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spinorbital BSE@G0T0

This commit is contained in:
Pierre-Francois Loos 2022-01-26 13:05:16 +01:00
parent 0f7cde9766
commit df5345e570
14 changed files with 436 additions and 14 deletions
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4
input/methods
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@ -1,5 +1,5 @@
# RHF UHF KS MOM
F F T F
T F F F
# MP2* MP3 MP2-F12
F F F
# CCD pCCD DCD CCSD CCSD(T)
@ -15,7 +15,7 @@
# G0W0* evGW* qsGW* ufG0W0 ufGW
F F F F F
# G0T0 evGT qsGT
F F F
T F F
# MCMP2
F
# * unrestricted version available

6
input/options
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@ -7,14 +7,14 @@
# spin: TDA singlet triplet spin_conserved spin_flip
F T T T T
# GF: maxSCF thresh DIIS n_diis lin eta renorm reg
256 0.00001 T 5 T 0.0 3 F
256 0.00001 T 5 T 0.0 3 F
# GW: maxSCF thresh DIIS n_diis lin eta COHSEX SOSEX TDA_W G0W GW0 reg
256 0.00001 T 5 T 0.0 F F F F F F
256 0.00001 T 5 T 0.0 F F F F F F
# GT: maxSCF thresh DIIS n_diis lin eta TDA_T reg
256 0.00001 T 5 T 0.0 F F
# ACFDT: AC Kx XBS
F F F
# BSE: BSE dBSE dTDA evDyn
T T T F
T F T F
# MCMP2: nMC nEq nWalk dt nPrint iSeed doDrift
1000000 100000 10 0.3 10000 1234 T

2
mol/h2.xyz
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@ -1,4 +1,4 @@
2
H 0. 0. 0.
H 0. 0. 2.000000
H 0. 0. 1.5

79
src/GT/Bethe_Salpeter_Tmatrix_so.f90 Normal file
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@ -0,0 +1,79 @@
subroutine Bethe_Salpeter_Tmatrix_so(eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,Omega1,X1,Y1,Omega2,X2,Y2,rho1,rho2, &
ERI,eT,eGT,EcBSE)
! Compute the Bethe-Salpeter excitation energies with the T-matrix kernel
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
integer,intent(in) :: nOO
integer,intent(in) :: nVV
double precision,intent(in) :: eT(nBas)
double precision,intent(in) :: eGT(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
double precision,intent(in) :: Omega1(nVV)
double precision,intent(in) :: X1(nVV,nVV)
double precision,intent(in) :: Y1(nOO,nVV)
double precision,intent(in) :: Omega2(nOO)
double precision,intent(in) :: X2(nVV,nOO)
double precision,intent(in) :: Y2(nOO,nOO)
double precision,intent(in) :: rho1(nBas,nBas,nVV)
double precision,intent(in) :: rho2(nBas,nBas,nOO)
! Local variables
integer :: ispin
double precision :: EcRPA
double precision,allocatable :: TA(:,:),TB(:,:)
double precision,allocatable :: OmBSE(:)
double precision,allocatable :: XpY_BSE(:,:)
double precision,allocatable :: XmY_BSE(:,:)
! Output variables
double precision,intent(out) :: EcBSE
! Memory allocation
allocate(TA(nS,nS),TB(nS,nS),OmBSE(nS),XpY_BSE(nS,nS),XmY_BSE(nS,nS))
!------------------!
! Compute T-matrix !
!------------------!
ispin = 4
call linear_response_pp(ispin,.false.,nBas,nC,nO,nV,nR,nOO,nVV,1d0,eT,ERI, &
Omega1,X1,Y1,Omega2,X2,Y2,EcRPA)
call static_Tmatrix_A(eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,1d0,Omega1,rho1,Omega2,rho2,TA)
call static_Tmatrix_B(eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,1d0,Omega1,rho1,Omega2,rho2,TB)
!------------------!
! Singlet manifold !
!------------------!
ispin = 3
EcBSE = 0d0
! Compute BSE singlet excitation energies
call linear_response_Tmatrix(ispin,.false.,.false.,eta,nBas,nC,nO,nV,nR,nS,1d0,eGT,ERI,TA,TB, &
EcBSE,OmBSE,XpY_BSE,XmY_BSE)
call print_excitation('BSE@GT ',ispin,nS,OmBSE)
end subroutine Bethe_Salpeter_Tmatrix_so

4
src/GT/G0T0.f90
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@ -184,8 +184,12 @@ subroutine G0T0(doACFDT,exchange_kernel,doXBS,BSE,TDA_T,TDA,dBSE,dTDA,evDyn,sing
if(linearize) then
! eG0T0(:) = eHF(:) + Z(:)*SigT(:)
eG0T0(:) = eHF(:) + Z(:)*(SigX(:) + SigT(:) - Vxc(:))
call matout(nBas,1,SigX)
call matout(nBas,1,Vxc)
else
eG0T0(:) = eHF(:) + SigX(:) + SigT(:) - Vxc(:)

80
src/GT/excitation_density_Tmatrix_so.f90 Normal file
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@ -0,0 +1,80 @@
subroutine excitation_density_Tmatrix_so(nBas,nC,nO,nV,nR,nOO,nVV,ERI,X1,Y1,rho1,X2,Y2,rho2)
! Compute excitation densities for T-matrix self-energy
implicit none
! Input variables
integer,intent(in) :: nBas,nC,nO,nV,nR,nOO,nVV
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
double precision,intent(in) :: X1(nVV,nVV)
double precision,intent(in) :: Y1(nOO,nVV)
double precision,intent(in) :: X2(nVV,nOO)
double precision,intent(in) :: Y2(nOO,nOO)
! Local variables
integer :: j,k,l
integer :: b,c,d
integer :: p,q
integer :: ab,cd,ij,kl
double precision,external :: Kronecker_delta
! Output variables
double precision,intent(out) :: rho1(nBas,nBas,nVV)
double precision,intent(out) :: rho2(nBas,nBAs,nOO)
! Initialization
rho1(:,:,:) = 0d0
rho2(:,:,:) = 0d0
do p=nC+1,nBas-nR
do q=nC+1,nBas-nR
do ab=1,nVV
cd = 0
do c=nO+1,nBas-nR
do d=c+1,nBas-nR
cd = cd + 1
rho1(p,q,ab) = rho1(p,q,ab) + (ERI(p,q,c,d) - ERI(p,q,d,c))*X1(cd,ab)
end do
end do
kl = 0
do k=nC+1,nO
do l=k+1,nO
kl = kl + 1
rho1(p,q,ab) = rho1(p,q,ab) + (ERI(p,q,k,l) - ERI(p,q,l,k))*Y1(kl,ab)
end do
end do
end do
do ij=1,nOO
cd = 0
do c=nO+1,nBas-nR
do d=c+1,nBas-nR
cd = cd + 1
rho2(p,q,ij) = rho2(p,q,ij) + (ERI(p,q,c,d) - ERI(p,q,d,c))*X2(cd,ij)
end do
end do
kl = 0
do k=nC+1,nO
do l=k+1,nO
kl = kl + 1
rho2(p,q,ij) = rho2(p,q,ij) + (ERI(p,q,k,l) - ERI(p,q,l,k))*Y2(kl,ij)
end do
end do
end do
end do
end do
end subroutine excitation_density_Tmatrix_so

63
src/GT/renormalization_factor_Tmatrix_so.f90 Normal file
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@ -0,0 +1,63 @@
subroutine renormalization_factor_Tmatrix_so(eta,nBas,nC,nO,nV,nR,nOO,nVV,e,Omega1,rho1,Omega2,rho2,Z)
! Compute renormalization factor of the T-matrix self-energy
implicit none
include 'parameters.h'
! Input variables
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
integer,intent(in) :: nOO
integer,intent(in) :: nVV
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Omega1(nVV)
double precision,intent(in) :: rho1(nBas,nBas,nVV)
double precision,intent(in) :: Omega2(nOO)
double precision,intent(in) :: rho2(nBas,nBas,nOO)
! Local variables
integer :: i,j,k,l,a,b,c,d,p,cd,kl
double precision :: eps
! Output variables
double precision,intent(out) :: Z(nBas)
! Initialize
Z(:) = 0d0
!----------------------------------------------
! T-matrix renormalization factor in the spinorbital basis
!----------------------------------------------
! Occupied part of the T-matrix self-energy
do p=nC+1,nBas-nR
do i=nC+1,nO
do cd=1,nVV
eps = e(p) + e(i) - Omega1(cd)
Z(p) = Z(p) + (rho1(p,i,cd)/eps)**2
enddo
enddo
enddo
! Virtual part of the T-matrix self-energy
do p=nC+1,nBas-nR
do a=nO+1,nBas-nR
do kl=1,nOO
eps = e(p) + e(a) - Omega2(kl)
Z(p) = Z(p) + (rho2(p,a,kl)/eps)**2
enddo
enddo
enddo
! Compute renormalization factor from derivative of SigT
Z(:) = 1d0/(1d0 + Z(:))
end subroutine renormalization_factor_Tmatrix_so

63
src/GT/self_energy_Tmatrix_diag_so.f90 Normal file
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@ -0,0 +1,63 @@
subroutine self_energy_Tmatrix_diag_so(eta,nBas,nC,nO,nV,nR,nOO,nVV,e,Omega1,rho1,Omega2,rho2,SigT)
! Compute diagonal of the correlation part of the T-matrix self-energy
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) :: nOO
integer,intent(in) :: nVV
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Omega1(nVV)
double precision,intent(in) :: rho1(nBas,nBas,nVV)
double precision,intent(in) :: Omega2(nOO)
double precision,intent(in) :: rho2(nBas,nBas,nOO)
! Local variables
integer :: i,j,k,l,a,b,c,d,p,cd,kl
double precision :: eps
! Output variables
double precision,intent(out) :: SigT(nBas)
! Initialize
SigT(:) = 0d0
!----------------------------------------------
! T-matrix self-energy in the spinorbital basis
!----------------------------------------------
! Occupied part of the T-matrix self-energy
do p=nC+1,nBas-nR
do i=nC+1,nO
do cd=1,nVV
eps = e(p) + e(i) - Omega1(cd)
SigT(p) = SigT(p) + rho1(p,i,cd)**2/eps
enddo
enddo
enddo
! Virtual part of the T-matrix self-energy
do p=nC+1,nBas-nR
do a=nO+1,nBas-nR
do kl=1,nOO
eps = e(p) + e(a) - Omega2(kl)
SigT(p) = SigT(p) + rho2(p,a,kl)**2/eps
enddo
enddo
enddo
end subroutine self_energy_Tmatrix_diag_so

124
src/GT/soG0T0.f90 Normal file
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@ -0,0 +1,124 @@
subroutine soG0T0(eta,nBas,nC,nO,nV,nR,ENuc,ERHF,ERI,eHF)
! Perform G0W0 calculation with a T-matrix self-energy (G0T0) in the spinorbital basis
implicit none
include 'parameters.h'
! Input variables
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
double precision,intent(in) :: ENuc
double precision,intent(in) :: ERHF
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: ispin
integer :: nOO
integer :: nVV
double precision :: EcRPA
double precision :: EcGM
double precision :: EcBSE
integer :: nBas2,nC2,nO2,nV2,nR2,nS2
double precision,allocatable :: Omega1(:)
double precision,allocatable :: X1(:,:)
double precision,allocatable :: Y1(:,:)
double precision,allocatable :: rho1(:,:,:)
double precision,allocatable :: Omega2(:)
double precision,allocatable :: X2(:,:)
double precision,allocatable :: Y2(:,:)
double precision,allocatable :: rho2(:,:,:)
double precision,allocatable :: SigT(:)
double precision,allocatable :: Z(:)
double precision,allocatable :: eG0T0(:)
double precision,allocatable :: seHF(:)
double precision,allocatable :: sERI(:,:,:,:)
! Hello world
write(*,*)
write(*,*)'************************************************'
write(*,*)'| One-shot soG0T0 calculation |'
write(*,*)'************************************************'
write(*,*)
! Define occupied and virtual spaces
nBas2 = 2*nBas
nO2 = 2*nO
nV2 = 2*nV
nC2 = 2*nC
nR2 = 2*nR
nS2 = nO2*nV2
! Spatial to spin orbitals
allocate(seHF(nBas2),sERI(nBas2,nBas2,nBas2,nBas2))
call spatial_to_spin_MO_energy(nBas,eHF,nBas2,seHF)
call spatial_to_spin_ERI(nBas,ERI,nBas2,sERI)
! Dimensions of the rr-RPA linear reponse matrices
nOO = nO2*(nO2 - 1)/2
nVV = nV2*(nV2 - 1)/2
! Memory allocation
allocate(Omega1(nVV),X1(nVV,nVV),Y1(nOO,nVV), &
Omega2(nOO),X2(nVV,nOO),Y2(nOO,nOO), &
rho1(nBas2,nBas2,nVV),rho2(nBas2,nBas2,nOO), &
eG0T0(nBas2),SigT(nBas2),Z(nBas2))
!----------------------------------------------
! Spinorbital basis
!----------------------------------------------
ispin = 4
! Compute linear response
call linear_response_pp(ispin,.false.,nBas2,nC2,nO2,nV2,nR2,nOO,nVV,1d0,seHF,sERI, &
Omega1,X1,Y1,Omega2,X2,Y2,EcRPA)
call print_excitation('pp-RPA (N+2)',ispin,nVV,Omega1)
call print_excitation('pp-RPA (N-2)',ispin,nOO,Omega2)
! Compute excitation densities for the T-matrix
call excitation_density_Tmatrix_so(nBas2,nC2,nO2,nV2,nR2,nOO,nVV,sERI,X1,Y1,rho1,X2,Y2,rho2)
!----------------------------------------------
! Compute T-matrix version of the self-energy
!----------------------------------------------
call self_energy_Tmatrix_diag_so(eta,nBas2,nC2,nO2,nV2,nR2,nOO,nVV,seHF, &
Omega1,rho1,Omega2,rho2,SigT)
! Compute renormalization factor for T-matrix self-energy
call renormalization_factor_Tmatrix_so(eta,nBas2,nC2,nO2,nV2,nR2,nOO,nVV,seHF, &
Omega1,rho1,Omega2,rho2,Z)
!----------------------------------------------
! Solve the quasi-particle equation
!----------------------------------------------
eG0T0(:) = seHF(:) + Z(:)*SigT(:)
!----------------------------------------------
! Dump results
!----------------------------------------------
call print_G0T0(nBas2,nO2,seHF,ENuc,ERHF,SigT,Z,eG0T0,EcGM,EcRPA)
call Bethe_Salpeter_Tmatrix_so(eta,nBas2,nC2,nO2,nV2,nR2,nS2,nOO,nVV,Omega1,X1,Y1,Omega2,X2,Y2,rho1,rho2, &
sERI,seHF,eG0T0,EcBSE)
end subroutine soG0T0

3
src/GW/self_energy_exchange_diag.f90
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@ -14,7 +14,8 @@ subroutine self_energy_exchange_diag(nBas,c,P,ERI,SigX)
! Local variables
integer :: q,mu,nu
integer :: mu,nu
integer :: q
double precision,allocatable :: Fx(:,:)
! Output variables

2
src/HF/RHF.f90
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@ -205,6 +205,6 @@ subroutine RHF(maxSCF,thresh,max_diis,guess_type,nNuc,ZNuc,rNuc,ENuc,nBas,nO,S,T
! Compute Vx for post-HF calculations
call mo_fock_exchange_potential(nBas,c,K,Vx)
call mo_fock_exchange_potential(nBas,c,P,ERI,Vx)
end subroutine RHF

2
src/HF/UHF.f90
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@ -253,7 +253,7 @@ subroutine UHF(maxSCF,thresh,max_diis,guess_type,mix,nNuc,ZNuc,rNuc,ENuc,nBas,nO
! Compute Vx for post-HF calculations
do ispin=1,nspin
call mo_fock_exchange_potential(nBas,c(:,:,ispin),K(:,:,ispin),Vx(:,ispin))
call mo_fock_exchange_potential(nBas,c(:,:,ispin),P(:,:,ispin),ERI,Vx(:,ispin))
end do
end subroutine UHF

17
src/HF/mo_fock_exchange_potential.f90
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@ -1,4 +1,4 @@
subroutine mo_fock_exchange_potential(nBas,c,Fx,Vx)
subroutine mo_fock_exchange_potential(nBas,c,P,ERI,Vx)
! Compute the exchange potential in the MO basis
@ -9,12 +9,14 @@ subroutine mo_fock_exchange_potential(nBas,c,Fx,Vx)
integer,intent(in) :: nBas
double precision,intent(in) :: c(nBas,nBas)
double precision,intent(in) :: Fx(nBas,nBas)
double precision,intent(in) :: P(nBas,nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: mu,nu
integer :: p
integer :: q
double precision,allocatable :: Fx(:,:)
! Output variables
@ -22,13 +24,18 @@ subroutine mo_fock_exchange_potential(nBas,c,Fx,Vx)
! Compute Vx
allocate(Fx(nBas,nBas))
call exchange_matrix_AO_basis(nBas,P,ERI,Fx)
Vx(:) = 0d0
do p=1,nBas
do q=1,nBas
do mu=1,nBas
do nu=1,nBas
Vx(p) = Vx(p) + c(mu,p)*Fx(mu,nu)*c(nu,p)
Vx(q) = Vx(q) + c(mu,q)*Fx(mu,nu)*c(nu,q)
end do
end do
end do
deallocate(Fx)
end subroutine mo_fock_exchange_potential

1
src/QuAcK/QuAcK.f90
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@ -1159,6 +1159,7 @@ program QuAcK
else
! call soG0T0(eta_GT,nBas,nC,nO,nV,nR,ENuc,ERHF,ERI_MO,eHF)
call G0T0(doACFDT,exchange_kernel,doXBS,BSE,TDA_T,TDA,dBSE,dTDA,evDyn,singlet,triplet, &
linGT,eta_GT,regGT,nBas,nC,nO,nV,nR,nS,ENuc,ERHF,ERI_AO,ERI_MO,dipole_int_MO, &
PHF,cHF,eHF,Vxc,eG0T0)