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quack/src/GW/UGW_phBSE_dynamic_kernel_A.f90

257 lines
7.3 KiB
Fortran
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subroutine UGW_phBSE_dynamic_kernel_A(ispin,eta,nBas,nC,nO,nV,nR,nSa,nSb,nSt,nS_sc,lambda,eGW, &
ERI_aaaa,ERI_aabb,ERI_bbbb,OmRPA,rho_RPA,OmBSE,A_dyn,ZA_dyn)
! Compute the extra term for dynamical Bethe-Salpeter equation for linear response in the unrestricted formalism
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: ispin
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) :: nSa
integer,intent(in) :: nSb
integer,intent(in) :: nSt
integer,intent(in) :: nS_sc
double precision,intent(in) :: eta
double precision,intent(in) :: lambda
double precision,intent(in) :: eGW(nBas,nspin)
double precision,intent(in) :: ERI_aaaa(nBas,nBas,nBas,nBas)
double precision,intent(in) :: ERI_aabb(nBas,nBas,nBas,nBas)
double precision,intent(in) :: ERI_bbbb(nBas,nBas,nBas,nBas)
double precision,intent(in) :: OmRPA(nS_sc)
double precision,intent(in) :: rho_RPA(nBas,nBas,nS_sc,nspin)
double precision,intent(in) :: OmBSE
! Local variables
double precision :: chi
double precision :: eps
integer :: i,j,a,b,ia,jb,kc
! Output variables
double precision,intent(out) :: A_dyn(nSt,nSt)
double precision,intent(out) :: ZA_dyn(nSt,nSt)
!--------------------------------------------------!
! Build BSE matrix for spin-conserving transitions !
!--------------------------------------------------!
A_dyn(:,:) = 0d0
if(ispin == 1) then
! aaaa block
ia = 0
do i=nC(1)+1,nO(1)
do a=nO(1)+1,nBas-nR(1)
ia = ia + 1
jb = 0
do j=nC(1)+1,nO(1)
do b=nO(1)+1,nBas-nR(1)
jb = jb + 1
chi = 0d0
do kc=1,nS_sc
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,1)*OmRPA(kc)/(OmRPA(kc)**2 + eta**2)
enddo
A_dyn(ia,jb) = A_dyn(ia,jb) - 2d0*lambda*chi
chi = 0d0
do kc=1,nS_sc
eps = + OmBSE - OmRPA(kc) - (eGW(a,1) - eGW(j,1))
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,1)*eps/(eps**2 + eta**2)
eps = + OmBSE - OmRPA(kc) - (eGW(b,1) - eGW(i,1))
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,1)*eps/(eps**2 + eta**2)
enddo
A_dyn(ia,jb) = A_dyn(ia,jb) - lambda*chi
chi = 0d0
do kc=1,nS_sc
eps = + OmBSE - OmRPA(kc) - (eGW(a,1) - eGW(j,1))
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,1)*(eps**2 - eta**2)/(eps**2 + eta**2)**2
eps = + OmBSE - OmRPA(kc) - (eGW(b,1) - eGW(i,1))
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,1)*(eps**2 - eta**2)/(eps**2 + eta**2)**2
enddo
ZA_dyn(ia,jb) = ZA_dyn(ia,jb) + lambda*chi
enddo
enddo
enddo
enddo
! bbbb block
ia = 0
do i=nC(2)+1,nO(2)
do a=nO(2)+1,nBas-nR(2)
ia = ia + 1
jb = 0
do j=nC(2)+1,nO(2)
do b=nO(2)+1,nBas-nR(2)
jb = jb + 1
chi = 0d0
do kc=1,nS_sc
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,2)*OmRPA(kc)/(OmRPA(kc)**2 + eta**2)
enddo
A_dyn(nSa+ia,nSa+jb) = A_dyn(nSa+ia,nSa+jb) - 2d0*lambda*chi
chi = 0d0
do kc=1,nS_sc
eps = + OmBSE - OmRPA(kc) - (eGW(a,2) - eGW(j,2))
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,2)*eps/(eps**2 + eta**2)
eps = + OmBSE - OmRPA(kc) - (eGW(b,2) - eGW(i,2))
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,2)*eps/(eps**2 + eta**2)
enddo
A_dyn(nSa+ia,nSa+jb) = A_dyn(nSa+ia,nSa+jb) - lambda*chi
chi = 0d0
do kc=1,nS_sc
eps = + OmBSE - OmRPA(kc) - (eGW(a,2) - eGW(j,2))
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,2)*(eps**2 - eta**2)/(eps**2 + eta**2)**2
eps = + OmBSE - OmRPA(kc) - (eGW(b,2) - eGW(i,2))
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,2)*(eps**2 - eta**2)/(eps**2 + eta**2)**2
enddo
ZA_dyn(nSa+ia,nSa+jb) = ZA_dyn(nSa+ia,nSa+jb) + lambda*chi
enddo
enddo
enddo
enddo
end if
!--------------------------------------------!
! Build BSE matrix for spin-flip transitions !
!--------------------------------------------!
if(ispin == 2) then
! abab block
ia = 0
do i=nC(1)+1,nO(1)
do a=nO(2)+1,nBas-nR(2)
ia = ia + 1
jb = 0
do j=nC(1)+1,nO(1)
do b=nO(2)+1,nBas-nR(2)
jb = jb + 1
chi = 0d0
do kc=1,nS_sc
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,2)*OmRPA(kc)/(OmRPA(kc)**2 + eta**2)
enddo
A_dyn(ia,jb) = A_dyn(ia,jb) - 2d0*lambda*chi
chi = 0d0
do kc=1,nS_sc
eps = + OmBSE - OmRPA(kc) - (eGW(a,2) - eGW(j,1))
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,2)*eps/(eps**2 + eta**2)
eps = + OmBSE - OmRPA(kc) - (eGW(b,2) - eGW(i,1))
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,2)*eps/(eps**2 + eta**2)
enddo
A_dyn(ia,jb) = A_dyn(ia,jb) - lambda*chi
chi = 0d0
do kc=1,nS_sc
eps = + OmBSE - OmRPA(kc) - (eGW(a,2) - eGW(j,1))
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,2)*(eps**2 - eta**2)/(eps**2 + eta**2)**2
eps = + OmBSE - OmRPA(kc) - (eGW(b,2) - eGW(i,1))
chi = chi + rho_RPA(i,j,kc,1)*rho_RPA(a,b,kc,2)*(eps**2 - eta**2)/(eps**2 + eta**2)**2
enddo
ZA_dyn(ia,jb) = ZA_dyn(ia,jb) + lambda*chi
end do
end do
end do
end do
! baba block
ia = 0
do i=nC(2)+1,nO(2)
do a=nO(1)+1,nBas-nR(1)
ia = ia + 1
jb = 0
do j=nC(2)+1,nO(2)
do b=nO(1)+1,nBas-nR(1)
jb = jb + 1
chi = 0d0
do kc=1,nS_sc
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,1)*OmRPA(kc)/(OmRPA(kc)**2 + eta**2)
enddo
A_dyn(nSa+ia,nSa+jb) = A_dyn(nSa+ia,nSa+jb) - 2d0*lambda*chi
chi = 0d0
do kc=1,nS_sc
eps = + OmBSE - OmRPA(kc) - (eGW(a,1) - eGW(j,2))
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,1)*eps/(eps**2 + eta**2)
eps = + OmBSE - OmRPA(kc) - (eGW(b,1) - eGW(i,2))
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,1)*eps/(eps**2 + eta**2)
enddo
A_dyn(nSa+ia,nSa+jb) = A_dyn(nSa+ia,nSa+jb) - lambda*chi
chi = 0d0
do kc=1,nS_sc
eps = + OmBSE - OmRPA(kc) - (eGW(a,1) - eGW(j,2))
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,1)*(eps**2 - eta**2)/(eps**2 + eta**2)**2
eps = + OmBSE - OmRPA(kc) - (eGW(b,1) - eGW(i,2))
chi = chi + rho_RPA(i,j,kc,2)*rho_RPA(a,b,kc,1)*(eps**2 - eta**2)/(eps**2 + eta**2)**2
enddo
ZA_dyn(nSa+ia,nSa+jb) = ZA_dyn(nSa+ia,nSa+jb) + lambda*chi
end do
end do
end do
end do
end if
end subroutine
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