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mirror of https://github.com/pfloos/quack synced 2024-12-22 20:34:46 +01:00

SRG-qsUGW

This commit is contained in:
Pierre-Francois Loos 2023-12-26 19:54:04 +01:00
parent 39edb33dcb
commit e691860b7d
5 changed files with 594 additions and 23 deletions

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@ -100,9 +100,9 @@ subroutine SRG_qsGW(dotest,maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,
! Hello world
write(*,*)
write(*,*)'************************************************'
write(*,*)'| Self-consistent SRG-qsGW calculation |'
write(*,*)'************************************************'
write(*,*)'***********************************'
write(*,*)'* Restricted SRG-qsGW Calculation *'
write(*,*)'***********************************'
write(*,*)
! Warning

425
src/GW/SRG_qsUGW.f90 Normal file
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@ -0,0 +1,425 @@
subroutine SRG_qsUGW(dotest,maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,BSE,TDA_W,TDA,dBSE,dTDA,spin_conserved,spin_flip, &
eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nC,nO,nV,nR,nS,EUHF,S,X,T,V,Hc,ERI_AO,ERI_aaaa,ERI_aabb,ERI_bbbb, &
dipole_int_AO,dipole_int_aa,dipole_int_bb,PHF,cHF,eHF)
! Perform a quasiparticle self-consistent GW calculation
implicit none
include 'parameters.h'
! Input variables
logical,intent(in) :: dotest
integer,intent(in) :: maxSCF
integer,intent(in) :: max_diis
double precision,intent(in) :: thresh
logical,intent(in) :: doACFDT
logical,intent(in) :: exchange_kernel
logical,intent(in) :: doXBS
logical,intent(in) :: BSE
logical,intent(in) :: TDA_W
logical,intent(in) :: TDA
logical,intent(in) :: dBSE
logical,intent(in) :: dTDA
logical,intent(in) :: spin_conserved
logical,intent(in) :: spin_flip
double precision,intent(in) :: eta
logical,intent(in) :: regularize
integer,intent(in) :: nNuc
double precision,intent(in) :: ZNuc(nNuc)
double precision,intent(in) :: rNuc(nNuc,ncart)
double precision,intent(in) :: ENuc
integer,intent(in) :: nBas
integer,intent(in) :: nC(nspin)
integer,intent(in) :: nO(nspin)
integer,intent(in) :: nV(nspin)
integer,intent(in) :: nR(nspin)
integer,intent(in) :: nS(nspin)
double precision,intent(in) :: EUHF
double precision,intent(in) :: eHF(nBas,nspin)
double precision,intent(in) :: cHF(nBas,nBas,nspin)
double precision,intent(in) :: PHF(nBas,nBas,nspin)
double precision,intent(in) :: S(nBas,nBas)
double precision,intent(in) :: T(nBas,nBas)
double precision,intent(in) :: V(nBas,nBas)
double precision,intent(in) :: Hc(nBas,nBas)
double precision,intent(in) :: X(nBas,nBas)
double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_aaaa(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_aabb(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_bbbb(nBas,nBas,nBas,nBas)
double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart)
double precision,intent(inout):: dipole_int_aa(nBas,nBas,ncart)
double precision,intent(inout):: dipole_int_bb(nBas,nBas,ncart)
! Local variables
logical :: dRPA
integer :: nSCF
integer :: nBasSq
integer :: ispin
integer :: ixyz
integer :: is
integer :: n_diis
integer :: nSa,nSb,nSt
double precision :: dipole(ncart)
double precision :: ET(nspin)
double precision :: EV(nspin)
double precision :: EJ(nsp)
double precision :: EK(nspin)
double precision :: EcRPA(nspin)
double precision :: EcGM(nspin)
double precision :: EqsGW
double precision :: EcBSE(nspin)
double precision :: Conv
double precision :: rcond(nspin)
double precision,external :: trace_matrix
double precision,allocatable :: err_diis(:,:,:)
double precision,allocatable :: F_diis(:,:,:)
double precision,allocatable :: Aph(:,:)
double precision,allocatable :: Bph(:,:)
double precision,allocatable :: Om(:)
double precision,allocatable :: XpY(:,:)
double precision,allocatable :: XmY(:,:)
double precision,allocatable :: rho(:,:,:,:)
double precision,allocatable :: c(:,:,:)
double precision,allocatable :: cp(:,:,:)
double precision,allocatable :: eGW(:,:)
double precision,allocatable :: P(:,:,:)
double precision,allocatable :: F(:,:,:)
double precision,allocatable :: Fp(:,:,:)
double precision,allocatable :: J(:,:,:)
double precision,allocatable :: K(:,:,:)
double precision,allocatable :: SigC(:,:,:)
double precision,allocatable :: SigCp(:,:,:)
double precision,allocatable :: Z(:,:)
double precision,allocatable :: err(:,:,:)
! Hello world
write(*,*)
write(*,*)'*************************************'
write(*,*)'* Unrestricted SRG-qsGW Calculation *'
write(*,*)'*************************************'
write(*,*)
! Warning
write(*,*) '!! ERIs in MO basis will be overwritten in qsUGW !!'
write(*,*)
! Stuff
nBasSq = nBas*nBas
dRPA = .true.
! TDA for W
if(TDA_W) then
write(*,*) 'Tamm-Dancoff approximation for dynamic screening!'
write(*,*)
end if
! TDA
if(TDA) then
write(*,*) 'Tamm-Dancoff approximation activated!'
write(*,*)
end if
! Memory allocation
nSa = nS(1)
nSb = nS(2)
nSt = nSa + nSb
allocate(Aph(nSt,nSt),Bph(nSt,nSt),eGW(nBas,nspin),c(nBas,nBas,nspin),cp(nBas,nBas,nspin),P(nBas,nBas,nspin), &
F(nBas,nBas,nspin),Fp(nBas,nBas,nspin),J(nBas,nBas,nspin),K(nBas,nBas,nspin), &
SigC(nBas,nBas,nspin),SigCp(nBas,nBas,nspin),Z(nBas,nspin),Om(nSt),XpY(nSt,nSt),XmY(nSt,nSt), &
rho(nBas,nBas,nSt,nspin),err(nBas,nBas,nspin),err_diis(nBasSq,max_diis,nspin),F_diis(nBasSq,max_diis,nspin))
! Initialization
nSCF = -1
n_diis = 0
ispin = 1
Conv = 1d0
P(:,:,:) = PHF(:,:,:)
eGW(:,:) = eHF(:,:)
c(:,:,:) = cHF(:,:,:)
F_diis(:,:,:) = 0d0
err_diis(:,:,:) = 0d0
rcond(:) = 0d0
!------------------------------------------------------------------------
! Main loop
!------------------------------------------------------------------------
do while(Conv > thresh .and. nSCF < maxSCF)
! Increment
nSCF = nSCF + 1
! Buid Hartree matrix
do is=1,nspin
call Hartree_matrix_AO_basis(nBas,P(:,:,is),ERI_AO(:,:,:,:),J(:,:,is))
end do
! Compute exchange part of the self-energy
do is=1,nspin
call exchange_matrix_AO_basis(nBas,P(:,:,is),ERI_AO(:,:,:,:),K(:,:,is))
end do
!--------------------------------------------------
! AO to MO transformation of two-electron integrals
!--------------------------------------------------
do ixyz=1,ncart
call AOtoMO(nBas,c(:,:,1),dipole_int_AO(:,:,ixyz),dipole_int_aa(:,:,ixyz))
call AOtoMO(nBas,c(:,:,2),dipole_int_AO(:,:,ixyz),dipole_int_bb(:,:,ixyz))
end do
! 4-index transform for (aa|aa) block
call AOtoMO_ERI_UHF(1,1,nBas,c,ERI_AO,ERI_aaaa)
! 4-index transform for (aa|bb) block
call AOtoMO_ERI_UHF(1,2,nBas,c,ERI_AO,ERI_aabb)
! 4-index transform for (bb|bb) block
call AOtoMO_ERI_UHF(2,2,nBas,c,ERI_AO,ERI_bbbb)
! Compute linear response
call phULR_A(ispin,dRPA,nBas,nC,nO,nV,nR,nSa,nSb,nSt,1d0,eGW,ERI_aaaa,ERI_aabb,ERI_bbbb,Aph)
if(.not.TDA) call phULR_B(ispin,dRPA,nBas,nC,nO,nV,nR,nSa,nSb,nSt,1d0,ERI_aaaa,ERI_aabb,ERI_bbbb,Bph)
call phULR(TDA_W,nSa,nSb,nSt,Aph,Bph,EcRPA(ispin),Om,XpY,XmY)
!----------------------!
! Excitation densities !
!----------------------!
call UGW_excitation_density(nBas,nC,nO,nR,nSa,nSb,nSt,ERI_aaaa,ERI_aabb,ERI_bbbb,XpY,rho)
!------------------------------------------------!
! Compute self-energy and renormalization factor !
!------------------------------------------------!
if(regularize) then
do is=1,nspin
call GW_regularization(nBas,nC(is),nO(is),nV(is),nR(is),nSt,eGW(:,is),Om,rho(:,:,:,is))
end do
end if
call USRG_self_energy(eta,nBas,nC,nO,nV,nR,nSt,eGW,Om,rho,EcGM,SigC,Z)
! Make correlation self-energy Hermitian and transform it back to AO basis
do is=1,nspin
call MOtoAO(nBas,S,c(:,:,is),SigC(:,:,is),SigCp(:,:,is))
end do
! Solve the quasi-particle equation
do is=1,nspin
F(:,:,is) = Hc(:,:) + J(:,:,is) + J(:,:,mod(is,2)+1) + K(:,:,is) + SigCp(:,:,is)
end do
! Check convergence
do is=1,nspin
err(:,:,is) = matmul(F(:,:,is),matmul(P(:,:,is),S(:,:))) - matmul(matmul(S(:,:),P(:,:,is)),F(:,:,is))
end do
if(nSCF > 1) Conv = maxval(abs(err))
! DIIS extrapolation
if(max_diis > 1) then
n_diis = min(n_diis+1,max_diis)
do is=1,nspin
if(nO(is) > 1) call DIIS_extrapolation(rcond(is),nBasSq,nBasSq,n_diis,err_diis(:,1:n_diis,is), &
F_diis(:,1:n_diis,is),err(:,:,is),F(:,:,is))
end do
end if
! Transform Fock matrix in orthogonal basis
do is=1,nspin
Fp(:,:,is) = matmul(transpose(X(:,:)),matmul(F(:,:,is),X(:,:)))
end do
! Diagonalize Fock matrix to get eigenvectors and eigenvalues
cp(:,:,:) = Fp(:,:,:)
do is=1,nspin
call diagonalize_matrix(nBas,cp(:,:,is),eGW(:,is))
end do
! Back-transform eigenvectors in non-orthogonal basis
do is=1,nspin
c(:,:,is) = matmul(X(:,:),cp(:,:,is))
end do
! Back-transform self-energy
do is=1,nspin
call AOtoMO(nBas,c(:,:,is),SigCp(:,:,is),SigC(:,:,is))
end do
! Compute density matrix
do is=1,nspin
P(:,:,is) = matmul(c(:,1:nO(is),is),transpose(c(:,1:nO(is),is)))
end do
!------------------------------------------------------------------------
! Compute total energy
!------------------------------------------------------------------------
! Kinetic energy
do is=1,nspin
ET(is) = trace_matrix(nBas,matmul(P(:,:,is),T(:,:)))
end do
! Potential energy
do is=1,nspin
EV(is) = trace_matrix(nBas,matmul(P(:,:,is),V(:,:)))
end do
! Hartree energy
EJ(1) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,1),J(:,:,1)))
EJ(2) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,1),J(:,:,2))) &
+ 0.5d0*trace_matrix(nBas,matmul(P(:,:,2),J(:,:,1)))
EJ(3) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,2),J(:,:,2)))
! Exchange energy
do is=1,nspin
EK(is) = 0.5d0*trace_matrix(nBas,matmul(P(:,:,is),K(:,:,is)))
end do
! Total energy
EqsGW = sum(ET(:)) + sum(EV(:)) + sum(EJ(:)) + sum(EK(:))
!------------------------------------------------------------------------
! Print results
!------------------------------------------------------------------------
call dipole_moment(nBas,P(:,:,1)+P(:,:,2),nNuc,ZNuc,rNuc,dipole_int_AO,dipole)
call print_qsUGW(nBas,nO,nSCF,Conv,thresh,eHF,eGW,c,S,ENuc,ET,EV,EJ,EK,EcGM,EcRPA(ispin),EqsGW,SigCp,Z,dipole)
end do
!------------------------------------------------------------------------
! End main loop
!------------------------------------------------------------------------
! Did it actually converge?
if(nSCF == maxSCF) then
write(*,*)
write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
write(*,*)' Convergence failed '
write(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
write(*,*)
stop
end if
! Deallocate memory
deallocate(cp,P,F,Fp,J,K,SigC,SigCp,Z,Om,XpY,XmY,rho,err,err_diis,F_diis)
! Perform BSE calculation
if(BSE) then
call UGW_phBSE(TDA_W,TDA,dBSE,dTDA,spin_conserved,spin_flip,eta,nBas,nC,nO,nV,nR,nS, &
S,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_aa,dipole_int_bb,c,eGW,eGW,EcBSE)
if(exchange_kernel) then
EcBSE(1) = 0.5d0*EcBSE(1)
EcBSE(2) = 0.5d0*EcBSE(2)
else
EcBSE(2) = 0.0d0
end if
write(*,*)
write(*,*)'-------------------------------------------------------------------------------'
write(*,'(2X,A50,F20.10,A3)') 'Tr@BSE@qsGW@UHF correlation energy (spin-conserved) = ',EcBSE(1),' au'
write(*,'(2X,A50,F20.10,A3)') 'Tr@BSE@qsGW@UHF correlation energy (spin-flip) = ',EcBSE(2),' au'
write(*,'(2X,A50,F20.10,A3)') 'Tr@BSE@qsGW@UHF correlation energy = ',sum(EcBSE),' au'
write(*,'(2X,A50,F20.10,A3)') 'Tr@BSE@qsGW@UHF total energy = ',ENuc + EqsGW + sum(EcBSE),' au'
write(*,*)'-------------------------------------------------------------------------------'
write(*,*)
! Compute the BSE correlation energy via the adiabatic connection
if(doACFDT) then
write(*,*) '--------------------------------------------------------------'
write(*,*) ' Adiabatic connection version of BSE@qsUGW correlation energy '
write(*,*) '--------------------------------------------------------------'
write(*,*)
if(doXBS) then
write(*,*) '*** scaled screening version (XBS) ***'
write(*,*)
end if
call UGW_phACFDT(exchange_kernel,doXBS,.true.,TDA_W,TDA,BSE,spin_conserved,spin_flip, &
eta,nBas,nC,nO,nV,nR,nS,ERI_aaaa,ERI_aabb,ERI_bbbb,eGW,eGW,EcRPA)
write(*,*)
write(*,*)'-------------------------------------------------------------------------------'
write(*,'(2X,A50,F20.10,A3)') 'AC@BSE@qsGW@UHF correlation energy (spin-conserved) = ',EcRPA(1),' au'
write(*,'(2X,A50,F20.10,A3)') 'AC@BSE@qsGW@UHF correlation energy (spin-flip) = ',EcRPA(2),' au'
write(*,'(2X,A50,F20.10,A3)') 'AC@BSE@qsGW@UHF correlation energy = ',sum(EcRPA),' au'
write(*,'(2X,A50,F20.10,A3)') 'AC@BSE@qsGW@UHF total energy = ',ENuc + EqsGW + sum(EcRPA),' au'
write(*,*)'-------------------------------------------------------------------------------'
write(*,*)
end if
end if
! Testing zone
if(dotest) then
call dump_test_value('U','qsGW correlation energy',EcRPA)
call dump_test_value('U','qsGW HOMOa energy',eGW(nO(1),1))
call dump_test_value('U','qsGW LUMOa energy',eGW(nO(1)+1,1))
call dump_test_value('U','qsGW HOMOa energy',eGW(nO(2),2))
call dump_test_value('U','qsGW LUMOa energy',eGW(nO(2)+1,2))
end if
end subroutine

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@ -114,9 +114,9 @@ subroutine UGW(dotest,doG0W0,doevGW,doqsGW,doufG0W0,doufGW,doSRGqsGW,maxSCF,thre
if(doqsGW) then
call wall_time(start_GW)
call qsUGW(dotest,maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,TDA_W,TDA,dBSE,dTDA,spin_conserved,spin_flip, &
eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nC,nO,nV,nR,nS,EUHF,S,X,T,V,Hc,ERI_AO,ERI_aaaa,ERI_aabb,ERI_bbbb, &
dipole_int_AO,dipole_int_aa,dipole_int_bb,PHF,cHF,eHF)
call qsUGW(dotest,maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,TDA_W,TDA,dBSE,dTDA, &
spin_conserved,spin_flip,eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nC,nO,nV,nR,nS,EUHF, &
S,X,T,V,Hc,ERI_AO,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_AO,dipole_int_aa,dipole_int_bb,PHF,cHF,eHF)
call wall_time(end_GW)
t_GW = end_GW - start_GW
@ -132,7 +132,9 @@ subroutine UGW(dotest,doG0W0,doevGW,doqsGW,doufG0W0,doufGW,doSRGqsGW,maxSCF,thre
if(doSRGqsGW) then
call wall_time(start_GW)
print*,'Unrestricted version of SRG-qsGW not yet implemented! Sorry.'
call SRG_qsUGW(dotest,maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,TDA_W,TDA,dBSE,dTDA, &
spin_conserved,spin_flip,eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nC,nO,nV,nR,nS,EUHF, &
S,X,T,V,Hc,ERI_AO,ERI_aaaa,ERI_aabb,ERI_bbbb,dipole_int_AO,dipole_int_aa,dipole_int_bb,PHF,cHF,eHF)
call wall_time(end_GW)
t_GW = end_GW - start_GW

150
src/GW/USRG_self_energy.f90 Normal file
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@ -0,0 +1,150 @@
subroutine USRG_self_energy(eta,nBas,nC,nO,nV,nR,nS,e,Om,rho,EcGM,SigC,Z)
! Compute correlation part of the self-energy
implicit none
include 'parameters.h'
! Input variables
double precision,intent(in) :: eta
integer,intent(in) :: nBas
integer,intent(in) :: nC(nspin)
integer,intent(in) :: nO(nspin)
integer,intent(in) :: nV(nspin)
integer,intent(in) :: nR(nspin)
integer,intent(in) :: nS
double precision,intent(in) :: e(nBas,nspin)
double precision,intent(in) :: Om(nS)
double precision,intent(in) :: rho(nBas,nBas,nS,nspin)
! Local variables
integer :: ispin
integer :: i,j,a,b
integer :: p,q,r
integer :: m
double precision :: Dpim,Dqim,Dpam,Dqam,Diam
double precision :: t1,t2
! Output variables
double precision,intent(out) :: EcGM
double precision,intent(out) :: SigC(nBas,nBas,nspin)
double precision,intent(out) :: Z(nBas,nspin)
! Initialize
SigC(:,:,:) = 0d0
!--------------------!
! SRG-GW self-energy !
!--------------------!
! Occupied part of the correlation self-energy
call wall_time(t1)
!$OMP PARALLEL &
!$OMP SHARED(SigC,rho,eta,nS,nC,nO,nBas,nR,e,Om) &
!$OMP PRIVATE(ispin,m,i,q,p,Dpim,Dqim) &
!$OMP DEFAULT(NONE)
!$OMP DO
do ispin=1,nspin
do q=nC(ispin)+1,nBas-nR(ispin)
do p=nC(ispin)+1,nBas-nR(ispin)
do m=1,nS
do i=nC(ispin)+1,nO(ispin)
Dpim = e(p,ispin) - e(i,ispin) + Om(m)
Dqim = e(q,ispin) - e(i,ispin) + Om(m)
SigC(p,q,ispin) = SigC(p,q,ispin) &
+ rho(p,i,m,ispin)*rho(q,i,m,ispin)*(1d0-dexp(-eta*Dpim*Dpim)*dexp(-eta*Dqim*Dqim)) &
*(Dpim + Dqim)/(Dpim*Dpim + Dqim*Dqim)
end do
end do
end do
end do
end do
!$OMP END DO
!$OMP END PARALLEL
call wall_time(t2)
print *, "first loop", (t2-t1)
! Virtual part of the correlation self-energy
call wall_time(t1)
!$OMP PARALLEL &
!$OMP SHARED(SigC,rho,eta,nS,nC,nO,nR,nBas,e,Om) &
!$OMP PRIVATE(ispin,m,a,q,p,Dpam,Dqam) &
!$OMP DEFAULT(NONE)
!$OMP DO
do ispin=1,nspin
do q=nC(ispin)+1,nBas-nR(ispin)
do p=nC(ispin)+1,nBas-nR(ispin)
do m=1,nS
do a=nO(ispin)+1,nBas-nR(ispin)
Dpam = e(p,ispin) - e(a,ispin) - Om(m)
Dqam = e(q,ispin) - e(a,ispin) - Om(m)
SigC(p,q,ispin) = SigC(p,q,ispin) &
+ rho(p,a,m,ispin)*rho(q,a,m,ispin)*(1d0-exp(-eta*Dpam*Dpam)*exp(-eta*Dqam*Dqam)) &
*(Dpam + Dqam)/(Dpam*Dpam + Dqam*Dqam)
end do
end do
end do
end do
end do
!$OMP END DO
!$OMP END PARALLEL
call wall_time(t2)
print *, "second loop", (t2-t1)
! Initialize
Z(:,:) = 0d0
do ispin=1,nspin
do p=nC(ispin)+1,nBas-nR(ispin)
do i=nC(ispin)+1,nO(ispin)
do m=1,nS
Dpim = e(p,ispin) - e(i,ispin) + Om(m)
Z(p,ispin) = Z(p,ispin) - rho(p,i,m,ispin)**2*(1d0-dexp(-2d0*eta*Dpim*Dpim))/Dpim**2
end do
end do
end do
end do
! Virtual part of the correlation self-energy
do ispin=1,nspin
do p=nC(ispin)+1,nBas-nR(ispin)
do a=nO(ispin)+1,nBas-nR(ispin)
do m=1,nS
Dpam = e(p,ispin) - e(a,ispin) - Om(m)
Z(p,ispin) = Z(p,ispin) - rho(p,a,m,ispin)**2*(1d0-dexp(-2d0*eta*Dpam*Dpam))/Dpam**2
end do
end do
end do
end do
! Compute renormalization factor from derivative of SigC
Z(:,:) = 1d0/(1d0 - Z(:,:))
! Galitskii-Migdal correlation energy
EcGM = 0d0
do ispin=1,nspin
do i=nC(ispin)+1,nO(ispin)
do a=nO(ispin)+1,nBas-nR(ispin)
do m=1,nS
Diam = e(a,ispin) - e(i,ispin) + Om(m)
EcGM = EcGM - rho(a,i,m,ispin)*rho(a,i,m,ispin)*(1d0-exp(-2d0*eta*Diam*Diam))/Diam
end do
end do
end do
end do
end subroutine

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@ -33,26 +33,20 @@ subroutine print_qsUGW(nBas,nO,nSCF,Conv,thresh,eHF,eGW,c,Ov,ENuc,ET,EV,EJ,Ex,Ec
logical :: dump_orb = .false.
integer :: p
integer :: ispin,ixyz
double precision :: HOMO(nspin)
double precision :: LUMO(nspin)
double precision :: Gap(nspin)
double precision :: eHOMO(nspin)
double precision :: eLUMO(nspin)
double precision :: Gap
double precision :: Sz
double precision :: Sx2,Sy2,Sz2
double precision,external :: trace_matrix
! HOMO and LUMO
do ispin=1,nspin
if(nO(ispin) > 0) then
HOMO(ispin) = eGW(nO(ispin),ispin)
LUMO(ispin) = eGW(nO(ispin)+1,ispin)
Gap(ispin) = LUMO(ispin) - HOMO(ispin)
else
HOMO(ispin) = 0d0
LUMO(ispin) = eGW(1,ispin)
Gap(ispin) = 0d0
end if
do ispin=1,nspin
eHOMO(ispin) = maxval(eGW(1:nO(ispin),ispin))
eLUMO(ispin) = minval(eGW(nO(ispin)+1:nBas,ispin))
end do
Gap = minval(eLUMO) -maxval(eHOMO)
Sz = 0.5d0*dble(nO(1) - nO(2))
Sx2 = 0.25d0*dble(nO(1) - nO(2)) + 0.5d0*nO(2) - 0.5d0*sum(matmul(transpose(c(:,1:nO(1),1)),matmul(Ov,c(:,1:nO(2),2)))**2)
@ -91,9 +85,9 @@ subroutine print_qsUGW(nBas,nO,nSCF,Conv,thresh,eHF,eGW,c,Ov,ENuc,ET,EV,EJ,Ex,Ec
write(*,'(2X,A14,F15.5)')'Convergence = ',Conv
write(*,*)'----------------------------------------------------------------'// &
'----------------------------------------------------------------'
write(*,'(2X,A60,F15.6,A3)') 'qsGW@UHF HOMO energy = ',maxval(HOMO)*HaToeV,' eV'
write(*,'(2X,A60,F15.6,A3)') 'qsGW@UHF LUMO energy = ',minval(LUMO)*HaToeV,' eV'
write(*,'(2X,A60,F15.6,A3)') 'qsGW@UHF HOMO-LUMO gap = ',(minval(LUMO)-maxval(HOMO))*HaToeV,' eV'
write(*,'(2X,A60,F15.6,A3)') 'qsGW@UHF HOMO energy = ',maxval(eHOMO)*HaToeV,' eV'
write(*,'(2X,A60,F15.6,A3)') 'qsGW@UHF LUMO energy = ',minval(eLUMO)*HaToeV,' eV'
write(*,'(2X,A60,F15.6,A3)') 'qsGW@UHF HOMO-LUMO gap = ',(minval(eLUMO)-maxval(eHOMO))*HaToeV,' eV'
write(*,*)'----------------------------------------------------------------'// &
'----------------------------------------------------------------'
write(*,'(2X,A60,F15.6,A3)') ' qsGW@UHF total energy = ',ENuc + EqsGW,' au'