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root search for cG0F2

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Loris Burth 2025-03-26 12:32:36 +01:00
parent ed7957600c
commit 541181594d
6 changed files with 330 additions and 1 deletions
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2
src/GF/cRG0F2.f90
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@ -93,7 +93,7 @@ subroutine cRG0F2(dotest,dophBSE,doppBSE,TDA,dBSE,dTDA,singlet,triplet,linearize
write(*,*) ' *** Quasiparticle energies obtained by root search *** NOT IMPLEMEMTED YET' write(*,*) ' *** Quasiparticle energies obtained by root search *** NOT IMPLEMEMTED YET'
write(*,*) write(*,*)
!call RGF2_QP_graph(eta,nOrb,nC,nO,nV,nR,eHF,ERI,eGFlin,eHF,eGF,Z) call cRGF2_QP_graph(eta,nOrb,nC,nO,nV,nR,eHF,e_cap,ERI,Re_eGFlin,Im_eGFlin,eHF,e_cap,Re_eGF,Im_eGF,Re_Z,Im_Z)
end if end if

59
src/GF/cRGF2_Im_SigC.f90 Normal file
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@ -0,0 +1,59 @@
double precision function cRGF2_Im_SigC(p,Re_w,Im_w,eta,nBas,nC,nO,nV,nR,eHF,e_cap,ERI)
! Compute diagonal of the correlation part of the self-energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: p
double precision,intent(in) :: Re_w
double precision,intent(in) :: Im_w
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: e_cap(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: i,j,a,b
double precision :: eps
double precision :: eta_tilde
double precision :: num
! Initialize
cRGF2_Im_SigC = 0d0
! Occupied part of the correlation self-energy
do i=nC+1,nO
do j=nC+1,nO
do a=nO+1,nBas-nR
eps = Re_w + eHF(a) - eHF(i) - eHF(j)
eta_tilde = eta - Im_w + e_cap(i) + e_cap(a) - e_cap(j)
num = (2d0*ERI(p,a,i,j) - ERI(p,a,j,i))*ERI(p,a,i,j)
cRGF2_Im_SigC = cRGF2_Im_SigC + num*eta_tilde/(eps**2 + eta_tilde**2)
end do
end do
end do
! Virtual part of the correlation self-energy
do i=nC+1,nO
do a=nO+1,nBas-nR
do b=nO+1,nBas-nR
eps = Re_w + eHF(i) - eHF(a) - eHF(b)
num = (2d0*ERI(p,i,a,b) - ERI(p,i,b,a))*ERI(p,i,a,b)
eta_tilde = eta + Im_w - e_cap(a) - e_cap(b) + e_cap(i)
cRGF2_Im_SigC = cRGF2_Im_SigC - num*eta_tilde/(eps**2 + eta_tilde**2)
end do
end do
end do
end function

56
src/GF/cRGF2_Im_dSigC.f90 Normal file
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@ -0,0 +1,56 @@
double precision function cRGF2_Im_dSigC(p,Re_w,Im_w,eta,nBas,nC,nO,nV,nR,eHF,e_cap,ERI)
! Compute diagonal of the correlation part of the self-energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: p
double precision,intent(in) :: Re_w
double precision,intent(in) :: Im_w
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: e_cap(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: i,j,a,b
double precision :: eps
double precision :: eta_tilde
double precision :: num
! Initialize
cRGF2_Im_dSigC = 0d0
! Occupied part of the correlation self-energy
do i=nC+1,nO
do j=nC+1,nO
do a=nO+1,nBas-nR
eps = Re_w + eHF(a) - eHF(i) - eHF(j)
eta_tilde = eta - Im_w + e_cap(i) + e_cap(a) - e_cap(j)
num = (2d0*ERI(p,a,i,j) - ERI(p,a,j,i))*ERI(p,a,i,j)
cRGF2_Im_dSigC = cRGF2_Im_dSigC - 2d0*num*eps*eta_tilde/(eps**2 + eta_tilde**2)**2
end do
end do
end do
! Virtual part of the correlation self-energy
do i=nC+1,nO
do a=nO+1,nBas-nR
do b=nO+1,nBas-nR
eps = Re_w + eHF(i) - eHF(a) - eHF(b)
num = (2d0*ERI(p,i,a,b) - ERI(p,i,b,a))*ERI(p,i,a,b)
eta_tilde = eta + Im_w - e_cap(a) - e_cap(b) + e_cap(i)
cRGF2_Im_dSigC = cRGF2_Im_dSigC + 2d0*num*eps*eta_tilde/(eps**2 + eta_tilde**2)**2
end do
end do
end do
end function

97
src/GF/cRGF2_QP_graph.f90 Normal file
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@ -0,0 +1,97 @@
subroutine cRGF2_QP_graph(eta,nBas,nC,nO,nV,nR,eHF,e_cap,ERI,Re_eGFlin,Im_eGFlin,Re_eOld,Im_eold,Re_eGF,Im_eGF,Re_Z,Im_Z)
! Compute the graphical solution of the GF2 QP equation
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
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: e_cap(nBas)
double precision,intent(in) :: Re_eGFlin(nBas)
double precision,intent(in) :: Im_eGFlin(nBas)
double precision,intent(in) :: Re_eOld(nBas)
double precision,intent(in) :: Im_eOld(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: p
integer :: nIt
integer,parameter :: maxIt = 64
double precision,parameter :: thresh = 1d-6
double precision,external :: cRGF2_Re_SigC,cRGF2_Im_SigC,cRGF2_Re_dSigC,cRGF2_Im_dSigC
double precision :: Re_SigC,Im_SigC,Re_dSigC,Im_dSigC
double precision :: Re_f,Im_f,Re_df,Im_df
double precision :: Re_w,Im_w
! Output variables
double precision,intent(out) :: Re_eGF(nBas),Im_eGF(nBas)
double precision,intent(out) :: Re_Z(nBas),Im_Z(nBas)
! Run Newton's algorithm to find the root
write(*,*)'-----------------------------------------------------'
write(*,'(A5,1X,A3,1X,A15,1X,A15,1X,A10)') 'Orb.','It.','Re(e_GFlin) (eV)','Re(e_GF) (eV)','Re(Z)'
write(*,'(A5,1X,A3,1X,A15,1X,A15,1X,A10)') 'Orb.','It.','Im(e_GFlin) (eV)','Im(e_GF) (eV)','Im(Z)'
write(*,*)'-----------------------------------------------------'
do p=nC+1,nBas-nR
Re_w = Re_eGFlin(p)
Im_w = Im_eGFlin(p)
nIt = 0
Re_f = 1d0
Im_f = 0d0
do while (abs(cmplx(Re_f,Im_f,kind=8)) > thresh .and. nIt < maxIt)
nIt = nIt + 1
Re_SigC = cRGF2_Re_SigC(p,Re_w,Im_w,eta,nBas,nC,nO,nV,nR,Re_eOld,Im_eOld,ERI)
Im_SigC = cRGF2_Im_SigC(p,Re_w,Im_w,eta,nBas,nC,nO,nV,nR,Re_eOld,Im_eOld,ERI)
Re_dSigC = cRGF2_Re_dSigC(p,Re_w,Im_w,eta,nBas,nC,nO,nV,nR,Re_eOld,Im_eOld,ERI)
Im_dSigC = cRGF2_Im_dSigC(p,Re_w,Im_w,eta,nBas,nC,nO,nV,nR,Re_eOld,Im_eOld,ERI)
Re_f = Re_w - eHF(p) - Re_SigC
Im_f = Im_w - e_cap(p) - Im_SigC
Re_df = (1d0 - Re_dSigC)/((1d0 - Re_dSigC)**2 + Im_dSigC**2)
Im_df = Im_dSigC/((1d0 - Re_dSigC)**2 + Im_dSigC**2)
Re_w = Re_w - Re_df*Re_f + Im_df*Im_f
Im_w = Im_w - Re_f*Im_df - Re_df*Im_f
end do
if(nIt == maxIt) then
Re_eGF(p) = Re_eGFlin(p)
Im_eGF(p) = Im_eGFlin(p)
write(*,'(I5,1X,I3,1X,F15.9,1X,F15.9,1X,F10.6,1X,A12)') p,nIt,Re_eGFlin(p)*HaToeV,Re_eGF(p)*HaToeV,Re_Z(p),'Cvg Failed!'
write(*,'(I5,1X,I3,1X,F15.9,1X,F15.9,1X,F10.6,1X,A12)') p,nIt,Im_eGFlin(p)*HaToeV,Im_eGF(p)*HaToeV,Im_Z(p),'Cvg Failed!'
else
Re_eGF(p) = Re_w
Im_eGF(p) = Im_w
Re_Z(p) = Re_df
Im_Z(p) = Im_df
write(*,'(I5,1X,I3,1X,F15.9,1X,F15.9,1X,F10.6)') p,nIt,Re_eGFlin(p)*HaToeV,Re_eGF(p)*HaToeV,Re_Z(p)
write(*,'(I5,1X,I3,1X,F15.9,1X,F15.9,1X,F10.6)') p,nIt,Im_eGFlin(p)*HaToeV,Im_eGF(p)*HaToeV,Im_Z(p)
write(*,*)'-----------------------------------------------------'
end if
end do
end subroutine

58
src/GF/cRGF2_Re_SigC.f90 Normal file
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@ -0,0 +1,58 @@
double precision function cRGF2_Re_SigC(p,Re_w,Im_w,eta,nBas,nC,nO,nV,nR,eHF,e_cap,ERI)
! Compute diagonal of the correlation part of the self-energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: p
double precision,intent(in) :: Re_w
double precision,intent(in) :: Im_w
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: e_cap(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: i,j,a,b
double precision :: eps
double precision :: eta_tilde
double precision :: num
! Initialize
cRGF2_Re_SigC = 0d0
! Occupied part of the correlation self-energy
do i=nC+1,nO
do j=nC+1,nO
do a=nO+1,nBas-nR
eps = Re_w + eHF(a) - eHF(i) - eHF(j)
eta_tilde = eta - Im_w + e_cap(i) + e_cap(a) - e_cap(j)
num = (2d0*ERI(p,a,i,j) - ERI(p,a,j,i))*ERI(p,a,i,j)
cRGF2_Re_SigC = cRGF2_Re_SigC + num*eps/(eps**2 + eta_tilde**2)
end do
end do
end do
! Virtual part of the correlation self-energy
do i=nC+1,nO
do a=nO+1,nBas-nR
do b=nO+1,nBas-nR
eps = Re_w + eHF(i) - eHF(a) - eHF(b)
num = (2d0*ERI(p,i,a,b) - ERI(p,i,b,a))*ERI(p,i,a,b)
eta_tilde = eta + Im_w - e_cap(a) - e_cap(b) + e_cap(i)
cRGF2_Re_SigC = cRGF2_Re_SigC + num*eps/(eps**2 + eta_tilde**2)
end do
end do
end do
end function

59
src/GF/cRGF2_Re_dSigC.f90 Normal file
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@ -0,0 +1,59 @@
double precision function cRGF2_Re_dSigC(p,Re_w,Im_w,eta,nBas,nC,nO,nV,nR,eHF,e_cap,ERI)
! Compute diagonal of the correlation part of the self-energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: p
double precision,intent(in) :: Re_w
double precision,intent(in) :: Im_w
double precision,intent(in) :: eta
integer,intent(in) :: nBas,nC,nO,nV,nR
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: e_cap(nBas)
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
! Local variables
integer :: i,j,a,b
double precision :: eps
double precision :: eta_tilde
double precision :: num
! Initialize
cRGF2_Re_dSigC = 0d0
! Occupied part of the correlation self-energy
do i=nC+1,nO
do j=nC+1,nO
do a=nO+1,nBas-nR
eps = Re_w + eHF(a) - eHF(i) - eHF(j)
eta_tilde = eta - Im_w + e_cap(i) + e_cap(a) - e_cap(j)
cRGF2_Re_dSigC = cRGF2_Re_dSigC -&
(2d0*ERI(p,a,i,j) - ERI(p,a,j,i))*ERI(p,a,i,j)*(eps**2 - eta_tilde**2)/(eps**2 + eta_tilde**2)**2
end do
end do
end do
! Virtual part of the correlation self-energy
do i=nC+1,nO
do a=nO+1,nBas-nR
do b=nO+1,nBas-nR
eps = Re_w + eHF(i) - eHF(a) - eHF(b)
eta_tilde = eta + Im_w - e_cap(a) - e_cap(b) + e_cap(i)
cRGF2_Re_dSigC = cRGF2_Re_dSigC -&
(2d0*ERI(p,i,a,b) - ERI(p,i,b,a))*ERI(p,i,a,b)*(eps**2 - eta_tilde**2)/(eps**2 + eta_tilde**2)**2
end do
end do
end do
end function