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ppBSE@G0W0

This commit is contained in:
Pierre-Francois Loos 2022-08-17 14:32:14 +02:00
parent 715c97a1e3
commit 93564f350d
20 changed files with 636 additions and 48 deletions
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2
input/methods
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@ -9,7 +9,7 @@
# CIS* CIS(D) CID CISD FCI
F F F F F
# RPA* RPAx* crRPA ppRPA
F F F F
F F F T
# G0F2* evGF2* qsGF2* G0F3 evGF3
F F F F F
# G0W0* evGW* qsGW* ufG0W0 ufGW

4
input/options
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@ -1,5 +1,5 @@
# HF: maxSCF thresh DIIS n_diis guess_type ortho_type mix_guess level_shift stability
512 0.0000001 T 5 2 1 F 1.0 F
512 0.0000001 T 5 2 1 F 0.0 F
# MP:
# CC: maxSCF thresh DIIS n_diis
@ -15,6 +15,6 @@
# ACFDT: AC Kx XBS
F F T
# BSE: BSE dBSE dTDA evDyn
T T T F
F F T F
# MCMP2: nMC nEq nWalk dt nPrint iSeed doDrift
1000000 100000 10 0.3 10000 1234 T

2
int/ERI.Hu.dat Normal file
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@ -0,0 +1,2 @@
1 1 1 1 1.
2 2 2 2 1.

2
int/Kin.Hu.dat Normal file
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@ -0,0 +1,2 @@
1 2 -1.0
2 1 -1.0

2
int/Nuc.Hu.dat Normal file
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@ -0,0 +1,2 @@
1 1 0.0
2 2 0.1

2
int/Ov.Hu.dat Normal file
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@ -0,0 +1,2 @@
1 1 1.0
2 2 1.0

0
int/x.Hu.dat Normal file
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0
int/y.Hu.dat Normal file
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0
int/z.Hu.dat Normal file
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136
src/GW/Bethe_Salpeter_pp.f90 Normal file
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@ -0,0 +1,136 @@
subroutine Bethe_Salpeter_pp(TDA_W,TDA,singlet,triplet,eta,nBas,nC,nO,nV,nR,nS,ERI,dipole_int,eW,eGW,EcBSE)
! Compute the Bethe-Salpeter excitation energies at the pp level
implicit none
include 'parameters.h'
! Input variables
logical,intent(in) :: TDA_W
logical,intent(in) :: TDA
logical,intent(in) :: singlet
logical,intent(in) :: triplet
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) :: eW(nBas)
double precision,intent(in) :: eGW(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
double precision,intent(in) :: dipole_int(nBas,nBas,ncart)
! Local variables
integer :: ispin
integer :: isp_W
integer :: nOO
integer :: nVV
double precision :: EcRPA
double precision,allocatable :: OmRPA(:)
double precision,allocatable :: XpY_RPA(:,:)
double precision,allocatable :: XmY_RPA(:,:)
double precision,allocatable :: rho_RPA(:,:,:)
double precision,allocatable :: Omega1(:)
double precision,allocatable :: X1(:,:)
double precision,allocatable :: Y1(:,:)
double precision,allocatable :: Omega2(:)
double precision,allocatable :: X2(:,:)
double precision,allocatable :: Y2(:,:)
double precision,allocatable :: WB(:,:)
double precision,allocatable :: WC(:,:)
double precision,allocatable :: WD(:,:)
! Output variables
double precision,intent(out) :: EcBSE(nspin)
!---------------------------------
! Compute (singlet) RPA screening
!---------------------------------
isp_W = 1
EcRPA = 0d0
! Memory allocation
allocate(OmRPA(nS),XpY_RPA(nS,nS),XmY_RPA(nS,nS),rho_RPA(nBas,nBas,nS))
call linear_response(isp_W,.true.,TDA_W,eta,nBas,nC,nO,nV,nR,nS,1d0,eW,ERI, &
EcRPA,OmRPA,XpY_RPA,XmY_RPA)
call excitation_density(nBas,nC,nO,nR,nS,ERI,XpY_RPA,rho_RPA)
!-------------------
! Singlet manifold
!-------------------
if(singlet) then
ispin = 1
EcBSE(ispin) = 0d0
nOO = nO*(nO+1)/2
nVV = nV*(nV+1)/2
allocate(Omega1(nVV),X1(nVV,nVV),Y1(nOO,nVV), &
Omega2(nOO),X2(nVV,nOO),Y2(nOO,nOO), &
WB(nVV,nOO),WC(nVV,nVV),WD(nOO,nOO))
if(.not.TDA) call static_screening_WB_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,1d0,ERI,OmRPA,rho_RPA,WB)
call static_screening_WC_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,1d0,ERI,OmRPA,rho_RPA,WC)
call static_screening_WD_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,1d0,ERI,OmRPA,rho_RPA,WD)
! Compute BSE excitation energies
call linear_response_pp_BSE(ispin,TDA,.true.,nBas,nC,nO,nV,nR,nOO,nVV,1d0,eGW,ERI,WB,WC,WD, &
Omega1,X1,Y1,Omega2,X2,Y2,EcBSE(ispin))
call print_excitation('pp-BSE (N+2)',ispin,nVV,Omega1)
call print_excitation('pp-BSE (N-2)',ispin,nOO,Omega2)
deallocate(Omega1,X1,Y1,Omega2,X2,Y2,WB,WC,WD)
end if
!-------------------
! Triplet manifold
!-------------------
if(triplet) then
ispin = 2
EcBSE(ispin) = 0d0
nOO = nO*(nO-1)/2
nVV = nV*(nV-1)/2
allocate(Omega1(nVV),X1(nVV,nVV),Y1(nOO,nVV), &
Omega2(nOO),X2(nVV,nOO),Y2(nOO,nOO), &
WB(nVV,nOO),WC(nVV,nVV),WD(nOO,nOO))
if(.not.TDA) call static_screening_WB_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,1d0,ERI,OmRPA,rho_RPA,WB)
call static_screening_WC_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,1d0,ERI,OmRPA,rho_RPA,WC)
call static_screening_WD_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,1d0,ERI,OmRPA,rho_RPA,WD)
! Compute BSE excitation energies
call linear_response_pp_BSE(ispin,TDA,.true.,nBas,nC,nO,nV,nR,nOO,nVV,1d0,eGW,ERI,WB,WC,WD, &
Omega1,X1,Y1,Omega2,X2,Y2,EcBSE(ispin))
call print_excitation('pp-BSE (N+2)',ispin,nVV,Omega1)
call print_excitation('pp-BSE (N-2)',ispin,nOO,Omega2)
deallocate(Omega1,X1,Y1,Omega2,X2,Y2,WB,WC,WD)
end if
end subroutine Bethe_Salpeter_pp

17
src/GW/G0W0.f90
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@ -15,6 +15,7 @@ subroutine G0W0(doACFDT,exchange_kernel,doXBS,COHSEX,BSE,TDA_W,TDA, &
logical,intent(in) :: doXBS
logical,intent(in) :: COHSEX
logical,intent(in) :: BSE
logical :: ppBSE = .true.
logical,intent(in) :: TDA_W
logical,intent(in) :: TDA
logical,intent(in) :: dBSE
@ -49,6 +50,7 @@ subroutine G0W0(doACFDT,exchange_kernel,doXBS,COHSEX,BSE,TDA_W,TDA, &
double precision :: EcRPA
double precision :: EcBSE(nspin)
double precision :: EcAC(nspin)
double precision :: EcppBSE(nspin)
double precision :: EcGM
double precision,allocatable :: SigX(:)
double precision,allocatable :: SigC(:)
@ -238,4 +240,19 @@ subroutine G0W0(doACFDT,exchange_kernel,doXBS,COHSEX,BSE,TDA_W,TDA, &
end if
if(ppBSE) then
call Bethe_Salpeter_pp(TDA_W,TDA,singlet,triplet,eta,nBas,nC,nO,nV,nR,nS,ERI_MO,dipole_int,eHF,eG0W0,EcppBSE)
write(*,*)
write(*,*)'-------------------------------------------------------------------------------'
write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@G0W0 correlation energy (singlet) =',EcppBSE(1)
write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@G0W0 correlation energy (triplet) =',3d0*EcppBSE(2)
write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@G0W0 correlation energy =',EcppBSE(1) + 3d0*EcppBSE(2)
write(*,'(2X,A50,F20.10)') 'Tr@ppBSE@G0W0 total energy =',ENuc + ERHF + EcppBSE(1) + 3d0*EcppBSE(2)
write(*,*)'-------------------------------------------------------------------------------'
write(*,*)
end if
end subroutine G0W0

99
src/GW/static_screening_WB_pp.f90 Normal file
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@ -0,0 +1,99 @@
subroutine static_screening_WB_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,lambda,ERI,Omega,rho,WB)
! Compute the VVOO block of the static screening W for the pp-BSE
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: ispin
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) :: eta
double precision,intent(in) :: lambda
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
double precision,intent(in) :: Omega(nS)
double precision,intent(in) :: rho(nBas,nBas,nS)
! Local variables
double precision :: chi
double precision :: eps
integer :: a,b,i,j,ab,ij,m
! Output variables
double precision,intent(out) :: WB(nVV,nOO)
! Initialization
WB(:,:) = 0d0
!---------------!
! Singlet block !
!---------------!
if(ispin == 1) then
ab = 0
do a=nO+1,nBas-nR
do b=a,nBas-nR
ab = ab + 1
ij = 0
do i=nC+1,nO
do j=i,nO
ij = ij + 1
chi = 0d0
do m=1,nS
eps = Omega(m)**2 + eta**2
chi = chi + rho(a,j,m)*rho(b,i,m)*Omega(m)/eps
enddo
WB(ab,ij) = WB(ab,ij) - 4d0*lambda*chi
end do
end do
end do
end do
end if
!---------------!
! Triplet block !
!---------------!
if(ispin == 2) then
ab = 0
do a=nO+1,nBas-nR
do b=a+1,nBas-nR
ab = ab + 1
ij = 0
do i=nC+1,nO
do j=i+1,nO
ij = ij + 1
chi = 0d0
do m=1,nS
eps = Omega(m)**2 + eta**2
chi = chi + rho(a,j,m)*rho(b,i,m)*Omega(m)/eps
enddo
WB(ab,ij) = WB(ab,ij) - 4d0*lambda*chi
end do
end do
end do
end do
end if
end subroutine static_screening_WB_pp

100
src/GW/static_screening_WC_pp.f90 Normal file
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@ -0,0 +1,100 @@
subroutine static_screening_WC_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,lambda,ERI,Omega,rho,WC)
! Compute the VVVV block of the static screening W for the pp-BSE
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: ispin
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) :: eta
double precision,intent(in) :: lambda
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
double precision,intent(in) :: Omega(nS)
double precision,intent(in) :: rho(nBas,nBas,nS)
! Local variables
double precision :: chi
double precision :: eps
integer :: a,b,c,d,ab,cd,m
! Output variables
double precision,intent(out) :: WC(nVV,nVV)
! Initialization
WC(:,:) = 0d0
!---------------!
! Singlet block !
!---------------!
if(ispin == 1) then
ab = 0
do a=nO+1,nBas-nR
do b=a,nBas-nR
ab = ab + 1
cd = 0
do c=nO+1,nBas-nR
do d=c,nBas-nR
cd = cd + 1
chi = 0d0
do m=1,nS
eps = Omega(m)**2 + eta**2
chi = chi + rho(a,d,m)*rho(b,c,m)*Omega(m)/eps
enddo
WC(ab,cd) = WC(ab,cd) - 4d0*lambda*chi
end do
end do
end do
end do
end if
!---------------!
! Triplet block !
!---------------!
if(ispin == 2) then
ab = 0
do a=nO+1,nBas-nR
do b=a+1,nBas-nR
ab = ab + 1
cd = 0
do c=nO+1,nBas-nR
do d=c+1,nBas-nR
cd = cd + 1
chi = 0d0
do m=1,nS
eps = Omega(m)**2 + eta**2
chi = chi + rho(a,d,m)*rho(b,c,m)*Omega(m)/eps
enddo
WC(ab,cd) = WC(ab,cd) - 4d0*lambda*chi
end do
end do
end do
end do
end if
end subroutine static_screening_WC_pp

99
src/GW/static_screening_WD_pp.f90 Normal file
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@ -0,0 +1,99 @@
subroutine static_screening_WD_pp(ispin,eta,nBas,nC,nO,nV,nR,nS,nOO,nVV,lambda,ERI,Omega,rho,WD)
! Compute the OOOO block of the static screening W for the pp-BSE
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: ispin
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) :: eta
double precision,intent(in) :: lambda
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
double precision,intent(in) :: Omega(nS)
double precision,intent(in) :: rho(nBas,nBas,nS)
! Local variables
double precision :: chi
double precision :: eps
integer :: i,j,k,l,ij,kl,m
! Output variables
double precision,intent(out) :: WD(nOO,nOO)
! Initialization
WD(:,:) = 0d0
!---------------!
! Singlet block !
!---------------!
if(ispin == 1) then
ij = 0
do i=nC+1,nO
do j=i,nO
ij = ij + 1
kl = 0
do k=nC+1,nO
do l=k,nO
kl = kl + 1
chi = 0d0
do m=1,nS
eps = Omega(m)**2 + eta**2
chi = chi + rho(i,l,m)*rho(j,k,m)*Omega(m)/eps
enddo
WD(ij,kl) = WD(ij,kl) - 4d0*lambda*chi
end do
end do
end do
end do
end if
!---------------!
! Triplet block !
!---------------!
if(ispin == 2) then
ij = 0
do i=nC+1,nO
do j=i+1,nO
ij = ij + 1
kl = 0
do k=nC+1,nO
do l=k+1,nO
kl = kl + 1
chi = 0d0
do m=1,nS
eps = Omega(m)**2 + eta**2
chi = chi + rho(i,l,m)*rho(j,k,m)*Omega(m)/eps
enddo
WD(ij,kl) = WD(ij,kl) - 4d0*lambda*chi
end do
end do
end do
end do
end if
end subroutine static_screening_WD_pp

2
src/LR/linear_response_BSE.f90
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@ -1,6 +1,6 @@
subroutine linear_response_BSE(ispin,dRPA,TDA,BSE,eta,nBas,nC,nO,nV,nR,nS,lambda,e,ERI,A_BSE,B_BSE,Ec,Omega,XpY,XmY)
! Compute linear response
! Compute linear response with BSE additional terms
implicit none
include 'parameters.h'

56
src/LR/linear_response_B_pp.f90
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@ -8,7 +8,13 @@ subroutine linear_response_B_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,ERI,B_pp)
! Input variables
integer,intent(in) :: ispin
integer,intent(in) :: nBas,nC,nO,nV,nR,nOO,nVV
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) :: lambda
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
@ -27,11 +33,11 @@ subroutine linear_response_B_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,ERI,B_pp)
ab = 0
do a=nO+1,nBas-nR
do b=a,nBas-nR
do b=a,nBas-nR
ab = ab + 1
ij = 0
do i=nC+1,nO
do j=i,nO
do j=i,nO
ij = ij + 1
B_pp(ab,ij) = lambda*(ERI(a,b,i,j) + ERI(a,b,j,i))/sqrt((1d0 + Kronecker_delta(a,b))*(1d0 + Kronecker_delta(i,j)))
@ -43,28 +49,6 @@ subroutine linear_response_B_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,ERI,B_pp)
end if
! Build the alpha-beta block of the B matrix
if(ispin == 3) then
ab = 0
do a=nO+1,nBas-nR
do b=nO+1,nBas-nR
ab = ab + 1
ij = 0
do i=nC+1,nO
do j=nC+1,nO
ij = ij + 1
B_pp(ab,ij) = lambda*ERI(a,b,i,j)
end do
end do
end do
end do
end if
! Build the B matrix for the triplet manifold, or alpha-alpha, or in the spin-orbital basis
if(ispin == 2 .or. ispin == 4) then
@ -87,4 +71,26 @@ subroutine linear_response_B_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,ERI,B_pp)
end if
! Build the alpha-beta block of the B matrix
if(ispin == 3) then
ab = 0
do a=nO+1,nBas-nR
do b=nO+1,nBas-nR
ab = ab + 1
ij = 0
do i=nC+1,nO
do j=nC+1,nO
ij = ij + 1
B_pp(ab,ij) = lambda*ERI(a,b,i,j)
end do
end do
end do
end do
end if
end subroutine linear_response_B_pp

8
src/LR/linear_response_C_pp.f90
View File

@ -8,7 +8,13 @@ subroutine linear_response_C_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,C_pp
! Input variables
integer,intent(in) :: ispin
integer,intent(in) :: nBas,nC,nO,nV,nR,nOO,nVV
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) :: lambda
double precision,intent(in) :: e(nBas),ERI(nBas,nBas,nBas,nBas)

8
src/LR/linear_response_D_pp.f90
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@ -8,7 +8,13 @@ subroutine linear_response_D_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,D_pp
! Input variables
integer,intent(in) :: ispin
integer,intent(in) :: nBas,nC,nO,nV,nR,nOO,nVV
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) :: lambda
double precision,intent(in) :: e(nBas),ERI(nBas,nBas,nBas,nBas)

24
src/LR/linear_response_pp.f90
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@ -63,22 +63,21 @@ subroutine linear_response_pp(ispin,TDA,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,Om
call linear_response_C_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,C)
call linear_response_D_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,D)
!call matout(nVV,nVV,C)
if(TDA) then
X1(:,:) = +C(:,:)
Y1(:,:) = 0d0
call diagonalize_matrix(nVV,X1,Omega1)
if(nVV > 0) call diagonalize_matrix(nVV,X1,Omega1)
X2(:,:) = 0d0
Y2(:,:) = -D(:,:)
call diagonalize_matrix(nOO,Y2,Omega2)
if(nOO > 0) call diagonalize_matrix(nOO,Y2,Omega2)
else
call linear_response_B_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,ERI,B)
!call matout(nVV,nOO,B)
!call matout(nOO,nOO,D)
! Diagonal blocks
M( 1:nVV , 1:nVV) = + C(1:nVV,1:nVV)
@ -88,8 +87,8 @@ subroutine linear_response_pp(ispin,TDA,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,Om
M( 1:nVV ,nVV+1:nOO+nVV) = - B(1:nVV,1:nOO)
M(nVV+1:nOO+nVV, 1:nVV) = + transpose(B(1:nVV,1:nOO))
!call matout(nOO+nVV,nOO+nVV,M)
! Diagonalize the p-h matrix
! Diagonalize the p-p matrix
if(nOO+nVV > 0) call diagonalize_general_matrix(nOO+nVV,M,Omega,Z)
@ -97,16 +96,6 @@ subroutine linear_response_pp(ispin,TDA,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,Om
call sort_ppRPA(nOO,nVV,Omega(:),Z(:,:),Omega1(:),X1(:,:),Y1(:,:),Omega2(:),X2(:,:),Y2(:,:))
! print*,'Omega1'
! call matout(nVV,1,Omega1)
! print*,'X1t.X1 - Y1t.Y1'
! call matout(nVV,nVV,matmul(transpose(X1),X1) - matmul(transpose(Y1),Y1))
! print*,'Omega2'
! call matout(nOO,1,Omega2)
! print*,'Y2t.Y2 - X2t.X2'
! call matout(nOO,nOO,matmul(transpose(Y2),Y2) - matmul(transpose(X2),X2))
end if
! Compute the RPA correlation energy
@ -114,6 +103,7 @@ subroutine linear_response_pp(ispin,TDA,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,Om
EcRPA = 0.5d0*( sum(Omega1(:)) - sum(Omega2(:)) - trace_matrix(nVV,C(:,:)) - trace_matrix(nOO,D(:,:)) )
EcRPA1 = +sum(Omega1(:)) - trace_matrix(nVV,C(:,:))
EcRPA2 = -sum(Omega2(:)) - trace_matrix(nOO,D(:,:))
if(abs(EcRPA - EcRPA1) > 1d-6 .or. abs(EcRPA - EcRPA2) > 1d-6) &
print*,'!!! Issue in pp-RPA linear reponse calculation RPA1 != RPA2 !!!'

121
src/LR/linear_response_pp_BSE.f90 Normal file
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@ -0,0 +1,121 @@
subroutine linear_response_pp_BSE(ispin,TDA,BSE,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,WB,WC,WD,Omega1,X1,Y1,Omega2,X2,Y2,EcBSE)
! Compute the p-p channel of BSE
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: ispin
logical,intent(in) :: TDA
logical,intent(in) :: BSE
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) :: lambda
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
double precision,intent(in) :: WB(nVV,nOO)
double precision,intent(in) :: WC(nVV,nVV)
double precision,intent(in) :: WD(nOO,nOO)
! Local variables
integer :: ab,cd,ij,kl
integer :: p,q,r,s
double precision :: trace_matrix
double precision :: EcBSE1
double precision :: EcBSE2
double precision,allocatable :: B(:,:)
double precision,allocatable :: C(:,:)
double precision,allocatable :: D(:,:)
double precision,allocatable :: M(:,:)
double precision,allocatable :: Z(:,:)
double precision,allocatable :: Omega(:)
! Output variables
double precision,intent(out) :: Omega1(nVV)
double precision,intent(out) :: X1(nVV,nVV)
double precision,intent(out) :: Y1(nOO,nVV)
double precision,intent(out) :: Omega2(nOO)
double precision,intent(out) :: X2(nVV,nOO)
double precision,intent(out) :: Y2(nOO,nOO)
double precision,intent(out) :: EcBSE
! Memory allocation
allocate(B(nVV,nOO),C(nVV,nVV),D(nOO,nOO),M(nOO+nVV,nOO+nVV),Z(nOO+nVV,nOO+nVV),Omega(nOO+nVV))
!-------------------------------------------------!
! Solve the p-p eigenproblem !
!-------------------------------------------------!
! !
! | C B | | X1 X2 | | w1 0 | | X1 X2 | !
! | | | | = | | | | !
! | -Bt -D | | Y1 Y2 | | 0 w2 | | Y1 Y2 | !
! !
!-------------------------------------------------!
! Build B, C and D matrices for the pp channel
call linear_response_C_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,C)
call linear_response_D_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,e,ERI,D)
if(BSE) then
C(:,:) = C(:,:) - WC(:,:)
D(:,:) = D(:,:) - WD(:,:)
end if
if(TDA) then
X1(:,:) = +C(:,:)
Y1(:,:) = 0d0
if(nVV > 0) call diagonalize_matrix(nVV,X1,Omega1)
X2(:,:) = 0d0
Y2(:,:) = -D(:,:)
if(nOO > 0) call diagonalize_matrix(nOO,Y2,Omega2)
else
call linear_response_B_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,lambda,ERI,B)
if(BSE) B(:,:) = B(:,:) - WB(:,:)
! Diagonal blocks
M( 1:nVV , 1:nVV) = + C(1:nVV,1:nVV)
M(nVV+1:nVV+nOO,nVV+1:nVV+nOO) = - D(1:nOO,1:nOO)
! Off-diagonal blocks
M( 1:nVV ,nVV+1:nOO+nVV) = - B(1:nVV,1:nOO)
M(nVV+1:nOO+nVV, 1:nVV) = + transpose(B(1:nVV,1:nOO))
! Diagonalize the p-p matrix
if(nOO+nVV > 0) call diagonalize_general_matrix(nOO+nVV,M,Omega,Z)
! Split the various quantities in p-p and h-h parts
call sort_ppRPA(nOO,nVV,Omega,Z,Omega1,X1,Y1,Omega2,X2,Y2)
end if
! Compute the BSE correlation energy
EcBSE = 0.5d0*( sum(Omega1(:)) - sum(Omega2(:)) - trace_matrix(nVV,C(:,:)) - trace_matrix(nOO,D(:,:)) )
EcBSE1 = +sum(Omega1(:)) - trace_matrix(nVV,C(:,:))
EcBSE2 = -sum(Omega2(:)) - trace_matrix(nOO,D(:,:))
if(abs(EcBSE - EcBSE1) > 1d-6 .or. abs(EcBSE - EcBSE2) > 1d-6) &
print*,'!!! Issue in pp-BSE linear reponse calculation BSE1 != BSE2 !!!'
end subroutine linear_response_pp_BSE