QuAcK/src/GW/GW_ppBSE_static_kernel_C.f90

subroutine GW_ppBSE_static_kernel_C(ispin,eta,nBas,nC,nO,nV,nR,nS,nVV,lambda,ERI,Om,rho,KC)

! 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)            :: nVV
  double precision,intent(in)   :: eta
  double precision,intent(in)   :: lambda
  double precision,intent(in)   :: ERI(nBas,nBas,nBas,nBas)
  double precision,intent(in)   :: Om(nS)
  double precision,intent(in)   :: rho(nBas,nBas,nS)

! Local variables

  double precision,external     :: Kronecker_delta
  double precision              :: chi
  double precision              :: eps
  integer                       :: a,b,c,d,ab,cd,m

! Output variables

  double precision,intent(out)  :: KC(nVV,nVV)

! Initialization

  KC(:,:) = 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 = Om(m)**2 + eta**2
                chi = chi - rho(a,c,m)*rho(b,d,m)*Om(m)/eps &
                          - rho(a,d,m)*rho(b,c,m)*Om(m)/eps
              end do

              KC(ab,cd) = 4d0*lambda*chi/sqrt((1d0 + Kronecker_delta(a,b))*(1d0 + Kronecker_delta(c,d)))

          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 = Om(m)**2 + eta**2
              chi = chi - rho(a,c,m)*rho(b,d,m)*Om(m)/eps &
                        + rho(a,d,m)*rho(b,c,m)*Om(m)/eps
            end do
           
            KC(ab,cd) = 4d0*lambda*chi

          end do
        end do
      end do
    end do

  end if

!---------------!
! SpinOrb block !
!---------------!

  if(ispin == 4) 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 = Om(m)**2 + eta**2
              chi = chi - rho(a,c,m)*rho(b,d,m)*Om(m)/eps &
                        + rho(a,d,m)*rho(b,c,m)*Om(m)/eps
            end do
           
            KC(ab,cd) = 2d0*lambda*chi

          end do
        end do
      end do
    end do

  end if

end subroutine