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xstd.f90
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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/>.
!
!! ------------------------------------------------------------------------
subroutine xstd_rpamat(nci,ncent,no,nv,mxcnf,iconf,dak,dax,ed,apb,ambsqr,alphak,betaj,xyz,nao,moci,clow,alpha,beta,epsi) ! (AA|BB) only
use commonlogicals
use stdacommon
use commonlibcint
use omp_lib
implicit none
integer, intent(in) :: nci,ncent,no,nv,mxcnf,iconf(mxcnf,2)
real*8, intent(in) :: xyz(4,ncent)
real*8, intent(in) :: dak,dax,ed(mxcnf),alpha,beta
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,iwrk2,k,l,a,b,m,n,o,p,aa,bb,ia,jb
real*4 ek,ej,sdot,ak,ax,de,alphak,betaj
real*4 :: start_time,end_time,start
integer :: ino,nno,inv,nnv
integer :: nao,moci
real*8 :: clow(nao*moci)
real*4,allocatable :: Q_ia(:,:,:),P_ia(:,:,:),Q_ij(:,:),Q_ab(:,:),P_ij(:,:),AABB_integral(:,:)
real*4 :: value1,value2,value3,rabx
real*8 :: epsi(moci)
alphaK=real(alpha,4)
betaJ=real(beta,4)
write(*,*)'using on_site AO integrals'
! Read AO integrals data
allocate(AABB_integral(nao,nao))
call two_elec_int(ncent,nao,nao,AABB_integral,1,nbas,1,nbas)
write(*,*)'AO integrals read'
call cpu_time(start_time)
! 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)) ! start with no+1
nnv=maxval(iconf(1:nci,2))
write(*,*)'Q transition charges computed for occ.',ino,'to',nno
write(*,*)'and for unocc.',inv,'to',nnv
if(abs(dax).lt.1.0d-6) then
allocate(Q_ia(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
Do k=1,nao
Q_ia(i,j,k)=clow(k+(i-1)*nao)*clow(k+(j-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
allocate(P_ia(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ia(i,j,:),1,0.0,P_ia(i,j,:),1)
enddo
enddo
!$omp end do
!$omp end parallel
deallocate(AABB_integral)
else
allocate(Q_ia(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
Do k=1,nao
Q_ia(i,j,k)=clow(k+(i-1)*nao)*clow(k+(j-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
allocate(P_ia(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ia(i,j,:),1,0.0,P_ia(i,j,:),1)
enddo
enddo
!$omp end do
!$omp end parallel
allocate(Q_ij(ino*(ino+1)/2:nno*(nno+1)/2,nao),P_ij(ino*(ino+1)/2:nno*(nno+1)/2,nao))
!$omp parallel private(i,k)
!$omp do
Do i=ino, nno
Do k=ino, i
Do j=1, nao
Q_ij(lin(i,k),j)=clow(j+(i-1)*nao)*clow(j+(k-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
!$omp parallel private(i,k)
!$omp do
Do i=ino, nno
Do k=ino, nno
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ij(lin(i,k),:),1,0.0,P_ij(lin(i,k),:),1)
enddo
enddo
!$omp end do
!$omp end parallel
deallocate(Q_ij,AABB_integral)
allocate(Q_ab(inv*(inv+1)/2:nnv*(nnv+1)/2,nao))
!$omp parallel private(j,l)
!$omp do
Do j=inv,nnv
Do l=inv, j
Do i=1,nao
Q_ab(lin(j,l),i)=clow(i+(j-1)*nao)*clow(i+(l-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
endif
write(*,*)"Intermediates computed"
call cpu_time(end_time)
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
!$omp parallel private(ij,i,j,io,iv,jo,jv,iiv,iwrk,jjv,jwrk,ek,de)
!$omp do
do i=1,nci
io=iconf(i,1)
iv=iconf(i,2)
iiv=iv-no
iwrk=(io-1)*nv + iiv
do j=1,i-1
ij=lin(i,j)
jo=iconf(j,1)
jv=iconf(j,2)
jjv=jv-no
jwrk=(jo-1)*nv+jjv
ek=sdot(nao,P_ia(io,iv,:),1,Q_ia(jo,jv,:),1)
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=sdot(nao,P_ia(io,iv,:),1,Q_ia(io,iv,:),1)
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(P_ia,Q_ia)
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)
!$omp parallel private(ij,i,j,io,iv,jo,jv,iiv,iwrk,jjv,jwrk,iwrk2,ek,ej)
!$omp do
do i=1,nci
io=iconf(i,1)
iv=iconf(i,2)
iiv=iv-no
iwrk=(io-1)*nv + iiv
do j=1,i-1
ij=lin(i,j)
jo=iconf(j,1)
jv=iconf(j,2)
jjv=jv-no
jwrk=(jo-1)*nv+jjv
! ek = (ia|jb)
ek=sdot(nao,P_ia(io,iv,:),1,Q_ia(jo,jv,:),1)
! ej = (ij|ab)
ej=ax*sdot(nao,P_ij(lin(io,jo),:),1,Q_ab(lin(iv,jv),:),1)
ambsqr(ij)=2.0*ak*ek
iwrk2=(io-1)*nv+jjv
jwrk=(jo-1)*nv+iiv
! now ek = (ib|aj), results from Fock-exchange, thus we scale by ax
ek=sdot(nao,P_ia(io,jv,:),1,Q_ia(jo,iv,:),1)
ambsqr(ij)=ambsqr(ij)-ax*ek-ej
apb(ij)=ax*ek-ej
enddo ! j
ij=lin(i,i)
ek=sdot(nao,P_ia(io,iv,:),1,Q_ia(io,iv,:),1)
ej=ax*sdot(nao,P_ij(lin(io,io),:),1,Q_ab(lin(iv,iv),:),1)
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(P_ia,Q_ia,P_ij,Q_ab)
! 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 xstd_rpamat
subroutine Xstda_mat(nci,ncent,no,nv,mxcnf,iconf,dak,dax,ed,hci,alphak,betaj,xyz,nao,moci,clow,alpha,beta,epsi) ! (AA|BB) only
use commonlogicals
use stdacommon
use commonlibcint
use omp_lib
implicit none
integer, intent(in) :: nci,ncent,no,nv,mxcnf,iconf(mxcnf,2)
real*8, intent(in) :: xyz(4,ncent)
real*8, intent(in) :: dak,dax,ed(mxcnf),alpha,beta
real*4, intent(out) :: hci(nci,nci)
integer i,j,ij,io,iv,jo,jv,ierr,lin,iiv,jjv,iwrk,jwrk,iwrk2,k,l,a,b,m,n,o,p,aa,bb,ia,jb
real*4 ek,ej,sdot,ak,ax,de,alphak,betaj
real*4 :: start_time,end_time,start
integer :: ino,nno,inv,nnv
integer :: nao,moci
real*8 :: clow(nao*moci)
real*4,allocatable :: Q_ia(:,:,:),P_ia(:,:,:),Q_ij(:,:),Q_ab(:,:),P_ij(:,:),AABB_integral(:,:)
real*4 :: value1,value2,value3,rabx
real*8 :: epsi(moci)
alphaK=real(alpha,4)
betaJ=real(beta,4)
write(*,*)'using on_site AO integrals'
! Read AO integrals data
allocate(AABB_integral(nao,nao))
call two_elec_int(ncent,nao,nao,AABB_integral,1,nbas,1,nbas)
write(*,*)'AO integrals read'
call cpu_time(start_time)
! 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)) ! start with no+1
nnv=maxval(iconf(1:nci,2))
write(*,*)'Q transition charges computed for occ.',ino,'to',nno
write(*,*)'and for unocc.',inv,'to',nnv
allocate(Q_ia(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
Do k=1,nao
Q_ia(i,j,k)=clow(k+(i-1)*nao)*clow(k+(j-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
allocate(P_ia(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ia(i,j,:),1,0.0,P_ia(i,j,:),1)
enddo
enddo
!$omp end do
!$omp end parallel
allocate(Q_ij(ino*(ino+1)/2:nno*(nno+1)/2,nao),P_ij(ino*(ino+1)/2:nno*(nno+1)/2,nao))
!$omp parallel private(i,k)
!$omp do
Do i=ino, nno
Do k=ino, i
Do j=1, nao
Q_ij(lin(i,k),j)=clow(j+(i-1)*nao)*clow(j+(k-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
!$omp parallel private(i,k)
!$omp do
Do i=ino, nno
Do k=ino, nno
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ij(lin(i,k),:),1,0.0,P_ij(lin(i,k),:),1)
enddo
enddo
!$omp end do
!$omp end parallel
deallocate(Q_ij,AABB_integral)
allocate(Q_ab(inv*(inv+1)/2:nnv*(nnv+1)/2,nao))
!$omp parallel private(j,l)
!$omp do
Do j=inv,nnv
Do l=inv, j
Do i=1,nao
Q_ab(lin(j,l),i)=clow(i+(j-1)*nao)*clow(i+(l-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
write(*,*)"Intermediates computed"
call cpu_time(end_time)
print '("time = ",f12.2," minutes.")',(end_time-start_time)/60.0
ak=real(dak)
ax=real(dax)
! calculate A+B and A-B
hci=0.0e0
!$omp parallel private(i,j,io,iv,jo,jv,ek,ej,de)
!$omp do
do i=1,nci
io=iconf(i,1)
iv=iconf(i,2)
do j=1,i-1
jo=iconf(j,1)
jv=iconf(j,2)
! ek = (ia|jb)
ek=sdot(nao,P_ia(io,iv,:),1,Q_ia(jo,jv,:),1)
! ej = (ij|ab)
ej=ax*sdot(nao,P_ij(lin(io,jo),:),1,Q_ab(lin(iv,jv),:),1)
hci(i,j)=ak*ek-ej
hci(j,i)=hci(i,j)
enddo ! j
ek=sdot(nao,P_ia(io,iv,:),1,Q_ia(io,iv,:),1)
ej=ax*sdot(nao,P_ij(lin(io,io),:),1,Q_ab(lin(iv,iv),:),1)
de=real(epsi(iconf(i,2))-epsi(iconf(i,1)),4)
hci(i,i)=de+ak*ek-ej
enddo ! i
!$omp end do
!$omp end parallel
deallocate(P_ia,Q_ia,P_ij,Q_ab)
return
end subroutine Xstda_mat
subroutine two_elec_int(ncent,nbfA,nbfB,integral,start_basA,end_basA,start_basB,end_basB)
use stdacommon
use commonlibcint
use omp_lib
implicit none
integer :: i,j,k,l,start_basA,end_basA,start_basB,end_basB
integer,target :: n,m,o,p,mm,nn
integer,pointer :: ddj,ddk,ddl,dddl
logical :: extra_step
integer :: ncent,nbfA,nbfB,canon
integer :: shls(4),counter
integer, target :: di,dj,dk,dl
integer :: orb_cart(1:10,1:10)
double precision, allocatable :: buf(:,:,:,:)
real*4 :: integral(nbfA,nbfB)
double precision :: norm_cart(1:10,1:10),thresh
integer,external :: CINTcgto_cart
integer*8 :: opt
integer :: sm_di(start_basA:end_basA),sm_dj(start_basB:end_basB)
! enforce not RSH integrals, putting mu to zero
env(9)=0.0d0
!only (aa|aa) to compute
! 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=1.0d0
norm_cart(6,1)=1.0d0
norm_cart(6,2)=dsqrt(3.0d0)
norm_cart(6,3)=dsqrt(3.0d0)
norm_cart(6,4)=1.0d0
norm_cart(6,5)=dsqrt(3.0d0)
norm_cart(6,6)=1.0d0
norm_cart(10,1)=1.0d0
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)=1.0d0
norm_cart(10,8)=dsqrt(5.0d0)
norm_cart(10,9)=dsqrt(5.0d0)
norm_cart(10,10)=1.0d0
endif
integral=0.0
thresh=1.0d-7
write(*,*)"number of AO's (aa|bb)",nbfA*nbfB
!compute (ij|kl)
call cint2e_cart_optimizer(opt,atm,ncent,bas,nbas,env)
sm_di(start_basA)=0
Do i=start_basA,end_basA-1
sm_di(i+1)=sm_di(i)+di_all(i)
enddo
sm_dj(start_basB)=0
Do i=start_basB,end_basB-1
sm_dj(i+1)=sm_dj(i)+di_all(i)
enddo
!$omp parallel private(i,j,m,o,shls,di,dj,dk,dl,buf)
!$omp do
Do i=start_basA,end_basA
shls(1)=i-1 ; di=di_all(i)
shls(2)=i-1 ; dj=di_all(i)
Do j=start_basB,end_basB
shls(3)=j-1 ; dk=di_all(j)
shls(4)=j-1 ; dl=di_all(j)
allocate(buf(di,dj,dk,dl))
call cint2e_cart(buf,shls,atm,ncent,bas,nbas,env,opt)
Do m=1,di
Do o=1,dk
integral(sm_di(i)+orb_cart(di,m),sm_dj(j)+orb_cart(dk,o))&
&=real(buf(m,m,o,o)*norm_cart(di,m)*norm_cart(di,m)*norm_cart(dk,o)*norm_cart(dk,o),4)
enddo
enddo
deallocate(buf)
enddo
enddo
!$omp end do
!$omp end parallel
call CINTdel_optimizer(opt)
write(*,*)"AO's (aa|bb) done"
end subroutine two_elec_int
subroutine two_elec_int_RSH(ncent,nbfA,nbfB,integral,start_basA,end_basA,start_basB,end_basB)
use stdacommon
use commonlibcint
use omp_lib
implicit none
integer :: i,j,k,l,start_basA,end_basA,start_basB,end_basB
integer,target :: n,m,o,p,mm,nn
integer,pointer :: ddj,ddk,ddl,dddl
logical :: extra_step
integer :: ncent,nbfA,nbfB,canon
integer :: shls(4),counter
integer, target :: di,dj,dk,dl
integer :: orb_cart(1:10,1:10)
double precision, allocatable :: buf(:,:,:,:)
real*4 :: integral(nbfA,nbfB)
double precision :: norm_cart(1:10,1:10),thresh
integer,external :: CINTcgto_cart
integer*8 :: opt
integer :: sm_di(start_basA:end_basA),sm_dj(start_basB:end_basB)
! Range separated hybrid functional
env(9)=RSH
!only (aa|aa) to compute
! 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=1.0d0
norm_cart(6,1)=1.0d0
norm_cart(6,2)=dsqrt(3.0d0)
norm_cart(6,3)=dsqrt(3.0d0)
norm_cart(6,4)=1.0d0
norm_cart(6,5)=dsqrt(3.0d0)
norm_cart(6,6)=1.0d0
norm_cart(10,1)=1.0d0
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)=1.0d0
norm_cart(10,8)=dsqrt(5.0d0)
norm_cart(10,9)=dsqrt(5.0d0)
norm_cart(10,10)=1.0d0
endif
integral=0.0
thresh=1.0d-7
write(*,*)"number of AO's (aa|bb)",nbfA*nbfB
!compute (ij|kl)
call cint2e_cart_optimizer(opt,atm,ncent,bas,nbas,env)
sm_di(start_basA)=0
Do i=start_basA,end_basA-1
sm_di(i+1)=sm_di(i)+di_all(i)
enddo
sm_dj(start_basB)=0
Do i=start_basB,end_basB-1
sm_dj(i+1)=sm_dj(i)+di_all(i)
enddo
!$omp parallel private(i,j,m,o,shls,di,dj,dk,dl,buf)
!$omp do
Do i=start_basA,end_basA
shls(1)=i-1 ; di=di_all(i)
shls(2)=i-1 ; dj=di_all(i)
Do j=start_basB,end_basB
shls(3)=j-1 ; dk=di_all(j)
shls(4)=j-1 ; dl=di_all(j)
allocate(buf(di,dj,dk,dl))
call cint2e_cart(buf,shls,atm,ncent,bas,nbas,env,opt)
Do m=1,di
Do o=1,dk
integral(sm_di(i)+orb_cart(di,m),sm_dj(j)+orb_cart(dk,o))&
&=real(buf(m,m,o,o)*norm_cart(di,m)*norm_cart(di,m)*norm_cart(dk,o)*norm_cart(dk,o),4)
enddo
enddo
deallocate(buf)
enddo
enddo
!$omp end do
!$omp end parallel
call CINTdel_optimizer(opt)
write(*,*)"AO's (aa|bb) done"
end subroutine two_elec_int_RSH
subroutine two_elec_int_RSH_SR(ncent,nbfA,nbfB,integral,start_basA,end_basA,start_basB,end_basB)
use stdacommon
use commonlibcint
use omp_lib
implicit none
integer :: i,j,k,l,start_basA,end_basA,start_basB,end_basB
integer,target :: n,m,o,p,mm,nn
integer,pointer :: ddj,ddk,ddl,dddl
logical :: extra_step
integer :: ncent,nbfA,nbfB,canon
integer :: shls(4),counter
integer, target :: di,dj,dk,dl
integer :: orb_cart(1:10,1:10)
double precision, allocatable :: buf(:,:,:,:)
real*4 :: integral(nbfA,nbfB)
double precision :: norm_cart(1:10,1:10),thresh
integer,external :: CINTcgto_cart
integer*8 :: opt
integer :: sm_di(start_basA:end_basA),sm_dj(start_basB:end_basB)
! Range separated hybrid functional
env(9)=-RSH2
!only (aa|aa) to compute
! 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=1.0d0
norm_cart(6,1)=1.0d0
norm_cart(6,2)=dsqrt(3.0d0)
norm_cart(6,3)=dsqrt(3.0d0)
norm_cart(6,4)=1.0d0
norm_cart(6,5)=dsqrt(3.0d0)
norm_cart(6,6)=1.0d0
norm_cart(10,1)=1.0d0
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)=1.0d0
norm_cart(10,8)=dsqrt(5.0d0)
norm_cart(10,9)=dsqrt(5.0d0)
norm_cart(10,10)=1.0d0
endif
integral=0.0
thresh=1.0d-7
write(*,*)"number of AO's (aa|bb)",nbfA*nbfB
!compute (ij|kl)
call cint2e_cart_optimizer(opt,atm,ncent,bas,nbas,env)
sm_di(start_basA)=0
Do i=start_basA,end_basA-1
sm_di(i+1)=sm_di(i)+di_all(i)
enddo
sm_dj(start_basB)=0
Do i=start_basB,end_basB-1
sm_dj(i+1)=sm_dj(i)+di_all(i)
enddo
!$omp parallel private(i,j,m,o,shls,di,dj,dk,dl,buf)
!$omp do
Do i=start_basA,end_basA
shls(1)=i-1 ; di=di_all(i)
shls(2)=i-1 ; dj=di_all(i)
Do j=start_basB,end_basB
shls(3)=j-1 ; dk=di_all(j)
shls(4)=j-1 ; dl=di_all(j)
allocate(buf(di,dj,dk,dl))
call cint2e_cart(buf,shls,atm,ncent,bas,nbas,env,opt)
Do m=1,di
Do o=1,dk
integral(sm_di(i)+orb_cart(di,m),sm_dj(j)+orb_cart(dk,o))&
&=real(buf(m,m,o,o)*norm_cart(di,m)*norm_cart(di,m)*norm_cart(dk,o)*norm_cart(dk,o),4)
enddo
enddo
deallocate(buf)
enddo
enddo
!$omp end do
!$omp end parallel
call CINTdel_optimizer(opt)
write(*,*)"AO's (aa|bb) done"
end subroutine two_elec_int_RSH_SR
subroutine xstd_rpamat_RSH(nci,ncent,no,nv,mxcnf,iconf,dak,dax,ed,apb,ambsqr,alphak,betaj,xyz,nao,moci,clow,alpha,beta,epsi) ! (AA|BB) only
use commonlogicals
use stdacommon
use commonlibcint
use omp_lib
implicit none
integer, intent(in) :: nci,ncent,no,nv,mxcnf,iconf(mxcnf,2)
real*8, intent(in) :: xyz(4,ncent)
real*8, intent(in) :: dak,dax,ed(mxcnf),alpha,beta
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,iwrk2,k,l,a,b,m,n,o,p,aa,bb,ia,jb
real*4 ek,ej,sdot,ak,ax,de,alphak,betaj,ek_RSH
real*4 :: start_time,end_time,start
integer :: ino,nno,inv,nnv
integer :: nao,moci
real*8 :: clow(nao*moci)
real*4,allocatable :: Q_ia(:,:,:),P_ia(:,:,:),Q_ij(:,:),Q_ab(:,:),P_ij(:,:),AABB_integral(:,:),P_ia_RSH(:,:,:),P_ij_RSH(:,:)
real*4,allocatable :: P_ia_RSH_SR(:,:,:),P_ij_RSH_SR(:,:)
real*4 :: value1,value2,value3,rabx
real*8 :: epsi(moci)
alphaK=real(alpha,4)
betaJ=real(beta,4)
write(*,*)'using on_site AO integrals'
! Read AO integrals data
allocate(AABB_integral(nao,nao))
call two_elec_int(ncent,nao,nao,AABB_integral,1,nbas,1,nbas)
write(*,*)'AO integrals read'
call cpu_time(start_time)
! 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)) ! start with no+1
nnv=maxval(iconf(1:nci,2))
write(*,*)'Q transition charges computed for occ.',ino,'to',nno
write(*,*)'and for unocc.',inv,'to',nnv
allocate(Q_ia(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
Do k=1,nao
Q_ia(i,j,k)=clow(k+(i-1)*nao)*clow(k+(j-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
allocate(P_ia(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ia(i,j,:),1,0.0,P_ia(i,j,:),1)
enddo
enddo
!$omp end do
!$omp end parallel
deallocate(AABB_integral)
allocate(Q_ij(ino*(ino+1)/2:nno*(nno+1)/2,nao))
!$omp parallel private(i,k)
!$omp do
Do i=ino, nno
Do k=ino, i
Do j=1, nao
Q_ij(lin(i,k),j)=clow(j+(i-1)*nao)*clow(j+(k-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
allocate(Q_ab(inv*(inv+1)/2:nnv*(nnv+1)/2,nao))
!$omp parallel private(j,l)
!$omp do
Do j=inv,nnv
Do l=inv, j
Do i=1,nao
Q_ab(lin(j,l),i)=clow(i+(j-1)*nao)*clow(i+(l-1)*nao)
enddo
enddo
enddo
!$omp end do
!$omp end parallel
!RSH integrals short range
allocate(AABB_integral(nao,nao))
call two_elec_int_RSH_SR(ncent,nao,nao,AABB_integral,1,nbas,1,nbas)
allocate(P_ia_RSH_SR(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ia(i,j,:),1,0.0,P_ia_RSH_SR(i,j,:),1)
enddo
enddo
!$omp end do
!$omp end parallel
allocate(P_ij_RSH_SR(ino*(ino+1)/2:nno*(nno+1)/2,nao))
!$omp parallel private(i,k)
!$omp do
Do i=ino, nno
Do k=ino, nno
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ij(lin(i,k),:),1,0.0,P_ij_RSH_SR(lin(i,k),:),1)
enddo
enddo
!$omp end do
!$omp end parallel
deallocate(AABB_integral)
!RSH integrals long range
allocate(AABB_integral(nao,nao))
call two_elec_int_RSH(ncent,nao,nao,AABB_integral,1,nbas,1,nbas)
allocate(P_ia_RSH(ino:nno,inv:nnv,nao))
!$omp parallel private(i,j)
!$omp do
Do i=ino, nno
Do j=inv,nnv
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ia(i,j,:),1,0.0,P_ia_RSH(i,j,:),1)
enddo
enddo
!$omp end do
!$omp end parallel
allocate(P_ij_RSH(ino*(ino+1)/2:nno*(nno+1)/2,nao))
!$omp parallel private(i,k)
!$omp do
Do i=ino, nno
Do k=ino, nno
call sgemv('T',nao,nao,1.0,AABB_integral,nao,Q_ij(lin(i,k),:),1,0.0,P_ij_RSH(lin(i,k),:),1)
enddo
enddo
!$omp end do
!$omp end parallel
deallocate(Q_ij,AABB_integral)
write(*,*)"Intermediates computed"
call cpu_time(end_time)
print '("time = ",f12.2," minutes.")',(end_time-start_time)/60.0
ak=real(dak)
ax=real(RSH_ax,4)
! calculate A+B and A-B
apb=0.0e0
ambsqr=0.0e0
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)
!$omp parallel private(ij,i,j,io,iv,jo,jv,iiv,iwrk,jjv,jwrk,iwrk2,ek,ej)
!$omp do
do i=1,nci
io=iconf(i,1)
iv=iconf(i,2)
iiv=iv-no
iwrk=(io-1)*nv + iiv
do j=1,i-1