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
  double precision              :: tmp_ab, lambda4, eta2
  integer                       :: a,b,c,d,ab,cd,m
  integer                       :: a0, aa

  double precision, allocatable :: Om_tmp(:)

! Output variables

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

!---------------!
! Singlet block !
!---------------!

  if(ispin == 1) then

    a0 = nBas - nR - nO
    lambda4 = 4.d0 * lambda
    eta2 = eta * eta

    allocate(Om_tmp(nS))

    !$OMP PARALLEL DEFAULT(NONE) PRIVATE(m) SHARED(nS, eta2, Om, Om_tmp)
    !$OMP DO
    do m = 1, nS
      Om_tmp(m) = Om(m) / (Om(m)*Om(m) + eta2)
    enddo
    !$OMP END DO
    !$OMP END PARALLEL

    !$OMP PARALLEL DEFAULT(NONE)                              &
    !$OMP          PRIVATE(a, b, aa, ab, c, d, cd, m, tmp_ab) &
    !$OMP          SHARED(nO, nBas, nR, nS, a0, lambda4, Om_tmp, rho, KC)
    !$OMP DO
    do a = nO+1, nBas-nR
      aa = a0 * (a - nO - 1) - (a - nO - 1) * (a - nO) / 2 - nO
      do b = a, nBas-nR
        ab = aa + b

        tmp_ab = lambda4
        if(a .eq. b) then
          tmp_ab = 0.7071067811865475d0 * lambda4
        endif

        cd = 0
        do c = nO+1, nBas-nR
          do d = c, nBas-nR
            cd = cd + 1

            KC(ab,cd) = 0d0
            do m = 1, nS
              KC(ab,cd) = KC(ab,cd) - rho(a,c,m) * rho(b,d,m) * Om_tmp(m) &
                                    - rho(a,d,m) * rho(b,c,m) * Om_tmp(m)
            end do

            KC(ab,cd) = tmp_ab * KC(ab,cd)
            if(c .eq. d) then
              KC(ab,cd) = 0.7071067811865475d0 * KC(ab,cd)
            endif
          enddo
        enddo
      enddo
    enddo
    !$OMP END DO
    !$OMP END PARALLEL

    deallocate(Om_tmp)

!    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

    a0 = nBas - nR - nO - 1
    lambda4 = 4.d0 * lambda
    eta2 = eta * eta

    allocate(Om_tmp(nS))

    !$OMP PARALLEL DEFAULT(NONE) PRIVATE(m) SHARED(nS, eta2, Om, Om_tmp)
    !$OMP DO
    do m = 1, nS
      Om_tmp(m) = Om(m) / (Om(m)*Om(m) + eta2)
    enddo
    !$OMP END DO
    !$OMP END PARALLEL

    !$OMP PARALLEL DEFAULT(NONE)                      &
    !$OMP          PRIVATE(a, b, aa, ab, c, d, cd, m) &
    !$OMP          SHARED(nO, nBas, nR, nS, a0, lambda4, Om_tmp, rho, KC)
    !$OMP DO
    do a = nO+1, nBas-nR
      aa = a0 * (a - nO - 1) - (a - nO - 1) * (a - nO) / 2 - nO - 1
      do b = a+1, nBas-nR
        ab = aa + b

        cd = 0
        do c = nO+1, nBas-nR
          do d = c+1, nBas-nR
            cd = cd + 1

            KC(ab,cd) = 0d0
            do m = 1, nS
              KC(ab,cd) = KC(ab,cd) - rho(a,c,m) * rho(b,d,m) * Om_tmp(m) &
                                    + rho(a,d,m) * rho(b,c,m) * Om_tmp(m)
            end do

            KC(ab,cd) = lambda4 * KC(ab,cd)
          enddo
        enddo
      enddo
    enddo
    !$OMP END DO
    !$OMP END PARALLEL

    deallocate(Om_tmp)

!    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