordered as:
C
C batch (1,2,3,4,nxyzt)
C
C hence we transpose the batch after the reordering.
C The space partitioning of the flp array for all of
C these steps will be as follows:
C
C
C | Zone 1 | Zone 2 |
C
C in which Zone 1 and 2 are 2 batches of HRR maximum
C size. This can be done because we have always the
C following dimension inequality:
C
C NXYZT =< NXYZHRR
C
C
IXOFF (1) = 1
IXOFF (2) = NCGTO1
IXOFF (3) = NCGTO1 * NCGTO2
IXOFF (4) = IXOFF (3) * NCGTO3
NCTR = IXOFF (4) * NCGTO4
MXSIZE = NCTR * NXYZHRR
IN = ZCBATCH
OUT = IN + MXSIZE
IF (EQUALAB .AND. NCGTOAB.GT.1) THEN
CALL ERD__CTR_RS_EXPAND
+
+ ( NXYZT,NCGTOAB,NCGTOCD,
+ NCGTOA,NCGTOB,
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished ctr rs expansion '
TEMP = IN
IN = OUT
OUT = TEMP
END IF
IF (EQUALCD .AND. NCGTOCD.GT.1) THEN
CALL ERD__CTR_TU_EXPAND
+
+ ( NXYZT*NCGTOA*NCGTOB,NCGTOCD,
+ NCGTOC,NCGTOD,
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished ctr tu expansion '
TEMP = IN
IN = OUT
OUT = TEMP
END IF
REORDER = TR1234 .OR. (SWAP12.NEQV.SWAPRS)
+ .OR. (SWAP34.NEQV.SWAPTU)
IF (REORDER .AND. NCTR.GT.1) THEN
IF (SWAPRS) THEN
INDEXR = INDEXB
INDEXS = INDEXA
NCGTOR = NCGTOB
NCGTOS = NCGTOA
ELSE
INDEXR = INDEXA
INDEXS = INDEXB
NCGTOR = NCGTOA
NCGTOS = NCGTOB
END IF
IF (SWAPTU) THEN
INDEXT = INDEXD
INDEXU = INDEXC
NCGTOT = NCGTOD
NCGTOU = NCGTOC
ELSE
INDEXT = INDEXC
INDEXU = INDEXD
NCGTOT = NCGTOC
NCGTOU = NCGTOD
END IF
CALL ERD__CTR_4INDEX_REORDER
+
+ ( NXYZT,NCTR,
+ NCGTOR,NCGTOS,NCGTOT,NCGTOU,
+ IXOFF (INDEXR),IXOFF (INDEXS),
+ IXOFF (INDEXT),IXOFF (INDEXU),
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished ctr reorder '
TEMP = IN
IN = OUT
OUT = TEMP
END IF
IF (NXYZT.GT.1 .AND. NCTR.GT.1) THEN
CALL ERD__TRANSPOSE_BATCH
+
+ ( NXYZT,NCTR,
+ TILE,
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished transpose batch '
TEMP = IN
IN = OUT
OUT = TEMP
END IF
C CALL ERD__PRINT_BATCH
C +
C + ( NCTR,NXYZT,1,1, ZCORE (IN) )
C +
C STOP
C
C
C ...enter the HRR contraction and cartesian -> spherical
C transformation / cartesian normalization section.
C The sequence of events is to apply the HRR followed
C by cartesian -> spherical transformations or cartesian
C normalizations and immediate final positioning of
C the finished parts to correspond with the contraction
C indices i,j,k,l. First we do the f0-part followed
C by the e0-part, which hence gives rise to the sequence
C (where ' means spherical or cartesian normalization
C and [] means the indices are in correspondence):
C
C batch (ijkl,e0,f0) --> batch (ijkl,e0,cd)
C batch (ijkl,e0,c,d) --> batch (ijkl,e0,c,d')
C batch (ijkl,e0,c,d') --> batch (ijkl[d'],e0,c)
C batch (ijkl[d'],e0,c) --> batch (ijkl[d'],e0,c')
C batch (ijkl[d'],e0,c') --> batch (ijkl[c'd'],e0)
C
C batch (ijkl[c'd'],e0) --> batch (ijkl[c'd'],ab)
C batch (ijkl[c'd'],a,b) --> batch (ijkl[c'd'],a,b')
C batch (ijkl[c'd'],a,b') --> batch (ijkl[b'c'd'],a)
C batch (ijkl[b'c'd'],a) --> batch (ijkl[b'c'd'],a')
C batch (ijkl[b'c'd'],a') --> batch (ijkl[a'b'c'd'])
C
C
C The space partitioning of the flp array will be
C as follows:
C
C
C | Zone 1 | Zone 2 | Zone 3 | Zone 4 |
C
C
C Zone 1 and 2: 2 batches of MXSIZE maximum size
C (set previously)
C
C Zone 3: cart -> spher transformation data
C or
C cartesian normalization factors
C
C Zone 4: HRR contraction data
C
C
C Determine memory allocation offsets for the entire HRR
C procedure + cartesian -> spherical transformations or
C cartesian normalizations and generate the transformation
C matrices + associated data for those shells > p-shell.
C The offsets are as follows (x=A,B,C,D):
C
C IN = offset for input HRR batch
C OUT = offset for output HRR batch
C
C ZSROTx = offset for x-part transformation matrix
C ISNROWx = offset for # of non-zero XYZ contribution row
C labels for x-part transformation matrix
C ISROWx = offset for non-zero XYZ contribution row
C labels for x-part transformation matrix
C
C ZHROT = offset for HRR transformation matrix
C IHNROW = offset for # of nonzero row labels for
C each HRR matrix column
C IHROW = offset for nonzero row labels for the HRR
C matrix
C IHSCR = integer scratch space for HRR matrix
C assembly
C
C In case of s- or p-shells no transformation matrix is
C generated, hence if we have s- and/or p-shells, then
c no call to the cartesian -> spherical transformation
C or cartesian normalization routines needs to be done.
C All integrals have already been multiplied by a factor
C SPNORM, which has the following value for each s- and
C p-shell:
C
C For s-type shell = 1
C
C For p-type shell = 2 * norm for s-type
C
C This factor was introduced together with the overall
C prefactor during evaluation of the primitive integrals
C in order to save multiplications.
C
C
ZBASE = MAX0 (IN,OUT) + MXSIZE
IF (SPHERIC) THEN
IF (MXSHELL.GT.1) THEN
CALL ERD__XYZ_TO_RY_ABCD
+
+ ( NXYZA,NXYZB,NXYZC,NXYZD,
+ NRYA,NRYB,NRYC,NRYD,
+ SHELLA,SHELLB,SHELLC,SHELLD,
+ 1,ZBASE,
+
+ NROWA,NROWB,NROWC,NROWD,
+ NROTA,NROTB,NROTC,NROTD,
+ ZSROTA,ZSROTB,ZSROTC,ZSROTD,
+ ISNROWA,ISNROWB,ISNROWC,ISNROWD,
+ ISROWA,ISROWB,ISROWC,ISROWD,
+ IUSED,ZUSED,
+ ICORE,ZCORE )
+
+
C WRITE (*,*) ' Finished xyz to ry abcd '
ELSE
IUSED = 0
ZUSED = 0
END IF
ELSE
IF (MXSHELL.GT.1) THEN
ZCNORM = ZBASE
CALL ERD__CARTESIAN_NORMS
+
+ ( MXSHELL,
+
+ ZCORE (ZCNORM))
+
+
C WRITE (*,*) ' Finished cartesian partial norms '
IUSED = 0
ZUSED = MXSHELL + 1
ELSE
IUSED = 0
ZUSED = 0
END IF
END IF
IHNROW = 1 + IUSED
IHROW = IHNROW + NCOLHRR + NCOLHRR
IHSCR = IHROW + NROTHRR + NROTHRR
ZHROT = ZBASE + ZUSED
C
C
C ...do the first stage of processing the integrals:
C
C batch (ijkl,e0,f0) --> batch (ijkl,e0,cd)
C batch (ijkl,e0,c,d) --> batch (ijkl,e0,c,d')
C batch (ijkl,e0,c,d') --> batch (ijkl[d'],e0,c)
C batch (ijkl[d'],e0,c) --> batch (ijkl[d'],e0,c')
C batch (ijkl[d'],e0,c') --> batch (ijkl[c'd'],e0)
C
C
IF (SHELLD.NE.0) THEN
CALL ERD__HRR_MATRIX
+
+ ( NROTHRR,NCOLHRR,
+ NXYZFT,NXYZC,NXYZQ,
+ SHELLC,SHELLD,SHELLQ,
+ NCDCOOR,
+ CDX,CDY,CDZ,
+ ICORE (IHSCR),
+
+ POS1,POS2,
+ NROWHRR,
+ ICORE (IHNROW),
+ ICORE (IHROW),
+ ZCORE (ZHROT) )
+
+
C WRITE (*,*) ' Finished HRR f0 matrix '
CALL ERD__HRR_TRANSFORM
+
+ ( NCTR*NXYZET,
+ NROWHRR,NXYZFT,NXYZC*NXYZD,
+ NXYZC,NXYZD,
+ ICORE (IHNROW+POS1-1),
+ ICORE (IHROW+POS2-1),
+ ZCORE (ZHROT+POS2-1),
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished HRR f0 '
TEMP = IN
IN = OUT
OUT = TEMP
IF (SHELLD.GT.1) THEN
IF (SPHERIC) THEN
CALL ERD__SPHERICAL_TRANSFORM
+
+ ( NCTR*NXYZET*NXYZC,
+ NROWD,NXYZD,NRYD,
+ ICORE (ISNROWD),
+ ICORE (ISROWD),
+ ZCORE (ZSROTD),
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished sph quart d '
TEMP = IN
IN = OUT
OUT = TEMP
ELSE
CALL ERD__NORMALIZE_CARTESIAN
+
+ ( NCTR*NXYZET*NXYZC,
+ NXYZD,
+ SHELLD,
+ ZCORE (ZCNORM),
+
+ ZCORE (IN) )
+
+
C WRITE (*,*) ' Finished normalize cart d '
END IF
END IF
END IF
IF (NRYD.GT.1) THEN
NBATCH = NCTR * NXYZET * NXYZC * NRYD
NOTMOVE = IXOFF (INDEXD)
MOVE = NBATCH / (NOTMOVE * NRYD)
IF (MOVE.GT.1) THEN
CALL ERD__MOVE_RY
+
+ ( NBATCH,4,
+ NOTMOVE,MOVE,NRYD,
+ INDEXD,
+ TILE,
+ ZCORE (IN),
+
+ IXOFF,
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished move ry d '
TEMP = IN
IN = OUT
OUT = TEMP
END IF
END IF
IF (SHELLC.GT.1) THEN
IF (SPHERIC) THEN
CALL ERD__SPHERICAL_TRANSFORM
+
+ ( NCTR*NXYZET*NRYD,
+ NROWC,NXYZC,NRYC,
+ ICORE (ISNROWC),
+ ICORE (ISROWC),
+ ZCORE (ZSROTC),
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished sph quart c '
TEMP = IN
IN = OUT
OUT = TEMP
ELSE
CALL ERD__NORMALIZE_CARTESIAN
+
+ ( NCTR*NXYZET*NRYD,
+ NXYZC,
+ SHELLC,
+ ZCORE (ZCNORM),
+
+ ZCORE (IN) )
+
+
C WRITE (*,*) ' Finished normalize cart c '
END IF
END IF
IF (NRYC.GT.1) THEN
NBATCH = NCTR * NRYD * NXYZET * NRYC
NOTMOVE = IXOFF (INDEXC)
MOVE = NBATCH / (NOTMOVE * NRYC)
IF (MOVE.GT.1) THEN
CALL ERD__MOVE_RY
+
+ ( NBATCH,4,
+ NOTMOVE,MOVE,NRYC,
+ INDEXC,
+ TILE,
+ ZCORE (IN),
+
+ IXOFF,
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished move ry c '
TEMP = IN
IN = OUT
OUT = TEMP
END IF
END IF
C
C
C ...do the second stage of processing the integrals:
C
C batch (ijkl[c'd'],e0) --> batch (ijkl[c'd'],ab)
C batch (ijkl[c'd'],a,b) --> batch (ijkl[c'd'],a,b')
C batch (ijkl[c'd'],a,b') --> batch (ijkl[b'c'd'],a)
C batch (ijkl[b'c'd'],a) --> batch (ijkl[b'c'd'],a')
C batch (ijkl[b'c'd'],a') --> batch (ijkl[a'b'c'd'])
C
C
IF (SHELLB.NE.0) THEN
CALL ERD__HRR_MATRIX
+
+ ( NROTHRR,NCOLHRR,
+ NXYZET,NXYZA,NXYZP,
+ SHELLA,SHELLB,SHELLP,
+ NABCOOR,
+ ABX,ABY,ABZ,
+ ICORE (IHSCR),
+
+ POS1,POS2,
+ NROWHRR,
+ ICORE (IHNROW),
+ ICORE (IHROW),
+ ZCORE (ZHROT) )
+
+
C WRITE (*,*) ' Finished HRR e0 matrix '
CALL ERD__HRR_TRANSFORM
+
+ ( NCTR*NRYC*NRYD,
+ NROWHRR,NXYZET,NXYZA*NXYZB,
+ NXYZA,NXYZB,
+ ICORE (IHNROW+POS1-1),
+ ICORE (IHROW+POS2-1),
+ ZCORE (ZHROT+POS2-1),
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished HRR e0 '
TEMP = IN
IN = OUT
OUT = TEMP
IF (SHELLB.GT.1) THEN
IF (SPHERIC) THEN
CALL ERD__SPHERICAL_TRANSFORM
+
+ ( NCTR*NRYC*NRYD*NXYZA,
+ NROWB,NXYZB,NRYB,
+ ICORE (ISNROWB),
+ ICORE (ISROWB),
+ ZCORE (ZSROTB),
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished sph quart b '
TEMP = IN
IN = OUT
OUT = TEMP
ELSE
CALL ERD__NORMALIZE_CARTESIAN
+
+ ( NCTR*NRYC*NRYD*NXYZA,
+ NXYZB,
+ SHELLB,
+ ZCORE (ZCNORM),
+
+ ZCORE (IN) )
+
+
C WRITE (*,*) ' Finished normalized cart b '
END IF
END IF
END IF
IF (NRYB.GT.1) THEN
NBATCH = NCTR * NRYC * NRYD * NXYZA * NRYB
NOTMOVE = IXOFF (INDEXB)
MOVE = NBATCH / (NOTMOVE * NRYB)
IF (MOVE.GT.1) THEN
CALL ERD__MOVE_RY
+
+ ( NBATCH,4,
+ NOTMOVE,MOVE,NRYB,
+ INDEXB,
+ TILE,
+ ZCORE (IN),
+
+ IXOFF,
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished move ry b '
TEMP = IN
IN = OUT
OUT = TEMP
END IF
END IF
IF (SHELLA.GT.1) THEN
IF (SPHERIC) THEN
CALL ERD__SPHERICAL_TRANSFORM
+
+ ( NCTR*NRYB*NRYC*NRYD,
+ NROWA,NXYZA,NRYA,
+ ICORE (ISNROWA),
+ ICORE (ISROWA),
+ ZCORE (ZSROTA),
+ ZCORE (IN),
+
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished sph quart a '
TEMP = IN
IN = OUT
OUT = TEMP
ELSE
CALL ERD__NORMALIZE_CARTESIAN
+
+ ( NCTR*NRYB*NRYC*NRYD,
+ NXYZA,
+ SHELLA,
+ ZCORE (ZCNORM),
+
+ ZCORE (IN) )
+
+
C WRITE (*,*) ' Finished normalized cart a '
END IF
END IF
NBATCH = NCTR * NRYB * NRYC * NRYD * NRYA
IF (NRYA.GT.1) THEN
NOTMOVE = IXOFF (INDEXA)
MOVE = NBATCH / (NOTMOVE * NRYA)
IF (MOVE.GT.1) THEN
CALL ERD__MOVE_RY
+
+ ( NBATCH,4,
+ NOTMOVE,MOVE,NRYA,
+ INDEXA,
+ TILE,
+ ZCORE (IN),
+
+ IXOFF,
+ ZCORE (OUT) )
+
+
C WRITE (*,*) ' Finished move ry a '
TEMP = IN
IN = OUT
OUT = TEMP
END IF
END IF
C
C
C ...set final pointer to integrals in ZCORE array.
C
C
NFIRST = IN
C
C
C ...ready!
C
C
RETURN
END
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