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sfstda.f
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! This file is part of std2.
!
! Copyright (C) 2013-2025 Stefan Grimme and 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/>.
!
!! ------------------------------------------------------------------------
! written by Marc de Wegifosse 2018-2019
SUBROUTINE sfstda(ncent,nmo,nao,xyz,c,eps,occ,csp,iaoat,thr,thrp,
. ax,alphak,betaj,fthr,nvec)
use commonlogicals
use omp_lib
IMPLICIT NONE
c input:
integer ncent,nmo,nao
integer iaoat(*)
real*8 thr,thrp,ax,othr,vthr
real*8 c(*),eps(*),occ(*),xyz(4,*)
integer csp(*)
logical ggavec,ex
c local variables:
integer :: STATUS
c l=dipole lengths, v=dipole velocity (d/dxyz), m=angular momentum
real*8, allocatable ::xla(:),yla(:),zla(:)
! real*8, allocatable ::xva(:),yva(:),zva(:)
! real*8, allocatable ::xma(:),yma(:),zma(:)
real*8, allocatable ::xlb(:),ylb(:),zlb(:)
! real*8, allocatable ::xvb(:),yvb(:),zvb(:)
! real*8, allocatable ::xmb(:),ymb(:),zmb(:)
real*8, allocatable ::help(:),scr(:),dum(:),x(:,:)
c MOs, orbital energies and CSF printout stuff
real*8, allocatable ::cca(:),epsia(:)
real*8, allocatable ::ccb(:),epsib(:)
real*8, allocatable ::umerk(:,:)
real*8, allocatable ::umrkx(:,:),umrky(:,:),umrkz(:,:)
real*8, allocatable ::rvp(:)
c stuff for diag of TDA matrix
c critical regarding memory
integer info,lwork,liwork,il,iu,nfound
real*4, allocatable ::uci (:,:)
real*4, allocatable ::eci (:)
real*4, allocatable ::hci (:,:)
real*4, allocatable ::work (:)
real*4 vu,vl
integer,allocatable ::iwork(:)
integer,allocatable::isuppz(:)
c Löwdin MOs, repulsion terms, charges and half-transformed stuff
c critical regarding memory
real*8, allocatable ::clowa(:)
real*8, allocatable ::clowb(:)
real*4, allocatable ::gamj(:,:)
! real*4, allocatable ::gamk(:,:)
! real*4, allocatable ::qiaa(:,:),qiab(:,:),piaa(:,:),piab(:,:)
real*4, allocatable ::pija(:,:),qija(:,:)
real*4, allocatable ::qabb(:,:)
real*4, allocatable ::q1a(:),q1b(:),q2(:)
! real*4 q1a(ncent),q1b(ncent),q2(ncent)
! prescreening vectors K_ia,ia
real*4 sdot
c the maximum size of the TDA expansion space
! integer maxconf1,maxconf2
! parameter (maxconf1=500000)
!c the maximum size of the TDA pt2 space
! parameter (maxconf2=maxconf1*10)
! integer kconfa(maxconf2,2)
! integer kconfb(maxconf2,2)
! real*8 edpta(maxconf2)
! real*8 edptb(maxconf2)
! maximum sizes of P-CSF and S-CSF expansion space
integer maxconfb
real*8, allocatable ::edb(:)
real*8, allocatable ::edptb(:)
integer, allocatable :: iconfb(:,:)
integer, allocatable :: kconfb(:,:)
c RPA stuff
real*4, allocatable ::apb(:)
real*4, allocatable ::ambsqr(:)
c intermediates
real*8 omax,vmin,pert,de,ek,ej,ak,xc,rabx,ef
real*8 pp,hilf,uu,sss,rl,rv,rm,time,coc(3)
real*8 fl,fv,ec,p23,xp,umax,xvu,yvu,zvu,xmu,ymu,zmu,xlu,ylu,zlu
real*8 xj,amat,xmolw,xk,loc,jii,jaa,xms,yms,zms
real*8 betaj,alphak,beta1,beta2,alpha1,alpha2,deps,fthr
integer moci,i,j,k,ii,io,iv,ihilf,jo,jv,m,l,idum1,idum2
integer*8 imem1,imem2,imem3
integer jj,kmem,imax,jmax,lmem,jmem,ij,lin,ierr
! state/orbital indices and dimensions
integer n,no,nv,noa,nob,nva,nvb,nuhf,nsomoa,nsomob
integer nexpt,nexpta,nexptb
integer nex,nexa,nexb
integer new,newa,newb
integer mocia,mocib
integer ispin,nci,nroot
! SOS polarizability and sum rule check
! real*8 alp_real(6),sumf
real*4 :: start_time, end_time, stda_time
! variables for vector printout
integer, allocatable :: vecchka(:),vecchkb(:)
integer nvec,jhomo,jhomoa,jhomob
c atomic Hubbard parameters
real*8 eta(94)
c atomic masses
common /amass/ ams(107)
real*8 ams
character*79 dummy
c For the computation of <S**2>
real*8, allocatable :: i_alpha_j_beta(:,:)
real*8, allocatable :: i_alpha_a_beta(:,:)
real*8 :: sum_ij,S2_UHF
real*8, allocatable :: Xia(:),Xiaib(:),Xiaka(:)
real*8, allocatable :: S2(:)
integer kk
c just a printout
call header('s T D A',0)
call cpu_time(start_time)
thr =thr /27.211385050d0
c estimate the orbital energy window which corresponds to the desired
c spectra range thr
deps=(1.+0.8*ax)*thr
c make it safe
deps=deps*2.0
omax=-1d+42
vmin= 1d+42
do i=1,nmo
if(occ(i).gt.0.99.and.eps(i).gt.omax) omax=eps(i)
if(occ(i).lt.0.01.and.eps(i).lt.vmin) vmin=eps(i)
enddo
! optional: if eigenvectors are wanted in TM format, check now how many occupied there are in general
! this is needed to get the CSF sorting of TM
jhomo=0
jhomoa=0
jhomob=0
do i=1,nmo
if(occ(i).gt.0.990d0) then
jhomo=jhomo+1
if(csp(i).eq.1) jhomoa = jhomoa + 1
if(csp(i).eq.2) jhomob = jhomob + 1
endif
enddo
nuhf=jhomoa-jhomob
othr=vmin-deps
vthr=deps+omax
write(*,*)'spectral range up to (eV) : ', thr*27.211385050d0
write(*,*)'occ MO cut-off (eV) : ', othr*27.211385050d0
write(*,*)'virtMO cut-off (eV) : ', vthr*27.211385050d0
write(*,*)'perturbation thr : ', thrp
if(fthr.lt.1.79d308) then
write(*,*)'max. CSF selection range (eV) : ', fthr
fthr = fthr /27.211385050d0
endif
mocia = 0
mocib = 0
do i = 1,nmo
if(eps(i).gt.othr.and.eps(i).lt.vthr) then
if(csp(i).eq.1) mocia = mocia + 1
if(csp(i).eq.2) mocib = mocib + 1
endif
enddo
moci = mocia + mocib
allocate(xla(mocia*(mocia+1)/2),yla(mocia*(mocia+1)/2),
. zla(mocia*(mocia+1)/2),
. xlb(mocib*(mocib+1)/2),ylb(mocib*(mocib+1)/2),
. zlb(mocib*(mocib+1)/2),help(nao*(nao+1)/2),
. clowa(nao*mocia),clowb(nao*mocib),
. scr(nao*nao),dum(nao*nao),x(nao,nao),
. gamj(ncent,ncent),
. cca(nao*mocia),epsia(mocia),
. ccb(nao*mocib),epsib(mocib)
. )
write(*,*) 'Active space MOs in TDA : ',moci,mocia,mocib
mocia=0
mocib=0
moci =0
do i = 1,nmo
if(occ(i).gt.0.99.and.eps(i).gt.othr)then
moci = moci + 1
if(csp(i).eq.1) then
mocia = mocia + 1
do j=1,nao
cca(j+(mocia-1)*nao)=c(j+(i-1)*nao)
enddo
epsia(mocia)=eps(i)
endif
if(csp(i).eq.2) then
mocib = mocib + 1
do j=1,nao
ccb(j+(mocib-1)*nao)=c(j+(i-1)*nao)
enddo
epsib(mocib)=eps(i)
endif
endif
enddo
no = moci
noa = mocia
nob = mocib
do i = 1,nmo
if(occ(i).lt.0.01.and.eps(i).lt.vthr)then
moci=moci+1
if(csp(i).eq.1) then
mocia = mocia + 1
do j=1,nao
cca(j+(mocia-1)*nao)=c(j+(i-1)*nao)
enddo
epsia(mocia)=eps(i)
endif
if(csp(i).eq.2) then
mocib = mocib + 1
do j=1,nao
ccb(j+(mocib-1)*nao)=c(j+(i-1)*nao)
enddo
epsib(mocib)=eps(i)
endif
endif
enddo
nv = moci - no
nva = mocia - noa
nvb = mocib - nob
write(*,*) 'Occupied active MOs in TDA: ', no,noa,nob
if(noa<=nob)then
write(*,*)'warning number of alpha < beta'
write(*,*)'only with alpha > beta'
call exit(status)
endif
write(*,*) 'Virtual active MOs in TDA: ', nv,nva,nvb
if((noa.eq.0.or.nva.eq.0).and.(nob.eq.0.or.nvb.eq.0)) then
stop 'no CSF, increase energy threshold (-e option)'
endif
! SPIN-FLIP i_alpha -> b_beta
maxconfb=noa*nvb
allocate(edb(maxconfb),edptb(maxconfb), stat=ierr)
if(ierr.ne.0)stop 'allocation failed for ed and edpt'
allocate(iconfb(maxconfb,2),kconfb(maxconfb,2), stat=ierr)
if(ierr.ne.0)stop 'allocation failed for iconf and kconf'
edb=0.0d0
edptb=0.0d0
iconfb=0
kconfb=0
c we arrange MOS according to energy from 1:HOMO to LUMO:MOCI
c (in TM they come in irreps)
write(*,*) 'Sorting MOs ...'
c sort for E diag
call sort_vec(mocia,nao,cca,epsia)
call sort_vec(mocib,nao,ccb,epsib)
write(*,*) 'Reading and transforming R..V..L AO ints ...'
c read L,V,M with xyz components each and transform
c to MO basis (original but sorted MOs in array ca)
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
c
c dipole lengths
c
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
open(unit=31,file='xlint',form='unformatted',status='old')
read(31) help
call onetri(1,help,dum,scr,cca,nao,mocia)
call shrink(mocia,dum,xla)
call onetri(1,help,dum,scr,ccb,nao,mocib)
call shrink(mocib,dum,xlb)
close(31,status='delete')
open(unit=32,file='ylint',form='unformatted',status='old')
read(32) help
call onetri(1,help,dum,scr,cca,nao,mocia)
call shrink(mocia,dum,yla)
call onetri(1,help,dum,scr,ccb,nao,mocib)
call shrink(mocib,dum,ylb)
close(32,status='delete')
open(unit=33,file='zlint',form='unformatted',status='old')
read(33) help
call onetri(1,help,dum,scr,cca,nao,mocia)
call shrink(mocia,dum,zla)
call onetri(1,help,dum,scr,ccb,nao,mocib)
call shrink(mocib,dum,zlb)
close(33,status='delete')
!
!
! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
! c
! c magnetic dipole
! c
! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
!
open(unit=34,file='xmint',form='unformatted',status='old')
! read(34) help
! call onetri(-1,help,dum,scr,cca,nao,mocia)
! call shrink(mocia,dum,xma)
! call onetri(-1,help,dum,scr,ccb,nao,mocib)
! call shrink(mocib,dum,xmb)
close(34,status='delete')
!
open(unit=35,file='ymint',form='unformatted',status='old')
! read(35) help
! call onetri(-1,help,dum,scr,cca,nao,mocia)
! call shrink(mocia,dum,yma)
! call onetri(-1,help,dum,scr,ccb,nao,mocib)
! call shrink(mocib,dum,ymb)
close(35,status='delete')
!
open(unit=36,file='zmint',form='unformatted',status='old')
! read(36) help
! call onetri(-1,help,dum,scr,cca,nao,mocia)
! call shrink(mocia,dum,zma)
! call onetri(-1,help,dum,scr,ccb,nao,mocib)
! call shrink(mocib,dum,zmb)
close(36,status='delete')
!
! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
! c
! c velocity dipole
! c
! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
!
open(unit=37,file='xvint',form='unformatted',status='old')
! read(37) help
! call onetri(-1,help,dum,scr,cca,nao,mocia)
! call shrink(mocia,dum,xva)
! call onetri(-1,help,dum,scr,ccb,nao,mocib)
! call shrink(mocib,dum,xvb)
close(37,status='delete')
!
open(unit=38,file='yvint',form='unformatted',status='old')
! read(38) help
! call onetri(-1,help,dum,scr,cca,nao,mocia)
! call shrink(mocia,dum,yva)
! call onetri(-1,help,dum,scr,ccb,nao,mocib)
! call shrink(mocib,dum,yvb)
close(38,status='delete')
!
open(unit=39,file='zvint',form='unformatted',status='old')
! read(39) help
! call onetri(-1,help,dum,scr,cca,nao,mocia)
! call shrink(mocia,dum,zva)
! call onetri(-1,help,dum,scr,ccb,nao,mocib)
! call shrink(mocib,dum,zvb)
close(39,status='delete')
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
c calc S^1/2 and q(GS)
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
open(unit=40,file='sint',form='unformatted',status='old')
read(40) help
write(*,*) 'ints done.'
close(40,status='delete')
write(*,*) 'S^1/2 ...'
call makel(nao,help,x)
call dgemm('n','n',nao,mocia,nao,1.d0,x,nao,cca,nao,0.d0,scr,nao)
do i=1,mocia
sss=0
do j=1,nao
sss = sss+scr(j+(i-1)*nao)**2
clowa(j+(i-1)*nao) = scr(j+(i-1)*nao)
enddo
if(abs(sss-1.).gt.1.d-2)then
write(*,*) 'alpha MO norm ',i,sss
stop 'internal MO norm error'
endif
enddo
call dgemm('n','n',nao,mocib,nao,1.d0,x,nao,ccb,nao,0.d0,scr,nao)
do i=1,mocib
sss=0
do j=1,nao
sss = sss+scr(j+(i-1)*nao)**2
clowb(j+(i-1)*nao) = scr(j+(i-1)*nao)
enddo
if(abs(sss-1.0d0).gt.1.d-2)then
write(*,*) 'beta MO norm ',i,sss
stop 'internal MO norm error'
endif
enddo
write(*,*) 'S^1/2 orthogonalized MO coefficients done.'
if(sf_s2)then
! for the computation of <S**2>
allocate(i_alpha_j_beta(noa,nob))
i_alpha_j_beta=0.0
sum_ij=0.0
do i=1,noa
do j=1,nob
do k=1,nao
i_alpha_j_beta(i,j)=i_alpha_j_beta(i,j)+
. clowa(k+(i-1)*nao)*clowb(k+(j-1)*nao)
enddo
sum_ij=sum_ij+i_alpha_j_beta(i,j)**2.0
enddo
enddo
S2_UHF=(noa-nob)/2.0*((noa-nob)/2.0+1.0)+nob-sum_ij
write(*,*) 'Unrestricted ground state <S**2>=',S2_UHF
allocate(i_alpha_a_beta(noa,nvb))
i_alpha_a_beta=0.0
do i=1,noa
do j=1,nvb
do k=1,nao
i_alpha_a_beta(i,j)=i_alpha_a_beta(i,j)+
. clowa(k+(i-1)*nao)*clowb(k+(j+nob-1)*nao)
enddo
enddo
enddo
endif
deallocate(scr,dum,help,x)
call cpu_time(time)
allocate(q1a(ncent),q1b(ncent),q2(ncent))
q1a=0.0
q1b=0.0
q2=0.0
allocate(qija(ncent,noa),
. qabb(ncent,nvb),stat=ierr)
if(ierr.ne.0) stop 'error in diag. J charges allocation'
qija=0.0
qabb=0.0
do i=1,noa
call lo12pop(i,i,ncent,nao,iaoat,clowa,q2)
q1a(1:ncent)=q1a(1:ncent)+q2(1:ncent)
qija(1:ncent,i)=q2(1:ncent)
enddo
! write(*,'(/'' SCF atom population (using active MOs):'')')
! write(*,'(10F7.3)') q1a(1:ncent)
! write(*,'(10F7.3)') q1b(1:ncent)
! write(*,'(10F7.3)') (q1a(1:ncent)+q1b(1:ncent))
! write(*,*)
! write(*,'('' # of alpha and beta electrons in TDA:'',2F8.3)')
! .sum(q1a(1:ncent)),sum(q1b(1:ncent))
! write(*,*)
do i=nob+1,mocib
j=i-nob
call lo12pop(i,i,ncent,nao,iaoat,clowb,q2)
qabb(1:ncent,j)=q2(1:ncent)
enddo
c UCIS scaling factor for K(ia|jb):
ak = 1.0d0
c the global parameters of the method:
beta1 = 0.3
beta2 = 1.0
if(betaj.lt.-99.0d0) then ! if no beta parameter was read in
betaj=beta1+beta2*ax
endif
write(*,*)
write(*,*) 'ax(DF) : ',ax
write(*,*) 's^K : ',ak
write(*,*) 'beta (J): ',betaj
write(*,*)
c set the hardness table
call setrep(eta)
write(*,*) 'hardness table read.'
write(*,*) 'setting up gammas ...'
c compute gamma(j)
xmolw=0
do i = 1,ncent
ii = idint(xyz(4,i))
c ams is the atomic mass (mol weight for output file)
xmolw = xmolw+ams(ii)
do j=1,i
jj = idint(xyz(4,j))
xj = 0.50d0*(eta(ii)+eta(jj)) * (ax+ax*0.4) !!!!!!!!!!!!!!!!!!!!!! SF this seems resonable
rabx = dsqrt((xyz(1,i)-xyz(1,j))**2
. +(xyz(2,i)-xyz(2,j))**2
. +(xyz(3,i)-xyz(3,j))**2)
gamj(j,i)=real(1./(rabx**betaj+1./xj**betaj)**(1.0d0/betaj))
gamj(i,j) = gamj(j,i)
enddo
enddo
! ! compute intermediates q's refer to charges, p's to gam*q (i.e., contracted)
! imem1=noa
! imem2=nva
! imem3=(noa*nva+nob*nvb)*2
! imem1=noa*(noa+1)/2+nob*(nob+1)/2
! imem2=nva*(nva+1)/2+nvb*(nvb+1)/2
! imem3=imem3+imem1+imem2
! hilf=dble(imem3)/1024.0**2
! hilf=dble(4*ncent)*hilf
! imem1=idint(hilf)
! write(*,*)'memory needed for qa and qb data (Mb) ',imem1
! write(*,*)'computing q(ij,n) ...'
! first alpha part
! Coulomb type terms: calc qij*gam^J
allocate(pija(ncent,noa), stat=ierr)
if(ierr.ne.0)stop 'allocation failed for (ii| intermediate'
pija=0.0
call ssymm('l','l',ncent,noa,1.0,gamj,ncent,qija,ncent,0.0,pija
. ,ncent)
allocate(uci(nvb,noa), stat=ierr)
if(ierr.ne.0)stop 'allocation failed for (ii|aa) matrix'
uci=0.0
! now calc (ii|aa)^J SPIN-FLIP (alpha|beta)
call sgemm('t','n',nvb,noa,ncent,1.0,qabb,ncent,pija,ncent,0.0,
. uci,nvb)
deallocate(pija)
nex=noa*nvb
c determine singles which are lower than thr using A(ia,ia) !! SPIN-FLIP
k=0
j=0
l=0
nsomoa=noa+nuhf
do io=1,noa
do iv=nob+1,mocib
c compute A(ia,ia) = eps(a)-eps(i) - (ii|aa) (alpha,beta)
de=epsib(iv)-epsia(io)
l=iv-nob
ej=0.0d0
ej=dble(uci(l,io))
de=de-ej
c the primary ones
if(de.le.thr)then
k=k+1
iconfb(k,1)=io
iconfb(k,2)=iv
edb(k)=de
endif
c for PT
if(de.gt.thr.and.de.lt.fthr)then ! needs to be on if fthr is specified
j=j+1
kconfb(j,1)=io
kconfb(j,2)=iv
edptb(j)=de
endif
enddo
enddo
nexb=k
nexptb=j
deallocate(uci)
nex = nexb
nexpt = nexptb
write(*,*)
write(*,*) '# CSF included by energy:',nex
write(*,*)
write(*,*) '# CSF considered in PT2:',nexpt
c errors and warning
if(nex.lt.1) stop 'No CSF, increase energy threshold (-e option)'
! if(nexa.eq.maxconf1.or.nexb.eq.maxconf1)
! . stop 'Primary CSF space exceeded. use -e option!'
! if(nexpta.eq.maxconf2.or.nexptb.eq.maxconf2)
! . write(*,*)'CSF PT2 space exceeded. try -p option!'
c sort for E diag in each spin manifold
do 142 ii = 2,nexb
i = ii - 1
k = i
pp= edb(i)
do 122 j = ii, nexb
if (edb(j) .ge. pp) go to 122
k = j
pp=edb(j)
122 continue
if (k .eq. i) go to 142
edb(k) = edb(i)
edb(i) = pp
do m=1,2
ihilf=iconfb(i,m)
iconfb(i,m)=iconfb(k,m)
iconfb(k,m)=ihilf
enddo
142 continue
c just printout
write(*,*) ' '
write(*,*)'Ordered frontier alpha orbitals:'
write(*,*)' eV'
j=max(1,noa-10)
do i=j,noa
write(*,'(i4,F10.3,F8.1)') i,epsia(i)*27.21139
enddo
write(*,*)'Unoccupied:'
j=min(mocia,noa+11)
do i=noa+1,j
write(*,'(i4,F10.3,F8.1)') i,epsia(i)*27.21139
enddo
write(*,*) ' '
write(*,*)'Ordered frontier beta orbitals:'
write(*,*)' eV'
j=max(1,nob-10)
do i=j,nob
write(*,'(i4,F10.3,F8.1)') i,epsib(i)*27.21139
enddo
write(*,*)'Unoccupied:'
j=min(mocib,nob+11)
do i=nob+1,j
write(*,'(i4,F10.3,F8.1)') i,epsib(i)*27.21139
enddo
write(*,*)
write(*,*)' Lowest CSF states:'
write(*,*)' Alpha to Beta Excitations:'
write(*,*)' eV nm excitation i->a eV'
do i=1,min(nexb,25)
io=iconfb(i,1)
iv=iconfb(i,2)
q1a(1:ncent)=qija(1:ncent,io)
call ssymv('l',ncent,1.0e0,gamj,ncent,q1a,1,0.0,q2,1)
jii=sdot(ncent,q1a,1,q2,1)
k=iv-nob
q1b(1:ncent)=qabb(1:ncent,k)
ej=sdot(ncent,q1b,1,q2,1)
call ssymv('l',ncent,1.0e0,gamj,ncent,q1b,1,0.0,q2,1)
jaa=sdot(ncent,q1b,1,q2,1)
! de is now the Kia shift
de=0
loc=ej/sqrt(jii*jaa) ! locality
write(*,16) i,27.211*edb(i),
. 1.d+7/(edb(i)*2.19474625d+5),iconfb(i,1:2),
. 27.211*(epsib(iv)-epsia(io)),27.211*ej,27.211*de,loc
enddo
deallocate(qija,qabb)
!!! now set up pij -alpha first
ihilf=noa*(noa+1)/2
allocate(qija(ncent,ihilf),stat=ierr)
if(ierr.ne.0) stop 'error in qij allocation'
qija=0.0
ij=0
!$omp parallel private(i,j,ij,q2)
!$omp do
do i=1,noa
do j=1,i
ij=lin(i,j)
call lo12pop(i,j,ncent,nao,iaoat,clowa,q2)
qija(1:ncent,ij)=q2(1:ncent)
enddo
enddo
!$omp end do
!$omp end parallel
allocate(pija(ncent,ihilf), stat=ierr)
if(ierr.ne.0)stop 'allocation failed for (ij| intermediate'
pija=0.0
call ssymm('l','l',ncent,ihilf,1.0,gamj,ncent,qija,ncent,0.0
. ,pija,ncent)
deallocate(qija,gamj)
if(XsTD.eqv..false.)then
deallocate(clowa)
endif
!!! now beta part of qab !!!
q2=0.0
ihilf=nvb*(nvb+1)/2
allocate(qabb(ncent,ihilf),stat=ierr)
if(ierr.ne.0) stop 'error in qab allocation'
ij=0
!$omp parallel private(i,j,l,k,ij,q2)
!$omp do
do i=nob+1,mocib
do j=nob+1,i
k=i-nob
l=j-nob
ij=lin(k,l)
call lo12pop(i,j,ncent,nao,iaoat,clowb,q2)
qabb(1:ncent,ij)=q2(1:ncent)
enddo
enddo
!$omp end do
!$omp end parallel
if(XsTD.eqv..false.)then
deallocate(clowb)
endif
!!!!!PTselect, for spin-flip!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
write(*,*)
write(*,*)'selecting CSF ...'
c determine singles which interact most strongly with all basis
c CSF which have been selected by the diagonal element A(ia,ia)
deallocate(q1a,q1b,q2)
call sf_ptselect_uks(nexb,ncent,noa,nva,nob,nvb,nexptb,
. maxconfb,iconfb,kconfb,
. ak,ax,edb,edptb,
. pija,qabb,thrp,newb)
deallocate(edptb,kconfb)
new = newb
c nroot at this point is the number of primary CSF. The
c number of roots in the range 0-thr (as desired) is not
c known but will be determined by the diag routine.
nroot = nex
write(*,*) 'CSF included by PT:',new
nexb = nexb + newb
nex= nexb
!!!!!PTselect, for spin-flip!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
nci = nex
write(*,*) 'CSF in total:',nex
cccccccccccccccccccccccccccc
c c
c Standard TDA procedure c
c c
cccccccccccccccccccccccccccc
c allocate the TDA matrix
allocate(hci(nci,nci),stat=ierr)
if(ierr.ne.0) stop 'allocation failed for TDA matrix'
********************************************************************************
c set the TDA matrix up *
write(*,*)'calculating TDA matrix ...'
********************************************************************************
if(XsTD)then
call SF_Xstda_mat(nci,nexb,ncent,noa,nva,nob,nvb,maxconfb,iconfb,
.ax,edb,hci,betaj,xyz,nao,mocia,mocib,clowa,clowb,epsia,epsib)
else
call sfstdamat(nci,nexb,ncent,noa,nob,nvb,
. maxconfb,iconfb,ax,edb,
. pija,qabb,hci)
endif
********************************************************************************
c big arrays not needed anymore
deallocate(pija,qabb,edb)
c Diagonalize hci (A-matrix)
write(*,*) 'Diagonalizing ...'
write(*,'('' estimated time (min) '',f8.2)')
. float(nci)**2*float(nroot)/8.d+8/60.
c if LAPACK does not work
c allocate(eci(nci),uci(nci,nroot),
c . stat=ierr)
c call sHQRII(hci,nci,nroot,eci,uci)
c faster by a factor of 2-3
lwork =26*nci
liwork=10*nci
c we allocate uci with nci (and not with nroot) as safe
c choice (other values gave segfaults)
nroot=min(nci,int(1.5*nroot))
allocate(eci(nci),uci(nci,nci),work(lwork),
. iwork(liwork),isuppz(nci),stat=ierr)
if(ierr.ne.0)stop 'allocation failed for TDA matrix diag'
vl=-10.0
vu=thr
call ssyevr('V','V','U',nci,hci,nci,vl,vu,il,iu,1.e-6,
. nfound,eci,uci,nci,isuppz,
. work,lwork,iwork,liwork,info)
nroot=nfound
if(nfound.lt.1) stop 'internal error in diag'
if(sf_s2)then
! Compute <S**2> for each SF states
allocate(Xia(nroot),Xiaib(nroot),Xiaka(nroot),S2(nroot))
Xia=0.0
Xiaib=0.0
Xiaka=0.0
Do i=1,nroot
!X_iAaB <iA aB>
Do j=1,nci
Xia(i)=Xia(i)+dble(uci(j,i))*
. i_alpha_a_beta(iconfb(j,1),iconfb(j,2)-nob)
enddo
Xia(i)=Xia(i)**2.0
!XjAaB XjAbB <iA aB><iA bB>
Do j=1,nci
Do kk=1,nci
if(iconfb(kk,1)==iconfb(j,1))then
Do k=1,noa
Xiaib(i)=Xiaib(i)+dble(uci(j,i))*dble(uci(kk,i))*
. i_alpha_a_beta(k,iconfb(j,2)-nob)*
. i_alpha_a_beta(k,iconfb(kk,2)-nob)
enddo
endif
enddo
enddo
!XiAaB XkAbB <iA jB><jA kB>
Do j=1,nci
Do kk=1,nci
if(iconfb(kk,2)==iconfb(j,2))then
Do k=1,nob
Xiaka(i)=Xiaka(i)+dble(uci(j,i))*dble(uci(kk,i))*
. i_alpha_j_beta(iconfb(j,1),k)*
. i_alpha_j_beta(iconfb(kk,1),k)
enddo
endif
enddo
enddo
S2(i)=nob+1-sum_ij-Xiaib(i)+Xiaka(i)+Xia(i)+
. 0.25*(noa-nob-2)*(noa-nob)
enddo
deallocate(Xia,Xiaib,Xiaka,i_alpha_j_beta,i_alpha_a_beta)
endif
write(*,'(i5,'' SF-roots found, lowest/highest eigenvalue : '',
.2F8.3,i4)') nroot,eci(1)*27.21139,eci(nroot)*27.21139,info
if(info.gt.0) stop 'diag error (ssyevr)'
allocate(umerk(14,nroot))
! largest configurations
Do i=1,nroot
umax=-1
kmem=1
! first largest
do j=1,nci
io=iconfb(j,1)
iv=iconfb(j,2)
idum1=max(io,iv)
idum2=min(io,iv)
ij=idum2+idum1*(idum1-1)/2
uu=dble(uci(j,i))
pp=dble(uci(j,i))
if(dabs(uu*pp).gt.umax)then
umax=uu*pp
imax=io
jmax=iv
kmem=j
endif
enddo
umerk(1,i)=imax
umerk(2,i)=jmax
umerk(3,i)=dble(uci(kmem,i))
! second largest
umax=-1
lmem=1
do j=1,nci
uu=dble(uci(j,i))
pp=dble(uci(j,i))
if((uu*pp).gt.umax.and.j.ne.kmem)then
umax=uu*pp
imax=iconfb(j,1)
jmax=iconfb(j,2)
lmem=j
endif
enddo
umerk(4,i)=imax
umerk(5,i)=jmax
umerk(6,i)=dble(uci(lmem,i))
! third largest
umax=-1
jmem=-1
do j=1,nci
uu=dble(uci(j,i))
pp=dble(uci(j,i))
if((uu*pp).gt.umax.and.j.ne.kmem.and.j.ne.lmem)then
umax=uu*pp
imax=iconfb(j,1)
jmax=iconfb(j,2)
jmem=j
endif
enddo
umerk(7,i)=imax
umerk(8,i)=jmax
umerk(9,i)=dble(uci(jmem,i))
enddo
20 format(i5,2f9.5,3(' ',i4,'(a) ->',i4,'(b) ',F6.2),f9.5)
21 format(i5,2f9.5,3(' ',i4,'(a) ->',i4,'(b) ',F6.2))
write(*,*)'SF states:'
if(sf_s2)then
Do i=1, nroot
write(*,20)i,eci(i),eci(i)*27.21139,
.int(umerk(1:2,i)),umerk(3,i),
.int(umerk(4:5,i)),umerk(6,i),
.int(umerk(7:8,i)),umerk(9,i),S2(i)
enddo
else
Do i=1, nroot
write(*,21)i,eci(i),eci(i)*27.21139,
.int(umerk(1:2,i)),umerk(3,i),
.int(umerk(4:5,i)),umerk(6,i),
.int(umerk(7:8,i)),umerk(9,i)
enddo
endif
call sf_lresp_ESA(nci,iconfb,maxconfb,xla,yla,zla,mocia,
. xlb,ylb,zlb,mocib,
. noa,nva,nob,nvb,eci,uci,nroot,xmolw,thr)
if(nto)then
call SFprint_nto(uci,cca,mocia,nci,nroot,nao,
. noa,nva,ccb,mocib,iconfb,
. maxconfb,nob,nvb)
endif
deallocate(hci)
11 format(i5,f9.3,f8.1,2f11.4)
12 format(i5,f6.2,f8.1, 5x,i4,' ->',i4,5x,'gap,J,K:',3f8.3,
. 3x,'Kshft:',f8.3)
13 format( 41x,f8.3,13x,f8.3)
14 format(3x,F6.2,'(',i4,'a','->',i4,'a',')')
15 format(3x,F6.2,'(',i4,'b','->',i4,'b',')')
16 format(i5,f6.2,f8.1, 5x,i4,' ->',i4,5x,'gap,J:',2f8.3,
. 3x,'Kshft:',f8.3,2x,'locality:',f6.3)
call cpu_time(end_time)
print '("sTD-DFT Time = ",f12.2," minutes.")'
. ,(end_time-stda_time)/60.0
write(*,*) 'SF-sTDA done.'
call EXIT(STATUS)
return
end SUBROUTINE sfstda
subroutine sfstdamat(nci,nexb,ncent,noa,nob,nvb,
. mxcnfb,iconfb,dax,edb,
. pija,qabb,hci)
use omp_lib
implicit none
integer, intent(in) :: nci,nexb,ncent,noa,nob,nvb
integer, intent(in) :: mxcnfb,iconfb(mxcnfb,2)
real*4, intent(in) :: pija(ncent,noa*(noa+1)/2)
real*4, intent(in) :: qabb(ncent,nvb*(nvb+1)/2)
real*4, intent(out) :: hci(nci,nci)
real*8, intent(in) :: dax,edb(mxcnfb)
real*4, allocatable :: qj(:)
integer i,j,ij,io,iv,jo,jv,ierr,lin,k,iiv,jjv,iwrk,jwrk
real*4 ek,ej,sdot,ax,de
allocate(qj(ncent), stat=ierr)
if(ierr.ne.0)stop 'allocation for qk crashed'
! calculate CIS matrix A
hci=0.0e0
ax=real(dax)