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full.f
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! This file is part of std2.
!
! Copyright (C) 2025 Marc de Wergifosse
!
! std2 is free software: you can redistribute it and/or modify it under
! the terms of the GNU Lesser General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! std2 is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU Lesser General Public License for more details.
!
! You should have received a copy of the GNU Lesser General Public License
! along with std2. If not, see <https://www.gnu.org/licenses/>.
!
!! ------------------------------------------------------------------------
!!! (|) integrals are computed exactly, for testing purpose only, not optimized !!!!!!!!
subroutine rrpamat_full(nci,ncent,no,nv,mxcnf,iconf,dak,dax,ed,
. apb,ambsqr,ca,nao,moci,nprims,epsi)
use commonlogicals
use omp_lib
implicit none
integer, intent(in) :: nci,ncent,no,nv,mxcnf,iconf(mxcnf,2)
real*8, intent(in) :: dak,dax,ed(mxcnf)
real*4, intent(out) :: apb(nci*(nci+1)/2),ambsqr(nci*(nci+1)/2)
integer i,j,ij,io,iv,jo,jv,ierr,lin,iiv,jjv,iwrk,jwrk,a,b,k,l,ii
real*4 ek,ej,sdot,ak,ax,de
real*8 :: ca(nao*moci)
real*4, allocatable :: integral2(:,:,:,:)
integer :: nao, moci, nprims
integer*8 :: lin8
real*4 :: start_time,end_time,start,finished
integer :: m,n,o,p
real*4, allocatable :: iatemp1(:,:),itemp(:,:,:)
real*4, allocatable :: iatemp2(:,:)
real*4, allocatable :: iajtemp1(:),iajtemp2(:)
real*4, allocatable :: K_iajb(:,:,:,:)
real*4, allocatable :: J_ijab(:,:,:,:)
real*8 :: ddot
integer :: canon
real*8 :: wtime
integer :: ino,nno,inv,nnv
integer*8 :: counter
real*8 :: epsi(moci)
start_time=wtime()
! call cpu_time(start)
! Compute ( | ) integrals with lbcint
! reduce the mo range to match the configuration space
ino=minval(iconf(1:nci,1))
nno=maxval(iconf(1:nci,1))
inv=minval(iconf(1:nci,2))-no
nnv=maxval(iconf(1:nci,2))-no
! write(*,*)'MO integrals computed for occ.',ino,'to',nno
! write(*,*)'and for unocc.',inv,'to',nnv
allocate(integral2(nno+1-ino,nao,nao,nao),stat=ierr)
if(ierr.ne.0)stop 'allocation failed for 2-e integrals'
call two_elec_int_i(ncent,nprims,nao,integral2,
.ino,nno,ca,moci)
! call cpu_time(finished)
end_time=wtime()
! print '("cpu time = ",f12.2," minutes.")'
! . ,(finished-start)/60.0
print '("time = ",f12.2," minutes.")'
. ,(end_time-start_time)/60.0
start_time=wtime()
call cpu_time(start)
allocate(itemp(nao,nao,nao))
allocate(iatemp1(nao,nao))
allocate(iatemp2(nao,nao))
allocate(iajtemp1(nao))
allocate(iajtemp2(nao))
if(abs(dax).lt.1.0d-6) then
allocate(K_iajb(ino:nno,inv:nnv,ino:nno,inv:nnv))
!$omp parallel private(ii,p,j,a,b,itemp,
!$omp& iatemp1)
!$omp& shared(ca,integral2,nao,no)
!$omp do
Do ii=ino, nno
!(i.|..)
itemp(:,:,:)=integral2(ii,:,:,:)
Do a=inv, nnv
iatemp1=0.0
Do p=1,nao
!(ia|..)
call sgemv('T',nao,nao,1.0,itemp(:,:,p),nao,
.real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1,0.0,iatemp1(:,p),1)
Do j=ino, nno
iajtemp1=0.0
!(ia|j.)
call sgemv('T',nao,nao,1.0,iatemp1,nao,
.real(ca(1+(j-1)*nao:nao+(j-1)*nao),4),1,0.0,iajtemp1,1)
enddo
Do b=inv, nnv
!(ia|jb)
K_iajb(ii,a,j,b)=sdot(nao,iajtemp1,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
enddo
enddo
enddo
enddo
!$omp end do
!$omp end parallel
else
allocate(K_iajb(ino:nno,inv:nnv,ino:nno,inv:nnv))
allocate(J_ijab(ino:nno,ino:nno,inv:nnv,inv:nnv))
!$omp parallel private(ii,p,j,a,b,itemp,
!$omp& iatemp1,iatemp2,iajtemp1,iajtemp2)
!$omp& shared(ca,integral2,nao,no)
!$omp do
Do ii=ino, nno
!(i.|..)
itemp(:,:,:)=integral2(ii,:,:,:) ! this is increasing the speed drastically :)
Do a=inv, nnv
iatemp1=0.0
iatemp2=0.0
Do p=1,nao
!(ia|..)
call sgemv('T',nao,nao,1.0,itemp(:,:,p),nao,
.real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1,0.0,iatemp1(:,p),1)
!(i.|a.)
call sgemv('N',nao,nao,1.0,itemp(:,:,p),nao,
.real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1,0.0,iatemp2(:,p),1)
enddo
Do j=ino, nno
iajtemp1=0.0
iajtemp2=0.0
!(ia|j.)
call sgemv('T',nao,nao,1.0,iatemp1,nao,
.real(ca(1+(j-1)*nao:nao+(j-1)*nao),4),1,0.0,iajtemp1,1)
!(ij|a.)
call sgemv('T',nao,nao,1.0,iatemp2,nao,
.real(ca(1+(j-1)*nao:nao+(j-1)*nao),4),1,0.0,iajtemp2,1)
Do b=inv, nnv
!(ia|jb) Since (ia|jb)=(jb|ia), I could decrease memory by collapsing the array... but with respect to integral
K_iajb(ii,a,j,b)=sdot(nao,iajtemp1,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
!(ij|ab)
J_ijab(ii,j,a,b)=sdot(nao,iajtemp2,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
enddo
enddo
enddo
enddo
!$omp end do
!$omp end parallel
endif
deallocate(itemp)
deallocate(iatemp1)
deallocate(iatemp2)
deallocate(iajtemp1)
deallocate(iajtemp2)
deallocate(integral2)
write(*,*)'MO ( | ) computed'
! call cpu_time(finished)
end_time=wtime()
! print '("cpu time = ",f12.2," minutes.")'
! . ,(finished-start)/60.0
print '("time = ",f12.2," minutes.")'
. ,(end_time-start_time)/60.0
ak=real(dak)
ax=real(dax)
! calculate A+B and A-B
apb=0.0e0
ambsqr=0.0e0
! if ax=0, A-B is diagonal and its off-diagonal elements do not need to be calculated
if(abs(dax).lt.1.0d-6) then
ij=0
!$omp parallel private(ij,i,j,ek,de)
!$omp do
do i=1,nci
do j=1,i-1
ij=lin(i,j)
ek=k_iajb(iconf(i,1),iconf(i,2)-no,iconf(j,1),iconf(j,2)-no) ! ek = (ia|jb)
apb(ij)=2.0*ak*ek
ambsqr(ij)=0.0
enddo ! j
de=real(epsi(iconf(i,2))-epsi(iconf(i,1)),4)
ij=lin(i,i)
ek=k_iajb(iconf(i,1),iconf(i,2)-no,iconf(i,1),iconf(i,2)-no)
if(aresp.or.resp.or.optrota) then
ambsqr(ij)=de ! diagonal element of (A-B)
else
ambsqr(ij)=sqrt(de) ! diagonal element of (A-B)^0.5
endif
apb(ij)=de+ak*ek*2.0 ! diagonal element of A+B
enddo ! i
!$omp end do
!$omp end parallel
deallocate(K_iajb)
open(unit=53,file='amb',form='unformatted',status='replace')
write(53) ambsqr
close(53)
else
ij=0
! for now ambsqr=A+B and apb=A-B, since we need to take the sqrt of A-B (but want to save memory)
!$omp parallel private(ij,i,j,ek,ej)
!$omp do
do i=1,nci
do j=1,i-1
ij=lin(i,j)
ek=k_iajb(iconf(i,1),iconf(i,2)-no,iconf(j,1),iconf(j,2)-no) ! ek = (ia|jb)
ej=J_ijab(iconf(i,1),iconf(j,1),iconf(i,2)-no,iconf(j,2)-no)*ax ! ej = (ij|ab)
ambsqr(ij)=2.0*ak*ek
ek=K_iajb(iconf(i,1),iconf(j,2)-no,iconf(j,1),iconf(i,2)-no) ! now ek = (ib|aj), results from Fock-exchange, thus we scale by ax
ambsqr(ij)=ambsqr(ij)-ax*ek-ej
apb(ij)=ax*ek-ej
enddo ! j
ij=lin(i,i)
ek=k_iajb(iconf(i,1),iconf(i,2)-no,iconf(i,1),iconf(i,2)-no)
ej=J_ijab(iconf(i,1),iconf(i,1),iconf(i,2)-no,iconf(i,2)-no)*ax
de=real(epsi(iconf(i,2))-epsi(iconf(i,1)),4)
apb(ij)=de+ax*ek -ej ! diagonal element of A-B
ambsqr(ij)=de-ax*ek+2.0*ak*ek -ej! diagonal element of A+B
enddo ! i
!$omp end do
!$omp end parallel
deallocate(K_iajb)
deallocate(J_ijab)
! call prmat4(6,apb,nci,0,'A-B')
! call prmat4(6,ambsqr,nci,0,'A+B')
if(aresp.or.resp.or.optrota) then
write(*,*) ' calculating (A-B)^0.5 not necessary...'
open(unit=53,file='amb',form='unformatted',status='replace')
write(53) apb
close(53)
apb=ambsqr
else
open(unit=52,file='apbmat',form='unformatted',status='replace')
write(52) ambsqr
open(unit=53,file='amb',form='unformatted',status='replace')
write(53) apb
write(*,*) ' calculating (A-B)^0.5 ...'
write(*,'('' estimated time (min) '',f8.2)')
. float(nci)**2*float(nci)/4.d+8/60.
call smatpow(nci,apb) ! calculate sqrt(a-b), termed ambsqr
ambsqr=apb
rewind(52)
read(52) apb
close(52,status='delete')
close(53)
endif
endif ! GGA/hybrid case
return
end subroutine rrpamat_full
function wtime ( )
implicit none
integer ( kind = 4 ) clock_max
integer ( kind = 4 ) clock_rate
integer ( kind = 4 ) clock_reading
real ( kind = 8 ) wtime
call system_clock ( clock_reading, clock_rate, clock_max )
wtime = real ( clock_reading, kind = 8 )
. / real ( clock_rate, kind = 8 )
return
end
subroutine two_elec_int_i(ncent,nprims,nbf,integral,
.ino,nno,ca,moci)
use stdacommon
use commonlibcint
use omp_lib
implicit none
integer :: i,j,k,l
integer,target :: n,m,o,p,mm,nn
integer,pointer :: ddj,ddk,ddl,dddl
logical :: extra_step
integer :: ncent,nprims,nbf,canon
integer :: ino,nno,moci
real*8 :: ca(nbf*moci)
integer :: shls(4)
integer, target :: di,dj,dk,dl
integer :: orb_cart(1:10,1:10)
double precision, allocatable :: buf(:,:,:,:)
real*4 :: integral(nno+1-ino,nbf,nbf,nbf)
double precision :: norm_cart(1:10,1:10),thresh
integer,external :: CINTcgto_cart
integer*8 :: opt
! enforce not RSH integrals, putting mu to zero
env(9)=0.0d0
! see Theoret. Chim. Acta 33 1-6 (1974) Diercksen
! and Methods in computational chemistry Vol 1, 1987, page 257
! It uses integral symmetries
! number of integrals nbf*(nbf+1)/2*(nbf*(nbf+1)/2+1)/2
! including vanishing ones
! integral canonical index for (ij|kl):
! i>=j k>=l
! ij=i(i-1)/2+j kl=k(k-1)/2+l
! ij>=kl
! canonical_index=ij(ij-1)/2+kl
! To get the same order as in libcint
orb_cart(1,1)=1
orb_cart(3,1)=1
orb_cart(3,2)=2
orb_cart(3,3)=3
orb_cart(6,1)=1
orb_cart(6,2)=4
orb_cart(6,3)=5
orb_cart(6,4)=2
orb_cart(6,5)=6
orb_cart(6,6)=3
orb_cart(10,1)=1
orb_cart(10,2)=4
orb_cart(10,3)=5
orb_cart(10,4)=6
orb_cart(10,5)=10
orb_cart(10,6)=8
orb_cart(10,7)=2
orb_cart(10,8)=7
orb_cart(10,9)=9
orb_cart(10,10)=3
! For cartesian basis libcint uses d and f not normalized
if(spherical)then
norm_cart=1.0
else
norm_cart=1.0
norm_cart(6,1)=1.0
norm_cart(6,2)=dsqrt(3.0d0)
norm_cart(6,3)=dsqrt(3.0d0)
norm_cart(6,4)=1.0
norm_cart(6,5)=dsqrt(3.0d0)
norm_cart(6,6)=1.0
norm_cart(10,1)=1.0
norm_cart(10,2)=dsqrt(5.0d0)
norm_cart(10,3)=dsqrt(5.0d0)
norm_cart(10,4)=dsqrt(5.0d0)
norm_cart(10,5)=dsqrt(15.0d0)
norm_cart(10,6)=dsqrt(5.0d0)
norm_cart(10,7)=1.0
norm_cart(10,8)=dsqrt(5.0d0)
norm_cart(10,9)=dsqrt(5.0d0)
norm_cart(10,10)=1.0
endif
integral=0.0d0
thresh=1.0d-7
write(*,*)'number of unique AO integrals',
.int(nbf,8)*(int(nbf,8)+1)/2*
. (int(nbf,8)*(int(nbf,8)+1)/2+1)/2
write(*,*)'number of (i.|..) that will be stored temporarily',
.int((nno+1-ino),8)*int(nbf,8)*int(nbf,8)*int(nbf,8)
!compute (ij|kl)
call cint2e_cart_optimizer(opt,atm,ncent,bas,nbas,env)
!$omp parallel private(i,j,k,l,m,n,o,p,shls,di,dj,dk,dl,buf,
!$omp& ddj,ddk,ddl,mm,extra_step)
!$omp& reduction(+:integral)
!$omp do
Do i=1,nbas
shls(1)=i-1 ; di=di_all(i)
Do j=1,i
shls(2)=j-1 ; dj=di_all(j)
Do k=1,i-1
shls(3)=k-1 ; dk=di_all(k)
Do l=1,k
shls(4)=l-1 ; dl=di_all(l)
allocate(buf(di,dj,dk,dl))
call cint2e_cart(buf,shls,atm,ncent,bas,nbas,env,opt)
! select case for writing into integral
nullify(ddj,ddk,ddl)
if(i==j)then
ddj=>m
else
ddj=>dj
endif
ddk=>dk
if(k==l)then
ddl=>o
else
ddl=>dl
endif
Do m=1,di
Do n=1,ddj
Do o=1,ddk
Do p=1,ddl
if(dabs(buf(m,n,o,p)
.*norm_cart(di,m)
.*norm_cart(dj,n)
.*norm_cart(dk,o)
.*norm_cart(dl,p))>thresh)then
call select_ijkl(sum_di(i)+orb_cart(di,m)
.,sum_di(j)+orb_cart(dj,n)
.,sum_di(k)+orb_cart(dk,o)
.,sum_di(l)+orb_cart(dl,p),ca,nbf,moci,integral,real(buf(m,n,o,p)
.*norm_cart(di,m)
.*norm_cart(dj,n)
.*norm_cart(dk,o)
.*norm_cart(dl,p),4),ino,nno)
endif
enddo
enddo
enddo
enddo
deallocate(buf)
enddo!l
enddo!k
k=i!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
shls(3)=k-1 ; dk=di_all(k)
Do l=1,j
shls(4)=l-1 ; dl=di_all(l)
allocate(buf(di,dj,dk,dl))
call cint2e_cart(buf,shls,atm,ncent,bas,nbas,env,opt)
! select case for writing into integral
extra_step=.false.
nullify(ddj,ddk,ddl)
if(i==j)then
ddj=>m
else
ddj=>dj
endif
if(k==l)then
ddk=>mm
ddl=>o
extra_step=.true.
else
if(j==l)then
ddk=>mm
ddl=>dl
extra_step=.true.
else
ddk=>dk
ddl=>dl
endif
endif
Do m=1,di
mm=m-1
Do n=1,ddj
Do o=1,ddk
Do p=1,ddl
if(dabs(buf(m,n,o,p)
.*norm_cart(di,m)
.*norm_cart(dj,n)
.*norm_cart(dk,o)
.*norm_cart(dl,p))>thresh)then
call select_ijkl(sum_di(i)+orb_cart(di,m)
.,sum_di(j)+orb_cart(dj,n)
.,sum_di(k)+orb_cart(dk,o)
.,sum_di(l)+orb_cart(dl,p),ca,nbf,moci,integral,real(buf(m,n,o,p)
.*norm_cart(di,m)
.*norm_cart(dj,n)
.*norm_cart(dk,o)
.*norm_cart(dl,p),4),ino,nno)
endif
enddo
enddo
if(extra_step)then
o=m
Do p=1,n
if(dabs(buf(m,n,o,p)
.*norm_cart(di,m)
.*norm_cart(dj,n)
.*norm_cart(dk,o)
.*norm_cart(dl,p))>thresh)then
call select_ijkl(sum_di(i)+orb_cart(di,m)
.,sum_di(j)+orb_cart(dj,n)
.,sum_di(k)+orb_cart(dk,o)
.,sum_di(l)+orb_cart(dl,p),ca,nbf,moci,integral,real(buf(m,n,o,p)
.*norm_cart(di,m)
.*norm_cart(dj,n)
.*norm_cart(dk,o)
.*norm_cart(dl,p),4),ino,nno)
endif
enddo
endif
enddo
enddo
deallocate(buf)
enddo
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
enddo
enddo
!$omp end do
!$omp end parallel
call CINTdel_optimizer(opt)
write(*,*)'(i.|..) integrals done'
end subroutine two_elec_int_i
subroutine select_ijkl(i,j,k,l,ca,nao,moci,itemp,value,ino,nno)
implicit none
integer :: i,j,k,l,p
integer :: ino,nno,moci,nao
real*4 :: itemp((nno+1-ino),nao,nao,nao)
real*4 :: value
real*8 :: ca(nao*moci)
if(i==j.and.i==k.and.i==l)then!iiii
Do p=ino,nno
itemp(p,i,i,i)=itemp(p,i,i,i)+value*ca(i+(p-1)*nao)
enddo
elseif(i==j.and.i==k.and.k/=l)then!iiil
Do p=ino,nno
itemp(p,i,i,l)=itemp(p,i,i,l)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,l,i)=itemp(p,i,l,i)+value*real(ca(i+(p-1)*nao),4)
itemp(p,l,i,i)=itemp(p,l,i,i)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,i,i)=itemp(p,i,i,i)+value*real(ca(l+(p-1)*nao),4)
enddo
elseif(i==j.and.i/=k.and.i==l)then!iiki
Do p=ino,nno
itemp(p,i,i,k)=itemp(p,i,i,k)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,k,i)=itemp(p,i,k,i)+value*real(ca(i+(p-1)*nao),4)
itemp(p,k,i,i)=itemp(p,k,i,i)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,i,i)=itemp(p,i,i,i)+value*real(ca(k+(p-1)*nao),4)
enddo
elseif(i/=j.and.i==k.and.i==l)then!ijii
Do p=ino,nno
itemp(p,i,i,j)=itemp(p,i,i,j)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,j,i)=itemp(p,i,j,i)+value*real(ca(i+(p-1)*nao),4)
itemp(p,j,i,i)=itemp(p,j,i,i)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,i,i)=itemp(p,i,i,i)+value*real(ca(j+(p-1)*nao),4)
enddo
elseif(i/=j.and.j==k.and.j==l)then!ijjj
Do p=ino,nno
itemp(p,j,j,i)=itemp(p,j,j,i)+value*real(ca(j+(p-1)*nao),4)
itemp(p,j,i,j)=itemp(p,j,i,j)+value*real(ca(j+(p-1)*nao),4)
itemp(p,i,j,j)=itemp(p,i,j,j)+value*real(ca(j+(p-1)*nao),4)
itemp(p,j,j,j)=itemp(p,j,j,j)+value*real(ca(i+(p-1)*nao),4)
enddo
elseif(i==j.and.i/=k.and.k==l)then!iikk
Do p=ino,nno
itemp(p,i,k,k)=itemp(p,i,k,k)+value*real(ca(i+(p-1)*nao),4)
itemp(p,k,i,i)=itemp(p,k,i,i)+value*real(ca(k+(p-1)*nao),4)
enddo
elseif(i==j.and.i/=k.and.k/=l)then!iikl
Do p=ino,nno
itemp(p,i,k,l)=itemp(p,i,k,l)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,l,k)=itemp(p,i,l,k)+value*real(ca(i+(p-1)*nao),4)
itemp(p,l,i,i)=itemp(p,l,i,i)+value*real(ca(k+(p-1)*nao),4)
itemp(p,k,i,i)=itemp(p,k,i,i)+value*real(ca(l+(p-1)*nao),4)
enddo
elseif(i/=j.and.i/=k.and.k==l)then!ijkk
Do p=ino,nno
itemp(p,j,k,k)=itemp(p,j,k,k)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,k,k)=itemp(p,i,k,k)+value*real(ca(j+(p-1)*nao),4)
itemp(p,k,i,j)=itemp(p,k,i,j)+value*real(ca(k+(p-1)*nao),4)
itemp(p,k,j,i)=itemp(p,k,j,i)+value*real(ca(k+(p-1)*nao),4)
enddo
elseif(i/=j.and.i==k.and.j==l)then!ijij or jiji
Do p=ino,nno
itemp(p,j,i,j)=itemp(p,j,i,j)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,i,j)=itemp(p,i,i,j)+value*real(ca(j+(p-1)*nao),4)
itemp(p,j,j,i)=itemp(p,j,j,i)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,j,i)=itemp(p,i,j,i)+value*real(ca(j+(p-1)*nao),4)
enddo
elseif(i/=j.and.i==l.and.j==k)then!ijji or jiij
Do p=ino,nno
itemp(p,j,i,j)=itemp(p,j,i,j)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,i,j)=itemp(p,i,i,j)+value*real(ca(j+(p-1)*nao),4)
itemp(p,j,j,i)=itemp(p,j,j,i)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,j,i)=itemp(p,i,j,i)+value*real(ca(j+(p-1)*nao),4)
enddo
else!ijkl ijil
Do p=ino,nno
itemp(p,j,k,l)=itemp(p,j,k,l)+value*real(ca(i+(p-1)*nao),4)
itemp(p,j,l,k)=itemp(p,j,l,k)+value*real(ca(i+(p-1)*nao),4)
itemp(p,i,k,l)=itemp(p,i,k,l)+value*real(ca(j+(p-1)*nao),4)
itemp(p,i,l,k)=itemp(p,i,l,k)+value*real(ca(j+(p-1)*nao),4)
itemp(p,l,i,j)=itemp(p,l,i,j)+value*real(ca(k+(p-1)*nao),4)
itemp(p,l,j,i)=itemp(p,l,j,i)+value*real(ca(k+(p-1)*nao),4)
itemp(p,k,i,j)=itemp(p,k,i,j)+value*real(ca(l+(p-1)*nao),4)
itemp(p,k,j,i)=itemp(p,k,j,i)+value*real(ca(l+(p-1)*nao),4)
enddo
endif
end subroutine select_ijkl
subroutine rrpamat_full_direct(nci,ncent,no,nv,mxcnf,iconf,
. dak,dax,ed,apb,ambsqr,ca,nao,moci,nprims,epsi)
use commonlogicals
use omp_lib
implicit none
integer, intent(in) :: nci,ncent,no,nv,mxcnf,iconf(mxcnf,2)
real*8, intent(in) :: dak,dax,ed(mxcnf)
real*4, intent(out) :: apb(nci*(nci+1)/2),ambsqr(nci*(nci+1)/2)
integer i,j,ij,io,iv,jo,jv,ierr,lin,iiv,jjv,iwrk,jwrk,a,b,k,l,ii
real*4 ek,ej,sdot,ak,ax,de
real*8 :: ca(nao*moci)
integer :: nao, moci, nprims
integer*8 :: lin8
real*4 :: start_time,end_time,start,finished
integer :: m,n,o,p
real*4, allocatable :: iatemp1(:,:),itemp(:,:,:)
real*4, allocatable :: iajtemp1(:)
real*4, allocatable :: K_iajb(:,:,:,:)
real*4, allocatable :: J_ijab(:,:,:,:)
real*8 :: ddot
integer :: canon
real*8 :: wtime
integer :: ino,nno,inv,nnv,step
integer*8 :: counter
real*8 :: epsi(moci)
start_time=wtime()
! call cpu_time(start)
! Compute ( | ) integrals with lbcint
! reduce the mo range to match the configuration space
ino=minval(iconf(1:nci,1))
nno=maxval(iconf(1:nci,1))
inv=minval(iconf(1:nci,2))-no
nnv=maxval(iconf(1:nci,2))-no
write(*,*)'MO integrals computed from occ.',ino,'to',nno
write(*,*)'and from unocc.',inv,'to',nnv
allocate(itemp(nao,nao,nao), stat=ierr )
if(ierr.ne.0)stop 'allocation failed for itemp'
allocate(iatemp1(nao,nao), stat=ierr )
if(ierr.ne.0)stop 'allocation failed for iatemp1'
allocate(iajtemp1(nao), stat=ierr )
if(ierr.ne.0)stop 'allocation failed for iajtemp1'
if(abs(dax).lt.1.0d-6) then
allocate(K_iajb(ino:nno,inv:nnv,ino:nno,inv:nnv), stat=ierr )
if(ierr.ne.0)stop 'allocation failed for K_iajb'
!$omp parallel private(i,p,j,a,b,itemp,
!$omp& iatemp1)
!$omp& shared(ca,nao,no)
!$omp do
Do i=ino, nno
!(i.|..)
call two_elec_int_i_direct(ncent,nprims,nao,itemp,
.ca,moci,i)
Do a=inv, nnv
iatemp1=0.0
Do p=1,nao
!(ia|..)
call sgemv('T',nao,nao,1.0,itemp(:,:,p),nao,
.real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1,0.0,iatemp1(:,p),1)
enddo
Do j=ino, i-1
iajtemp1=0.0
!(ia|j.)
call sgemv('T',nao,nao,1.0,iatemp1,nao,
.real(ca(1+(j-1)*nao:nao+(j-1)*nao),4),1,0.0,iajtemp1,1)
Do b=inv, nnv
!(ia|jb)
K_iajb(i,a,j,b)=sdot(nao,iajtemp1,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
K_iajb(j,b,i,a)=K_iajb(i,a,j,b)
enddo
enddo
iajtemp1=0.0
!(ia|i.)
call sgemv('T',nao,nao,1.0,iatemp1,nao,
.real(ca(1+(i-1)*nao:nao+(i-1)*nao),4),1,0.0,iajtemp1,1)
Do b=inv, a-1
!(ia|ib)
K_iajb(i,a,i,b)=sdot(nao,iajtemp1,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
K_iajb(i,b,i,a)=K_iajb(i,a,i,b)
enddo
!(ia|ia)
K_iajb(i,a,i,a)=sdot(nao,iajtemp1,1,
. real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1)
enddo
enddo
!$omp end do
!$omp end parallel
else
allocate(K_iajb(ino:nno,inv:nnv,ino:nno,inv:nnv), stat=ierr )
if(ierr.ne.0)stop 'allocation failed for K_iajb'
allocate(J_ijab(ino:nno,ino:nno,inv:nnv,inv:nnv), stat=ierr )
if(ierr.ne.0)stop 'allocation failed for J_ijab'
!$omp parallel private(i,p,j,a,b,itemp,
!$omp& iatemp1,iajtemp1)
!$omp& shared(ca,nao,no)
!$omp do
Do i=ino, nno
!(i.|..)
call two_elec_int_i_direct(ncent,nprims,nao,itemp,
.ca,moci,i)
Do a=inv, nnv
iatemp1=0.0
Do p=1,nao
!(ia|..)
call sgemv('T',nao,nao,1.0,itemp(:,:,p),nao,
.real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1,0.0,iatemp1(:,p),1)
enddo
Do j=ino, i-1
iajtemp1=0.0
!(ia|j.)
call sgemv('T',nao,nao,1.0,iatemp1,nao,
.real(ca(1+(j-1)*nao:nao+(j-1)*nao),4),1,0.0,iajtemp1,1)
Do b=inv, nnv
!(ia|jb)
K_iajb(i,a,j,b)=sdot(nao,iajtemp1,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
K_iajb(j,b,i,a)=K_iajb(i,a,j,b)
enddo
enddo
iajtemp1=0.0
!(ia|i.)
call sgemv('T',nao,nao,1.0,iatemp1,nao,
.real(ca(1+(i-1)*nao:nao+(i-1)*nao),4),1,0.0,iajtemp1,1)
Do b=inv, a-1
!(ia|ib)
K_iajb(i,a,i,b)=sdot(nao,iajtemp1,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
K_iajb(i,b,i,a)=K_iajb(i,a,i,b)
enddo
!(ia|ia)
K_iajb(i,a,i,a)=sdot(nao,iajtemp1,1,
. real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1)
iatemp1=0.0
Do p=1,nao
!(i.|a.)
call sgemv('N',nao,nao,1.0,itemp(:,:,p),nao,
.real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1,0.0,iatemp1(:,p),1)
enddo
Do j=ino, i-1
iajtemp1=0.0
!(ij|a.)
call sgemv('T',nao,nao,1.0,iatemp1,nao,
.real(ca(1+(j-1)*nao:nao+(j-1)*nao),4),1,0.0,iajtemp1,1)
Do b=inv, nnv
!(ij|ab)
J_ijab(i,j,a,b)=sdot(nao,iajtemp1,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
J_ijab(j,i,b,a)=J_ijab(i,j,a,b)
enddo
enddo
iajtemp1=0.0
!(ii|a.)
call sgemv('T',nao,nao,1.0,iatemp1,nao,
.real(ca(1+(i-1)*nao:nao+(i-1)*nao),4),1,0.0,iajtemp1,1)
Do b=inv, a-1
!(ii|ab)
J_ijab(i,i,a,b)=sdot(nao,iajtemp1,1,
. real(ca(1+(b+no-1)*nao:nao+(b+no-1)*nao),4),1)
J_ijab(i,i,b,a)=J_ijab(i,i,a,b)
enddo
!(ii|aa)
J_ijab(i,i,a,a)=sdot(nao,iajtemp1,1,
. real(ca(1+(a+no-1)*nao:nao+(a+no-1)*nao),4),1)
enddo
enddo
!$omp end do
!$omp end parallel
endif
deallocate(itemp)
deallocate(iatemp1)
deallocate(iajtemp1)
write(*,*)'MO ( | ) computed'
! call cpu_time(finished)
end_time=wtime()
! print '("cpu time = ",f12.2," minutes.")'
! . ,(finished-start)/60.0
print '("time = ",f12.2," minutes.")'
. ,(end_time-start_time)/60.0
ak=real(dak)
ax=real(dax)
! calculate A+B and A-B
apb=0.0e0
ambsqr=0.0e0
! if ax=0, A-B is diagonal and its off-diagonal elements do not need to be calculated
if(abs(dax).lt.1.0d-6) then
ij=0
!$omp parallel private(ij,i,j,ek,de)
!$omp do
do i=1,nci
do j=1,i-1
ij=lin(i,j)
ek=k_iajb(iconf(i,1),iconf(i,2)-no,iconf(j,1),iconf(j,2)-no) ! ek = (ia|jb)
apb(ij)=2.0*ak*ek
ambsqr(ij)=0.0
enddo ! j
de=real(epsi(iconf(i,2))-epsi(iconf(i,1)),4)
ij=lin(i,i)
ek=k_iajb(iconf(i,1),iconf(i,2)-no,iconf(i,1),iconf(i,2)-no)
if(aresp.or.resp.or.optrota) then
ambsqr(ij)=de ! diagonal element of (A-B)
else
ambsqr(ij)=sqrt(de) ! diagonal element of (A-B)^0.5
endif
apb(ij)=de+ak*ek*2.0 ! diagonal element of A+B
enddo ! i
!$omp end do
!$omp end parallel
deallocate(K_iajb)
open(unit=53,file='amb',form='unformatted',status='replace')
write(53) ambsqr
close(53)
else
ij=0
! for now ambsqr=A+B and apb=A-B, since we need to take the sqrt of A-B (but want to save memory)
!$omp parallel private(ij,i,j,ek,ej)
!$omp do
do i=1,nci
do j=1,i-1
ij=lin(i,j)
ek=k_iajb(iconf(i,1),iconf(i,2)-no,iconf(j,1),iconf(j,2)-no) ! ek = (ia|jb)
ej=J_ijab(iconf(i,1),iconf(j,1),iconf(i,2)-no,iconf(j,2)-no)*ax ! ej = (ij|ab)
ambsqr(ij)=2.0*ak*ek
ek=K_iajb(iconf(i,1),iconf(j,2)-no,iconf(j,1),iconf(i,2)-no) ! now ek = (ib|aj), results from Fock-exchange, thus we scale by ax
ambsqr(ij)=ambsqr(ij)-ax*ek-ej
apb(ij)=ax*ek-ej
enddo ! j
ij=lin(i,i)
ek=k_iajb(iconf(i,1),iconf(i,2)-no,iconf(i,1),iconf(i,2)-no)
ej=J_ijab(iconf(i,1),iconf(i,1),iconf(i,2)-no,iconf(i,2)-no)*ax
de=real(epsi(iconf(i,2))-epsi(iconf(i,1)),4)
apb(ij)=de+ax*ek-ej ! diagonal element of A-B
ambsqr(ij)=de-ax*ek+2.0*ak*ek-ej ! diagonal element of A+B
enddo ! i
!$omp end do
!$omp end parallel
deallocate(K_iajb)
deallocate(J_ijab)
! call prmat4(6,apb,nci,0,'A-B')
! call prmat4(6,ambsqr,nci,0,'A+B')
if(aresp.or.resp.or.optrota) then
write(*,*) ' calculating (A-B)^0.5 not necessary...'
open(unit=53,file='amb',form='unformatted',status='replace')
write(53) apb
close(53)
apb=ambsqr
else
open(unit=52,file='apbmat',form='unformatted',status='replace')
write(52) ambsqr
open(unit=53,file='amb',form='unformatted',status='replace')
write(53) apb
write(*,*) ' calculating (A-B)^0.5 ...'
write(*,'('' estimated time (min) '',f8.2)')
. float(nci)**2*float(nci)/4.d+8/60.
call smatpow(nci,apb) ! calculate sqrt(a-b), termed ambsqr
ambsqr=apb
rewind(52)
read(52) apb
close(52,status='delete')
close(53)
endif
endif ! GGA/hybrid case
return
end subroutine rrpamat_full_direct
subroutine two_elec_int_i_direct(ncent,nprims,nbf,integral,
.ca,moci,ii)
use stdacommon
use commonlibcint
use omp_lib
implicit none
integer :: i,j,k,l,ii
integer,target :: n,m,o,p,mm,nn
integer,pointer :: ddj,ddk,ddl,dddl
logical :: extra_step
integer :: ncent,nprims,nbf,canon
integer :: moci
real*8 :: ca(nbf*moci)
integer :: shls(4)
integer, target :: di,dj,dk,dl
integer :: orb_cart(1:10,1:10)
double precision, allocatable :: buf(:,:,:,:)
real*4 :: integral(nbf,nbf,nbf)
double precision :: norm_cart(1:10,1:10),thresh
integer,external :: CINTcgto_cart
integer*8 :: opt
! see Theoret. Chim. Acta 33 1-6 (1974) Diercksen
! and Methods in computational chemistry Vol 1, 1987, page 257
! It uses integral symmetries
! number of integrals nbf*(nbf+1)/2*(nbf*(nbf+1)/2+1)/2
! including vanishing ones
! integral canonical index for (ij|kl):
! i>=j k>=l
! ij=i(i-1)/2+j kl=k(k-1)/2+l
! ij>=kl
! canonical_index=ij(ij-1)/2+kl
! To get the same order as in libcint
orb_cart(1,1)=1
orb_cart(3,1)=1
orb_cart(3,2)=2
orb_cart(3,3)=3
orb_cart(6,1)=1
orb_cart(6,2)=4
orb_cart(6,3)=5
orb_cart(6,4)=2
orb_cart(6,5)=6
orb_cart(6,6)=3
orb_cart(10,1)=1
orb_cart(10,2)=4
orb_cart(10,3)=5
orb_cart(10,4)=6
orb_cart(10,5)=10
orb_cart(10,6)=8
orb_cart(10,7)=2
orb_cart(10,8)=7
orb_cart(10,9)=9
orb_cart(10,10)=3
! For cartesian basis libcint uses d and f not normalized
if(spherical)then
norm_cart=1.0