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working on qsGGW

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This commit is contained in:
Pierre-Francois Loos 2023-11-08 15:44:06 +01:00
parent 8fd6f6361e
commit d04eb0950e
9 changed files with 342 additions and 120 deletions
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2
input/methods
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@ -13,6 +13,6 @@
# G0F2 evGF2 qsGF2 G0F3 evGF3 # G0F2 evGF2 qsGF2 G0F3 evGF3
F F F F F F F F F F
# G0W0 evGW qsGW SRG-qsGW ufG0W0 ufGW # G0W0 evGW qsGW SRG-qsGW ufG0W0 ufGW
T F F F F F F F T F F F
# G0T0pp evGTpp qsGTpp G0T0eh evGTeh qsGTeh # G0T0pp evGTpp qsGTpp G0T0eh evGTeh qsGTeh
F F F F F F F F F F F F

2
input/options
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@ -1,5 +1,5 @@
# HF: maxSCF thresh DIIS guess mix shift stab search # HF: maxSCF thresh DIIS guess mix shift stab search
10000 0.0000001 5 2 0.0 0.0 T T 10000 0.0000001 5 1 0.0 0.0 F F
# MP: reg # MP: reg
F F
# CC: maxSCF thresh DIIS # CC: maxSCF thresh DIIS

37
src/GW/GGW.f90
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@ -1,6 +1,6 @@
subroutine GGW(doG0W0,doevGW,doqsGW,maxSCF,thresh,max_diis,doACFDT, & subroutine GGW(doG0W0,doevGW,doqsGW,maxSCF,thresh,max_diis,doACFDT, &
exchange_kernel,doXBS,dophBSE,dophBSE2,doppBSE,TDA_W,TDA,dBSE,dTDA, & exchange_kernel,doXBS,dophBSE,dophBSE2,doppBSE,TDA_W,TDA,dBSE,dTDA, &
linearize,eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nC,nO,nV,nR,nS,EHF,S,X,T,V,Hc, & linearize,eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nBas2,nC,nO,nV,nR,nS,EHF,S,X,T,V,Hc, &
ERI_AO,ERI,dipole_int_AO,dipole_int,PHF,cHF,epsHF) ERI_AO,ERI,dipole_int_AO,dipole_int,PHF,cHF,epsHF)
! GW module ! GW module
@ -40,6 +40,7 @@ subroutine GGW(doG0W0,doevGW,doqsGW,maxSCF,thresh,max_diis,doACFDT, &
double precision,intent(in) :: ENuc double precision,intent(in) :: ENuc
integer,intent(in) :: nBas integer,intent(in) :: nBas
integer,intent(in) :: nBas2
integer,intent(in) :: nC integer,intent(in) :: nC
integer,intent(in) :: nO integer,intent(in) :: nO
integer,intent(in) :: nV integer,intent(in) :: nV
@ -47,18 +48,18 @@ subroutine GGW(doG0W0,doevGW,doqsGW,maxSCF,thresh,max_diis,doACFDT, &
integer,intent(in) :: nS integer,intent(in) :: nS
double precision,intent(in) :: EHF double precision,intent(in) :: EHF
double precision,intent(in) :: epsHF(nBas) double precision,intent(in) :: epsHF(nBas2)
double precision,intent(in) :: cHF(nBas,nBas) double precision,intent(in) :: cHF(nBas2,nBas2)
double precision,intent(in) :: PHF(nBas,nBas) double precision,intent(in) :: PHF(nBas2,nBas2)
double precision,intent(in) :: S(nBas,nBas) double precision,intent(in) :: S(nBas2,nBas2)
double precision,intent(in) :: T(nBas,nBas) double precision,intent(in) :: T(nBas2,nBas2)
double precision,intent(in) :: V(nBas,nBas) double precision,intent(in) :: V(nBas2,nBas2)
double precision,intent(in) :: Hc(nBas,nBas) double precision,intent(in) :: Hc(nBas2,nBas2)
double precision,intent(in) :: X(nBas,nBas) double precision,intent(in) :: X(nBas2,nBas2)
double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas) double precision,intent(in) :: ERI_AO(nBas2,nBas2,nBas2,nBas2)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas) double precision,intent(in) :: ERI(nBas2,nBas2,nBas2,nBas2)
double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart) double precision,intent(in) :: dipole_int_AO(nBas2,nBas2,ncart)
double precision,intent(in) :: dipole_int(nBas,nBas,ncart) double precision,intent(in) :: dipole_int(nBas2,nBas2,ncart)
! Local variables ! Local variables
@ -72,7 +73,7 @@ subroutine GGW(doG0W0,doevGW,doqsGW,maxSCF,thresh,max_diis,doACFDT, &
call wall_time(start_GW) call wall_time(start_GW)
call GG0W0(doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA,dBSE,dTDA,doppBSE, & call GG0W0(doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA,dBSE,dTDA,doppBSE, &
linearize,eta,regularize,nBas,nC,nO,nV,nR,nS,ENuc,EHF,ERI,dipole_int,epsHF) linearize,eta,regularize,nBas2,nC,nO,nV,nR,nS,ENuc,EHF,ERI,dipole_int,epsHF)
call wall_time(end_GW) call wall_time(end_GW)
t_GW = end_GW - start_GW t_GW = end_GW - start_GW
@ -89,7 +90,7 @@ subroutine GGW(doG0W0,doevGW,doqsGW,maxSCF,thresh,max_diis,doACFDT, &
call wall_time(start_GW) call wall_time(start_GW)
call evGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA,dBSE,dTDA,doppBSE, & call evGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA,dBSE,dTDA,doppBSE, &
linearize,eta,regularize,nBas,nC,nO,nV,nR,nS,ENuc,EHF,ERI,dipole_int,epsHF) linearize,eta,regularize,nBas2,nC,nO,nV,nR,nS,ENuc,EHF,ERI,dipole_int,epsHF)
call wall_time(end_GW) call wall_time(end_GW)
t_GW = end_GW - start_GW t_GW = end_GW - start_GW
@ -105,9 +106,9 @@ subroutine GGW(doG0W0,doevGW,doqsGW,maxSCF,thresh,max_diis,doACFDT, &
if(doqsGW) then if(doqsGW) then
call wall_time(start_GW) call wall_time(start_GW)
! call qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA,dBSE,dTDA,doppBSE, & call qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA,dBSE,dTDA,doppBSE, &
! eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nBas2,nC,nO,nV,nR,nS,EHF,S,X,T,V,Hc,ERI_AO,ERI, & eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nBas2,nC,nO,nV,nR,nS,EHF,S,X,T,V,Hc,ERI_AO,ERI, &
! dipole_int_AO,dipole_int,PHF,cHF,epsHF) dipole_int_AO,dipole_int,PHF,cHF,epsHF)
call wall_time(end_GW) call wall_time(end_GW)
t_GW = end_GW - start_GW t_GW = end_GW - start_GW

109
src/GW/GGW_self_energy.f90 Normal file
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@ -0,0 +1,109 @@
subroutine GGW_self_energy(eta,nBas,nC,nO,nV,nR,nS,e,Om,rho,EcGM,Sig,Z)
! Compute correlation part of the self-energy and the renormalization factor
implicit none
include 'parameters.h'
! Input variables
double precision,intent(in) :: eta
integer,intent(in) :: nBas
integer,intent(in) :: nC
integer,intent(in) :: nO
integer,intent(in) :: nV
integer,intent(in) :: nR
integer,intent(in) :: nS
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Om(nS)
double precision,intent(in) :: rho(nBas,nBas,nS)
! Local variables
integer :: i,j,a,b
integer :: p,q,m
double precision :: num,eps
! Output variables
double precision,intent(out) :: EcGM
double precision,intent(out) :: Sig(nBas,nBas)
double precision,intent(out) :: Z(nBas)
! Initialize
Sig(:,:) = 0d0
Z(:) = 0d0
!----------------!
! GW self-energy !
!----------------!
! Occupied part of the correlation self-energy
!$OMP PARALLEL &
!$OMP SHARED(Sig,Z,rho,eta,nS,nC,nO,nBas,nR,e,Om) &
!$OMP PRIVATE(m,i,q,p,eps,num) &
!$OMP DEFAULT(NONE)
!$OMP DO
do q=nC+1,nBas-nR
do p=nC+1,nBas-nR
do m=1,nS
do i=nC+1,nO
eps = e(p) - e(i) + Om(m)
num = rho(p,i,m)*rho(q,i,m)
Sig(p,q) = Sig(p,q) + num*eps/(eps**2 + eta**2)
if(p == q) Z(p) = Z(p) - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
end do
end do
end do
end do
!$OMP END DO
!$OMP END PARALLEL
! Virtual part of the correlation self-energy
!$OMP PARALLEL &
!$OMP SHARED(Sig,Z,rho,eta,nS,nC,nO,nBas,nR,e,Om) &
!$OMP PRIVATE(m,a,q,p,eps,num) &
!$OMP DEFAULT(NONE)
!$OMP DO
do q=nC+1,nBas-nR
do p=nC+1,nBas-nR
do m=1,nS
do a=nO+1,nBas-nR
eps = e(p) - e(a) - Om(m)
num = rho(p,a,m)*rho(q,a,m)
Sig(p,q) = Sig(p,q) + num*eps/(eps**2 + eta**2)
if(p == q) Z(p) = Z(p) - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
end do
end do
end do
end do
!$OMP END DO
!$OMP END PARALLEL
! Galitskii-Migdal correlation energy
EcGM = 0d0
do m=1,nS
do a=nO+1,nBas-nR
do i=nC+1,nO
eps = e(a) - e(i) + Om(m)
num = rho(a,i,m)*rho(a,i,m)
EcGM = EcGM - num*eps/(eps**2 + eta**2)
end do
end do
end do
! Compute renormalization factor from derivative
Z(:) = 1d0/(1d0 - Z(:))
end subroutine

12
src/GW/SRG_qsGW.f90
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@ -48,13 +48,14 @@ subroutine SRG_qsGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,BSE,BSE
double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas) double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_MO(nBas,nBas,nBas,nBas) double precision,intent(inout):: ERI_MO(nBas,nBas,nBas,nBas)
double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart) double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart)
double precision,intent(in) :: dipole_int_MO(nBas,nBas,ncart) double precision,intent(inout):: dipole_int_MO(nBas,nBas,ncart)
! Local variables ! Local variables
integer :: nSCF integer :: nSCF
integer :: nBasSq integer :: nBasSq
integer :: ispin integer :: ispin
integer :: ixyz
integer :: n_diis integer :: n_diis
double precision :: ET double precision :: ET
double precision :: EV double precision :: EV
@ -166,9 +167,14 @@ subroutine SRG_qsGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,BSE,BSE
! AO to MO transformation of two-electron integrals ! AO to MO transformation of two-electron integrals
call wall_time(tao1) call wall_time(tao1)
call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_MO) dipole_int_MO(:,:,:) = dipole_int_AO(:,:,:)
do ixyz=1,ncart
call AOtoMO_transform(nBas,cHF,dipole_int_MO(:,:,ixyz))
end do
call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_MO)
call wall_time(tao2) call wall_time(tao2)

277
src/GW/qsGGW.f90
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@ -1,8 +1,8 @@
subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA,dBSE,dTDA,doppBSE, & subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA,dBSE,dTDA,doppBSE, &
singlet,triplet,eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nBas2,nC,nO,nV,nR,nS,ERHF,S,X,T,V,Hc,ERI_AO, & eta,regularize,nNuc,ZNuc,rNuc,ENuc,nBas,nBas2,nC,nO,nV,nR,nS,EGHF,Ov,Or,T,V,Hc,ERI_AO, &
ERI_MO,dipole_int_AO,dipole_int_MO,PHF,cHF,eHF) ERI_MO,dipole_int_AO,dipole_int_MO,PHF,cHF,eHF)
! Perform a quasiparticle self-consistent GW calculation ! Generalized version of quasiparticle self-consistent GW
implicit none implicit none
include 'parameters.h' include 'parameters.h'
@ -22,8 +22,6 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
logical,intent(in) :: dBSE logical,intent(in) :: dBSE
logical,intent(in) :: dTDA logical,intent(in) :: dTDA
logical,intent(in) :: doppBSE logical,intent(in) :: doppBSE
logical,intent(in) :: singlet
logical,intent(in) :: triplet
double precision,intent(in) :: eta double precision,intent(in) :: eta
logical,intent(in) :: regularize logical,intent(in) :: regularize
@ -39,30 +37,32 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
integer,intent(in) :: nV integer,intent(in) :: nV
integer,intent(in) :: nR integer,intent(in) :: nR
integer,intent(in) :: nS integer,intent(in) :: nS
double precision,intent(in) :: ERHF double precision,intent(in) :: EGHF
double precision,intent(in) :: eHF(nBas) double precision,intent(in) :: eHF(nBas2)
double precision,intent(in) :: cHF(nBas,nBas) double precision,intent(in) :: cHF(nBas2,nBas2)
double precision,intent(in) :: PHF(nBas,nBas) double precision,intent(in) :: PHF(nBas2,nBas2)
double precision,intent(in) :: S(nBas,nBas) double precision,intent(in) :: Ov(nBas,nBas)
double precision,intent(in) :: T(nBas,nBas) double precision,intent(in) :: T(nBas,nBas)
double precision,intent(in) :: V(nBas,nBas) double precision,intent(in) :: V(nBas,nBas)
double precision,intent(in) :: Hc(nBas,nBas) double precision,intent(in) :: Hc(nBas,nBas)
double precision,intent(in) :: X(nBas,nBas) double precision,intent(in) :: Or(nBas,nBas)
double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas) double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_MO(nBas,nBas,nBas,nBas) double precision,intent(inout):: ERI_MO(nBas2,nBas2,nBas2,nBas2)
double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart) double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart)
double precision,intent(in) :: dipole_int_MO(nBas,nBas,ncart) double precision,intent(inout):: dipole_int_MO(nBas2,nBas2,ncart)
! Local variables ! Local variables
integer :: nSCF integer :: nSCF
integer :: nBasSq integer :: nBasSq
integer :: nBas2Sq
integer :: ispin integer :: ispin
integer :: ixyz
integer :: n_diis integer :: n_diis
double precision :: ET double precision :: ET,ETaa,ETbb
double precision :: EV double precision :: EV,EVaa,EVbb
double precision :: EJ double precision :: EJ,EJaaaa,EJaabb,EJbbaa,EJbbbb
double precision :: Ex double precision :: EK,EKaaaa,EKabba,EKbaab,EKbbbb
double precision :: EqsGW double precision :: EqsGW
double precision :: EcRPA double precision :: EcRPA
double precision :: EcBSE(nspin) double precision :: EcBSE(nspin)
@ -74,7 +74,7 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
logical :: dRPA = .true. logical :: dRPA = .true.
logical :: print_W = .true. logical :: print_W = .true.
double precision,allocatable :: error_diis(:,:) double precision,allocatable :: err_diis(:,:)
double precision,allocatable :: F_diis(:,:) double precision,allocatable :: F_diis(:,:)
double precision,allocatable :: Aph(:,:) double precision,allocatable :: Aph(:,:)
double precision,allocatable :: Bph(:,:) double precision,allocatable :: Bph(:,:)
@ -82,20 +82,27 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
double precision,allocatable :: XpY(:,:) double precision,allocatable :: XpY(:,:)
double precision,allocatable :: XmY(:,:) double precision,allocatable :: XmY(:,:)
double precision,allocatable :: rho(:,:,:) double precision,allocatable :: rho(:,:,:)
double precision,allocatable :: c(:,:)
double precision,allocatable :: cp(:,:) double precision,allocatable :: Ca(:,:),Cb(:,:)
double precision,allocatable :: ERI_tmp(:,:,:,:)
double precision,allocatable :: Jaa(:,:),Jbb(:,:)
double precision,allocatable :: Kaa(:,:),Kab(:,:),Kba(:,:),Kbb(:,:)
double precision,allocatable :: Faa(:,:),Fab(:,:),Fba(:,:),Fbb(:,:)
double precision,allocatable :: Paa(:,:),Pab(:,:),Pba(:,:),Pbb(:,:)
double precision,allocatable :: C(:,:)
double precision,allocatable :: Cp(:,:)
double precision,allocatable :: eGW(:) double precision,allocatable :: eGW(:)
double precision,allocatable :: eOld(:) double precision,allocatable :: eOld(:)
double precision,allocatable :: P(:,:) double precision,allocatable :: P(:,:)
double precision,allocatable :: F(:,:) double precision,allocatable :: F(:,:)
double precision,allocatable :: H(:,:)
double precision,allocatable :: S(:,:)
double precision,allocatable :: X(:,:)
double precision,allocatable :: Fp(:,:) double precision,allocatable :: Fp(:,:)
double precision,allocatable :: J(:,:)
double precision,allocatable :: K(:,:)
double precision,allocatable :: SigC(:,:) double precision,allocatable :: SigC(:,:)
double precision,allocatable :: SigCp(:,:)
double precision,allocatable :: SigCm(:,:)
double precision,allocatable :: Z(:) double precision,allocatable :: Z(:)
double precision,allocatable :: error(:,:) double precision,allocatable :: err(:,:)
! Hello world ! Hello world
@ -113,6 +120,7 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
! Stuff ! Stuff
nBasSq = nBas*nBas nBasSq = nBas*nBas
nBas2Sq = nBas2*nBas2
! TDA for W ! TDA for W
@ -130,24 +138,49 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
! Memory allocation ! Memory allocation
allocate(eGW(nBas),eOld(nBas),c(nBas,nBas),cp(nBas,nBas),P(nBas,nBas),F(nBas,nBas),Fp(nBas,nBas), &
J(nBas,nBas),K(nBas,nBas),SigC(nBas,nBas),SigCp(nBas,nBas),SigCm(nBas,nBas),Z(nBas), & allocate(P(nBas2,nBas2),Jaa(nBas,nBas),Jbb(nBas,nBas), &
Aph(nS,nS),Bph(nS,nS),Om(nS),XpY(nS,nS),XmY(nS,nS),rho(nBas,nBas,nS), & Kaa(nBas,nBas),Kab(nBas,nBas),Kba(nBas,nBas),Kbb(nBas,nBas), &
error(nBas,nBas),error_diis(nBasSq,max_diis),F_diis(nBasSq,max_diis)) Faa(nBas,nBas),Fab(nBas,nBas),Fba(nBas,nBas),Fbb(nBas,nBas), &
Paa(nBas,nBas),Pab(nBas,nBas),Pba(nBas,nBas),Pbb(nBas,nBas), &
F(nBas2,nBas2),Fp(nBas2,nBas2),C(nBas2,nBas2),Cp(nBas2,nBas2), &
H(nBas2,nBas2),S(nBas2,nBas2),X(nBas2,nBas2),err(nBas2,nBas2), &
err_diis(nBas2Sq,max_diis),F_diis(nBas2Sq,max_diis))
allocate(eGW(nBas2),eOld(nBas2),SigC(nBas2,nBas2),Z(nBas2), &
Aph(nS,nS),Bph(nS,nS),Om(nS),XpY(nS,nS),XmY(nS,nS),rho(nBas2,nBas2,nS))
! Initialization ! Initialization
nSCF = -1 nSCF = -1
n_diis = 0 n_diis = 0
ispin = 3 ispin = 3
Conv = 1d0 Conv = 1d0
P(:,:) = PHF(:,:) P(:,:) = PHF(:,:)
eGW(:) = eHF(:) eGW(:) = eHF(:)
eOld(:) = eHF(:) eOld(:) = eHF(:)
c(:,:) = cHF(:,:) c(:,:) = cHF(:,:)
F_diis(:,:) = 0d0 F_diis(:,:) = 0d0
error_diis(:,:) = 0d0 err_diis(:,:) = 0d0
rcond = 0d0 rcond = 0d0
! Construct super overlap matrix
S( : , : ) = 0d0
S( 1:nBas , 1:nBas ) = Ov(1:nBas,1:nBas)
S(nBas+1:nBas2,nBas+1:nBas2) = Ov(1:nBas,1:nBas)
! Construct super orthogonalization matrix
X( : , : ) = 0d0
X( 1:nBas , 1:nBas ) = Or(1:nBas,1:nBas)
X(nBas+1:nBas2,nBas+1:nBas2) = Or(1:nBas,1:nBas)
! Construct super orthogonalization matrix
H( : , : ) = 0d0
H( 1:nBas , 1:nBas ) = Hc(1:nBas,1:nBas)
H(nBas+1:nBas2,nBas+1:nBas2) = Hc(1:nBas,1:nBas)
!------------------------------------------------------------------------ !------------------------------------------------------------------------
! Main loop ! Main loop
@ -155,107 +188,169 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
do while(Conv > thresh .and. nSCF <= maxSCF) do while(Conv > thresh .and. nSCF <= maxSCF)
! Increment ! Increment
nSCF = nSCF + 1 nSCF = nSCF + 1
! Buid Hartree matrix ! Buid Hartree matrix
call Hartree_matrix_AO_basis(nBas,P,ERI_AO,J) call Hartree_matrix_AO_basis(nBas,Paa,ERI_AO,Jaa)
call Hartree_matrix_AO_basis(nBas,Pbb,ERI_AO,Jbb)
! Compute exchange part of the self-energy ! Compute exchange part of the self-energy
call exchange_matrix_AO_basis(nBas,P,ERI_AO,K) call exchange_matrix_AO_basis(nBas,Paa,ERI_AO,Kaa)
call exchange_matrix_AO_basis(nBas,Pba,ERI_AO,Kab)
call exchange_matrix_AO_basis(nBas,Pab,ERI_AO,Kba)
call exchange_matrix_AO_basis(nBas,Pbb,ERI_AO,Kbb)
! AO to MO transformation of two-electron integrals ! AO to MO transformation of two-electron integrals
call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_MO) allocate(Ca(nBas,nBas2),Cb(nBas,nBas2),ERI_tmp(nBas2,nBas2,nBas2,nBas2))
Ca(:,:) = C(1:nBas,1:nBas2)
Cb(:,:) = C(nBas+1:nBas2,1:nBas2)
! Compute linear response do ixyz=1,ncart
call AOtoMO_transform_GHF(nBas,nBas2,Ca,Cb,dipole_int_AO(:,:,ixyz),dipole_int_MO(:,:,ixyz))
end do
call phLR_A(ispin,dRPA,nBas,nC,nO,nV,nR,nS,1d0,eGW,ERI_MO,Aph) call AOtoMO_integral_transform_GHF(nBas,nBas2,Ca,Ca,Ca,Ca,ERI_AO,ERI_tmp)
if(.not.TDA_W) call phLR_B(ispin,dRPA,nBas,nC,nO,nV,nR,nS,1d0,ERI_MO,Bph) ERI_MO(:,:,:,:) = ERI_tmp(:,:,:,:)
call AOtoMO_integral_transform_GHF(nBas,nBas2,Ca,Cb,Ca,Cb,ERI_AO,ERI_tmp)
ERI_MO(:,:,:,:) = ERI_MO(:,:,:,:) + ERI_tmp(:,:,:,:)
call AOtoMO_integral_transform_GHF(nBas,nBas2,Cb,Ca,Cb,Ca,ERI_AO,ERI_tmp)
ERI_MO(:,:,:,:) = ERI_MO(:,:,:,:) + ERI_tmp(:,:,:,:)
call AOtoMO_integral_transform_GHF(nBas,nBas2,Cb,Cb,Cb,Cb,ERI_AO,ERI_tmp)
ERI_MO(:,:,:,:) = ERI_MO(:,:,:,:) + ERI_tmp(:,:,:,:)
deallocate(Ca,Cb,ERI_tmp)
! Compute linear response
call phLR_A(ispin,dRPA,nBas2,nC,nO,nV,nR,nS,1d0,eGW,ERI_MO,Aph)
if(.not.TDA_W) call phLR_B(ispin,dRPA,nBas2,nC,nO,nV,nR,nS,1d0,ERI_MO,Bph)
call phLR(TDA_W,nS,Aph,Bph,EcRPA,Om,XpY,XmY) call phLR(TDA_W,nS,Aph,Bph,EcRPA,Om,XpY,XmY)
if(print_W) call print_excitation_energies('phRPA@qsGW',ispin,nS,Om) if(print_W) call print_excitation_energies('phRPA@qsGGW',ispin,nS,Om)
! Compute correlation part of the self-energy ! Compute correlation part of the self-energy
call GW_excitation_density(nBas,nC,nO,nR,nS,ERI_MO,XpY,rho) call GW_excitation_density(nBas2,nC,nO,nR,nS,ERI_MO,XpY,rho)
if(regularize) call GW_regularization(nBas,nC,nO,nV,nR,nS,eGW,Om,rho) if(regularize) call GW_regularization(nBas2,nC,nO,nV,nR,nS,eGW,Om,rho)
call GW_self_energy(eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho,EcGM,SigC,Z) call GGW_self_energy(eta,nBas2,nC,nO,nV,nR,nS,eGW,Om,rho,EcGM,SigC,Z)
! Make correlation self-energy Hermitian and transform it back to AO basis ! Make correlation self-energy Hermitian and transform it back to AO basis
SigCp = 0.5d0*(SigC + transpose(SigC)) SigC = 0.5d0*(SigC + transpose(SigC))
SigCm = 0.5d0*(SigC - transpose(SigC))
call MOtoAO_transform(nBas,S,c,SigCp) ! call MOtoAO_transform(nBas2,S,C,SigC)
! Solve the quasi-particle equation ! Build individual Fock matrices
F(:,:) = Hc(:,:) + J(:,:) + 0.5d0*K(:,:) + SigCp(:,:) Faa(:,:) = Hc(:,:) + Jaa(:,:) + Jbb(:,:) + Kaa(:,:)
Fab(:,:) = + Kab(:,:)
Fba(:,:) = + Kba(:,:)
Fbb(:,:) = Hc(:,:) + Jbb(:,:) + Jaa(:,:) + Kbb(:,:)
! Compute commutator and convergence criteria ! Build super Fock matrix
error = matmul(F,matmul(P,S)) - matmul(matmul(S,P),F) F( 1:nBas , 1:nBas ) = Faa(1:nBas,1:nBas)
F( 1:nBas ,nBas+1:nBas2) = Fab(1:nBas,1:nBas)
F(nBas+1:nBas2, 1:nBas ) = Fba(1:nBas,1:nBas)
F(nBas+1:nBas2,nBas+1:nBas2) = Fbb(1:nBas,1:nBas)
! DIIS extrapolation ! ... and add self-energy
F(:,:) = F(:,:) + SigC(:,:)
! Compute commutator and convergence criteria
err = matmul(F,matmul(P,S)) - matmul(matmul(S,P),F)
! DIIS extrapolation
if(max_diis > 1) then if(max_diis > 1) then
n_diis = min(n_diis+1,max_diis) n_diis = min(n_diis+1,max_diis)
call DIIS_extrapolation(rcond,nBasSq,nBasSq,n_diis,error_diis,F_diis,error,F) call DIIS_extrapolation(rcond,nBas2Sq,nBas2Sq,n_diis,err_diis,F_diis,err,F)
end if end if
! Diagonalize Hamiltonian in AO basis ! Diagonalize Fock matrix to get eigenvectors and eigenvalues
Fp = matmul(transpose(X),matmul(F,X)) Cp(:,:) = Fp(:,:)
cp(:,:) = Fp(:,:) call diagonalize_matrix(nBas2,Cp,eGW)
call diagonalize_matrix(nBas,cp,eGW)
c = matmul(X,cp)
SigCp = matmul(transpose(c),matmul(SigCp,c))
! Compute new density matrix in the AO basis ! Back-transform eigenvectors in non-orthogonal basis
P(:,:) = 2d0*matmul(c(:,1:nO),transpose(c(:,1:nO))) C(:,:) = matmul(X,Cp)
SigC = matmul(transpose(c),matmul(SigC,c))
! Form super density matrix
P(:,:) = matmul(C(:,1:nO),transpose(C(:,1:nO)))
! Compute individual density matrices
Paa(:,:) = P( 1:nBas , 1:nBas )
Pab(:,:) = P( 1:nBas ,nBas+1:nBas2)
Pba(:,:) = P(nBas+1:nBas2, 1:nBas )
Pbb(:,:) = P(nBas+1:nBas2,nBas+1:nBas2)
! Save quasiparticles energy for next cycle ! Save quasiparticles energy for next cycle
Conv = maxval(abs(error)) Conv = maxval(abs(err))
eOld(:) = eGW(:) eOld(:) = eGW(:)
!------------------------------------------------------------------------ !------------------------------------------------------------------------
! Compute total energy ! Compute total energy
!------------------------------------------------------------------------ !------------------------------------------------------------------------
! Kinetic energy ! Kinetic energy
ET = trace_matrix(nBas,matmul(P,T)) ETaa = trace_matrix(nBas,matmul(Paa,T))
ETbb = trace_matrix(nBas,matmul(Pbb,T))
! Potential energy ET = ETaa + ETbb
EV = trace_matrix(nBas,matmul(P,V)) ! Potential energy
! Hartree energy EVaa = trace_matrix(nBas,matmul(Paa,V))
EVbb = trace_matrix(nBas,matmul(Pbb,V))
EJ = 0.5d0*trace_matrix(nBas,matmul(P,J)) EV = EVaa + EVbb
! Exchange energy ! Hartree energy
Ex = 0.25d0*trace_matrix(nBas,matmul(P,K)) EJaaaa = 0.5d0*trace_matrix(nBas,matmul(Paa,Jaa))
EJaabb = 0.5d0*trace_matrix(nBas,matmul(Paa,Jbb))
EJbbaa = 0.5d0*trace_matrix(nBas,matmul(Pbb,Jaa))
EJbbbb = 0.5d0*trace_matrix(nBas,matmul(Pbb,Jbb))
! Total energy EJ = EJaaaa + EJaabb + EJbbaa + EJbbbb
EqsGW = ET + EV + EJ + Ex ! Exchange energy
EKaaaa = 0.5d0*trace_matrix(nBas,matmul(Paa,Kaa))
EKabba = 0.5d0*trace_matrix(nBas,matmul(Pab,Kba))
EKbaab = 0.5d0*trace_matrix(nBas,matmul(Pba,Kab))
EKbbbb = 0.5d0*trace_matrix(nBas,matmul(Pbb,Kbb))
EK = EKaaaa + EKabba + EKbaab + EKbbbb
! Total energy
EqsGW = ET + EV + EJ + EK
! Print results ! Print results
call dipole_moment(nBas,P,nNuc,ZNuc,rNuc,dipole_int_AO,dipole) call dipole_moment(nBas2,P,nNuc,ZNuc,rNuc,dipole_int_AO,dipole)
call print_qsGW(nBas,nO,nSCF,Conv,thresh,eHF,eGW,c,SigCp,Z,ENuc,ET,EV,EJ,Ex,EcGM,EcRPA,EqsGW,dipole) call print_qsGW(nBas2,nO,nSCF,Conv,thresh,eHF,eGW,c,SigC,Z,ENuc,ET,EV,EJ,EK,EcGM,EcRPA,EqsGW,dipole)
enddo enddo
!------------------------------------------------------------------------ !------------------------------------------------------------------------
@ -276,15 +371,11 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
endif endif
! Deallocate memory
deallocate(c,cp,P,F,Fp,J,K,SigC,SigCp,SigCm,Z,Om,XpY,XmY,rho,error,error_diis,F_diis)
! Perform BSE calculation ! Perform BSE calculation
if(dophBSE) then if(dophBSE) then
call GW_phBSE(dophBSE2,TDA_W,TDA,dBSE,dTDA,singlet,triplet,eta,nBas,nC,nO,nV,nR,nS,ERI_MO,dipole_int_MO,eGW,eGW,EcBSE) call GGW_phBSE(dophBSE2,TDA_W,TDA,dBSE,dTDA,eta,nBas2,nC,nO,nV,nR,nS,ERI_MO,dipole_int_MO,eGW,eGW,EcBSE)
if(exchange_kernel) then if(exchange_kernel) then
@ -342,7 +433,7 @@ subroutine qsGGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,do
! write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@qsGW correlation energy (singlet) =',EcBSE(1) ! write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@qsGW correlation energy (singlet) =',EcBSE(1)
! write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@qsGW correlation energy (triplet) =',3d0*EcBSE(2) ! write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@qsGW correlation energy (triplet) =',3d0*EcBSE(2)
! write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@qsGW correlation energy =',EcBSE(1) + 3d0*EcBSE(2) ! write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@qsGW correlation energy =',EcBSE(1) + 3d0*EcBSE(2)
! write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@qsGW total energy =',ENuc + ERHF + EcBSE(1) + 3d0*EcBSE(2) ! write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@qsGW total energy =',ENuc + EGHF + EcBSE(1) + 3d0*EcBSE(2)
! write(*,*)'-------------------------------------------------------------------------------' ! write(*,*)'-------------------------------------------------------------------------------'
! write(*,*) ! write(*,*)

8
src/GW/qsGW.f90
View File

@ -50,13 +50,14 @@ subroutine qsGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,dop
double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas) double precision,intent(in) :: ERI_AO(nBas,nBas,nBas,nBas)
double precision,intent(inout):: ERI_MO(nBas,nBas,nBas,nBas) double precision,intent(inout):: ERI_MO(nBas,nBas,nBas,nBas)
double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart) double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart)
double precision,intent(in) :: dipole_int_MO(nBas,nBas,ncart) double precision,intent(inout):: dipole_int_MO(nBas,nBas,ncart)
! Local variables ! Local variables
integer :: nSCF integer :: nSCF
integer :: nBasSq integer :: nBasSq
integer :: ispin integer :: ispin
integer :: ixyz
integer :: n_diis integer :: n_diis
double precision :: ET double precision :: ET
double precision :: EV double precision :: EV
@ -168,6 +169,11 @@ subroutine qsGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,dophBSE,dop
! AO to MO transformation of two-electron integrals ! AO to MO transformation of two-electron integrals
dipole_int_MO(:,:,:) = dipole_int_AO(:,:,:)
do ixyz=1,ncart
call AOtoMO_transform(nBas,cHF,dipole_int_MO(:,:,ixyz))
end do
call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_MO) call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_MO)
! Compute linear response ! Compute linear response

13
src/GW/qsUGW.f90
View File

@ -52,14 +52,15 @@ subroutine qsUGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,BSE,TDA_W,
double precision,intent(inout):: ERI_aabb(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(inout):: ERI_bbbb(nBas,nBas,nBas,nBas)
double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart) double precision,intent(in) :: dipole_int_AO(nBas,nBas,ncart)
double precision,intent(in) :: dipole_int_aa(nBas,nBas,ncart) double precision,intent(inout):: dipole_int_aa(nBas,nBas,ncart)
double precision,intent(in) :: dipole_int_bb(nBas,nBas,ncart) double precision,intent(inout):: dipole_int_bb(nBas,nBas,ncart)
! Local variables ! Local variables
integer :: nSCF integer :: nSCF
integer :: nBasSq integer :: nBasSq
integer :: ispin integer :: ispin
integer :: ixyz
integer :: is integer :: is
integer :: n_diis integer :: n_diis
integer :: nS_aa,nS_bb,nS_sc integer :: nS_aa,nS_bb,nS_sc
@ -181,6 +182,14 @@ subroutine qsUGW(maxSCF,thresh,max_diis,doACFDT,exchange_kernel,doXBS,BSE,TDA_W,
! AO to MO transformation of two-electron integrals ! AO to MO transformation of two-electron integrals
!-------------------------------------------------- !--------------------------------------------------
dipole_int_aa(:,:,:) = dipole_int_AO(:,:,:)
dipole_int_bb(:,:,:) = dipole_int_AO(:,:,:)
do ixyz=1,ncart
call AOtoMO_transform(nBas,cHF(:,:,1),dipole_int_aa(:,:,ixyz))
call AOtoMO_transform(nBas,cHF(:,:,2),dipole_int_bb(:,:,ixyz))
end do
! 4-index transform for (aa|aa) block ! 4-index transform for (aa|aa) block
call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_aaaa) call AOtoMO_integral_transform(1,1,1,1,nBas,c,ERI_AO,ERI_aaaa)

2
src/QuAcK/GQuAcK.f90
View File

@ -254,7 +254,7 @@ subroutine GQuAcK(doGHF,dostab,dosearch,doMP2,doMP3,dophRPA,dophRPAx,doppRPA,
call wall_time(start_GW) call wall_time(start_GW)
call GGW(doG0W0,doevGW,doqsGW,maxSCF_GW,thresh_GW,max_diis_GW,doACFDT,exchange_kernel,doXBS, & call GGW(doG0W0,doevGW,doqsGW,maxSCF_GW,thresh_GW,max_diis_GW,doACFDT,exchange_kernel,doXBS, &
dophBSE,dophBSE2,doppBSE,TDA_W,TDA,dBSE,dTDA,lin_GW,eta_GW,reg_GW,nNuc,ZNuc,rNuc,ENuc, & dophBSE,dophBSE2,doppBSE,TDA_W,TDA,dBSE,dTDA,lin_GW,eta_GW,reg_GW,nNuc,ZNuc,rNuc,ENuc, &
nBas2,nC,nO,nV,nR,nS,EHF,S,X,T,V,Hc,ERI_AO,ERI_MO,dipole_int_AO,dipole_int_MO,PHF,cHF,epsHF) nBas,nBas2,nC,nO,nV,nR,nS,EHF,S,X,T,V,Hc,ERI_AO,ERI_MO,dipole_int_AO,dipole_int_MO,PHF,cHF,epsHF)
call wall_time(end_GW) call wall_time(end_GW)
t_GW = end_GW - start_GW t_GW = end_GW - start_GW