2024-09-10 16:27:49 +02:00
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! ---
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subroutine ppLR_GW_HR_calc(ispin, nOrb, nC, nO, nR, nOO, nVV, nS, lambda, e, eF, n_states_diag, &
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ERI, eta, rho, Om, U, W)
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implicit none
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integer, intent(in) :: ispin
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integer, intent(in) :: n_states_diag
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integer, intent(in) :: nOO, nVV, nOrb, nC, nO, nR, nS
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double precision, intent(in) :: lambda, eF, eta
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double precision, intent(in) :: e(nOrb)
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double precision, intent(in) :: ERI(nOrb,nOrb,nOrb,nOrb)
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2024-09-11 00:25:42 +02:00
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double precision, intent(in) :: rho(nS,nOrb,nOrb), Om(nS)
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2024-09-10 16:27:49 +02:00
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double precision, intent(in) :: U(nOO+nVV,n_states_diag)
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double precision, intent(out) :: W(nOO+nVV,n_states_diag)
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2024-09-11 00:25:42 +02:00
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integer :: i, j, ij
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integer :: ab
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integer :: m
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integer :: state
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double precision :: eta2
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double precision :: t1, t2
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double precision :: diff_tot, diff_loc
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double precision, allocatable :: M_ref(:,:)
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double precision, allocatable :: Bpp_ref(:,:), Cpp_ref(:,:), Dpp_ref(:,:)
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double precision, allocatable :: KB_sta(:,:), KC_sta(:,:), KD_sta(:,:)
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double precision, allocatable :: W_ref(:,:)
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double precision, allocatable :: rho_t(:,:,:)
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! call wall_time(t1)
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if((nOO+nVV) .le. 20000) then
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call ppLR_GW_HR_calc_oneshot(ispin, nOrb, nC, nO, nR, nOO, nVV, nS, lambda, e(1), eF, n_states_diag, &
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ERI(1,1,1,1), eta, rho(1,1,1), Om(1), U(1,1), W(1,1))
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else
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call ppLR_GW_HR_calc_batches(ispin, nOrb, nC, nO, nR, nOO, nVV, nS, lambda, e(1), eF, n_states_diag, &
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ERI(1,1,1,1), eta, rho(1,1,1), Om(1), U(1,1), W(1,1))
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endif
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! print*, ' debug ppLR_GW_H_diag:'
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! allocate(M_ref(nOO+nVV,nOO+nVV))
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! allocate(Bpp_ref(nVV,nOO), Cpp_ref(nVV,nVV), Dpp_ref(nOO,nOO))
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! allocate(KB_sta(nVV,nOO), KC_sta(nVV,nVV), KD_sta(nOO,nOO))
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! allocate(rho_t(nOrb,nOrb,nS))
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! allocate(W_ref(nOO+nVV,n_states_diag))
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!
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! call ppLR_C(ispin, nOrb, nC, nO, nOrb-nO, nR, nVV, 1d0, e, ERI, Cpp_ref)
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! call ppLR_D(ispin, nOrb, nC, nO, nOrb-nO, nR, nOO, 1d0, e, ERI, Dpp_ref)
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! call ppLR_B(ispin, nOrb, nC, nO, nOrb-nO, nR, nOO, nVV, 1d0, ERI, Bpp_ref)
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!
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! do j = 1, nOrb
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! do i = 1, nOrb
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! do m = 1, nS
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! rho_t(i,j,m) = rho(m,i,j)
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! enddo
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! enddo
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! enddo
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!
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! call RGW_ppBSE_static_kernel_C(ispin, eta, nOrb, nC, nO, nOrb-nO, nR, nS, nVV, 1.d0, ERI, Om, rho_t, KC_sta)
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! call RGW_ppBSE_static_kernel_D(ispin, eta, nOrb, nC, nO, nOrb-nO, nR, nS, nOO, 1.d0, ERI, Om, rho_t, KD_sta)
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! call RGW_ppBSE_static_kernel_B(ispin, eta, nOrb, nC, nO, nOrb-nO, nR, nS, nOO, nVV, 1.d0, ERI, Om, rho_t, KB_sta)
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!
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! Cpp_ref = Cpp_ref + KC_sta
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! Dpp_ref = Dpp_ref + KD_sta
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! Bpp_ref = Bpp_ref + KB_sta
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!
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! M_ref = 0.d0
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! M_ref( 1:nVV , 1:nVV) = + Cpp_ref(1:nVV,1:nVV)
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! M_ref(nVV+1:nVV+nOO,nVV+1:nVV+nOO) = - Dpp_ref(1:nOO,1:nOO)
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! M_ref( 1:nVV ,nVV+1:nOO+nVV) = - Bpp_ref(1:nVV,1:nOO)
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! M_ref(nVV+1:nOO+nVV, 1:nVV) = + transpose(Bpp_ref(1:nVV,1:nOO))
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!
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! call dgemm('N', 'N', nOO+nVV, n_states_diag, nOO+nVV, 1.d0, &
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! M_ref(1,1), size(M_ref, 1), U(1,1), size(U, 1), &
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! 0.d0, W_ref(1,1), size(W_ref, 1))
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!
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! diff_tot = 0.d0
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! do state = 1, n_states_diag
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! do ab = 1, nOO
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! diff_loc = dabs(W(ab,state) - W_ref(ab,state))
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! if(diff_loc .gt. 1d-10) then
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! print*, ' important diff on:', ab, state
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! print*, W(ab,state), W_ref(ab,state)
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! stop
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! endif
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! diff_tot = diff_tot + diff_loc
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! enddo
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! do ij = nVV+1, nVV+nOO
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! diff_loc = dabs(W(ij,state) - W_ref(ij,state))
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! if(diff_loc .gt. 1d-10) then
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! print*, ' important diff on:', ij, state
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! print*, W(ij,state), W_ref(ij,state)
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! stop
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! endif
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! diff_tot = diff_tot + diff_loc
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! enddo
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! enddo
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! print*, 'diff_tot = ', diff_tot
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!
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! deallocate(M_ref)
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! deallocate(Bpp_ref, Cpp_ref, Dpp_ref)
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! deallocate(KB_sta, KC_sta, KD_sta)
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! deallocate(W_ref)
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! deallocate(rho_t)
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! call wall_time(t2)
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! write(*,'(A50, F12.4)') 'total wall time for ppLR_GW_HR_calc (sec): ', t2-t1
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return
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end
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! ---
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subroutine ppLR_GW_H_diag(ispin, nOrb, nC, nO, nR, nOO, nVV, nS, lambda, e, eF, ERI, eta, rho, Om, H_diag)
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implicit none
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integer, intent(in) :: ispin
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integer, intent(in) :: nOO, nVV, nOrb, nC, nO, nR, nS
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double precision, intent(in) :: lambda, eF, eta
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double precision, intent(in) :: e(nOrb)
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double precision, intent(in) :: ERI(nOrb,nOrb,nOrb,nOrb)
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double precision, intent(in) :: rho(nS,nOrb,nOrb), Om(nS)
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double precision, intent(out) :: H_diag(nOO+nVV)
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2024-09-10 16:27:49 +02:00
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integer :: i, j, ij, k, l, kl
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integer :: a, b, c, d, ab, cd
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integer :: m
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2024-09-11 00:25:42 +02:00
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double precision :: chi, eps
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double precision :: t1, t2
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2024-09-10 16:27:49 +02:00
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double precision, external :: Kronecker_delta
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2024-09-11 00:25:42 +02:00
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call wall_time(t1)
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2024-09-10 16:27:49 +02:00
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if(ispin .eq. 1) then
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ab = 0
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do a = nO+1, nOrb-nR
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do b = a, nOrb-nR
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ab = ab + 1
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2024-09-11 00:25:42 +02:00
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cd = 0
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do c = nO+1, nOrb-nR
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do d = c, nOrb-nR
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cd = cd + 1
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if(a .ne. c) cycle
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if(b .ne. d) cycle
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H_diag(ab) = e(a) + e(b) - eF &
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+ lambda * (ERI(a,b,c,d) + ERI(a,b,d,c)) / dsqrt( (1.d0 + Kronecker_delta(a, b)) &
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* (1.d0 + Kronecker_delta(c, d)))
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chi = 0.d0
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do m = 1, nS
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eps = Om(m)**2 + eta**2
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chi = chi - rho(m,a,c) * rho(m,b,d) * Om(m) / eps &
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- rho(m,a,d) * rho(m,b,c) * Om(m) / eps
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end do
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H_diag(ab) = H_diag(ab) + 4.d0 * lambda * chi / dsqrt( (1.d0 + Kronecker_delta(a, b)) &
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* (1.d0 + Kronecker_delta(c, d)))
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enddo
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enddo
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enddo ! b
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enddo ! a
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2024-09-10 16:27:49 +02:00
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2024-09-11 00:25:42 +02:00
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ij = nVV
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do i = nC+1, nO
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do j = i, nO
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ij = ij + 1
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kl = 0
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do k = nC+1, nO
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do l = k, nO
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kl = kl + 1
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if(i .ne. k) cycle
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if(j .ne. l) cycle
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H_diag(ij) = e(i) + e(j) - eF &
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- lambda * (ERI(i,j,k,l) + ERI(i,j,l,k)) / dsqrt( (1.d0 + Kronecker_delta(i, j)) &
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* (1.d0 + Kronecker_delta(k, l)))
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chi = 0.d0
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do m = 1, nS
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eps = Om(m)**2 + eta**2
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chi = chi - rho(m,i,k) * rho(m,j,l) * Om(m) / eps &
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- rho(m,i,l) * rho(m,j,k) * Om(m) / eps
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enddo
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H_diag(ij) = H_diag(ij) - 4.d0 * lambda * chi / dsqrt( (1.d0 + Kronecker_delta(i, j)) &
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* (1.d0 + Kronecker_delta(k, l)))
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2024-09-10 16:27:49 +02:00
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enddo
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2024-09-11 00:25:42 +02:00
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enddo
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enddo ! j
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enddo ! i
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2024-09-10 16:27:49 +02:00
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2024-09-11 00:25:42 +02:00
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elseif(ispin .eq. 2) then
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2024-09-10 16:27:49 +02:00
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2024-09-11 00:25:42 +02:00
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ab = 0
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do a = nO+1, nOrb-nR
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do b = a+1, nOrb-nR
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ab = ab + 1
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cd = 0
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do c = nO+1, nOrb-nR
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do d = c+1, nOrb-nR
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cd = cd + 1
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if(a .ne. c) cycle
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if(b .ne. d) cycle
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H_diag(ab) = e(a) + e(b) - eF + lambda * (ERI(a,b,c,d) - ERI(a,b,d,c))
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chi = 0.d0
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do m = 1, nS
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eps = Om(m)**2 + eta**2
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chi = chi - rho(m,a,c) * rho(m,b,d) * Om(m) / eps &
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+ rho(m,a,d) * rho(m,b,c) * Om(m) / eps
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2024-09-10 16:27:49 +02:00
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enddo
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H_diag(ab) = H_diag(ab) + 4.d0 * lambda * chi
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enddo
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enddo
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enddo ! b
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enddo ! a
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ij = nVV
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do i = nC+1, nO
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do j = i+1, nO
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ij = ij + 1
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kl = 0
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do k = nC+1, nO
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do l = k+1, nO
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kl = kl + 1
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if(i .ne. k) cycle
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if(j .ne. l) cycle
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H_diag(ij) = e(i) + e(j) - eF - lambda * (ERI(i,j,k,l) - ERI(i,j,l,k))
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chi = 0.d0
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do m = 1, nS
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eps = Om(m)**2 + eta**2
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chi = chi - rho(m,i,k) * rho(m,j,l) * Om(m) / eps &
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+ rho(m,i,l) * rho(m,j,k) * Om(m) / eps
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end do
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H_diag(ij) = H_diag(ij) - 4.d0 * lambda * chi
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2024-09-10 16:27:49 +02:00
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enddo
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2024-09-11 00:25:42 +02:00
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enddo
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enddo ! j
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enddo ! i
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else
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print*, ' Error in ppLR_GW_H_diag'
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print*, ' ispin is not supported'
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print*, ' ispin = ', ispin
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stop
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endif
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call wall_time(t2)
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write(*,'(A50, F12.4)') 'total wall time for ppLR_GW_H_diag (sec): ', t2-t1
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return
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end
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! ---
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subroutine ppLR_GW_HR_calc_oneshot(ispin, nOrb, nC, nO, nR, nOO, nVV, nS, lambda, e, eF, n_states_diag, &
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ERI, eta, rho, Om, U, W)
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implicit none
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integer, intent(in) :: ispin
|
|
|
|
|
integer, intent(in) :: n_states_diag
|
|
|
|
|
integer, intent(in) :: nOO, nVV, nOrb, nC, nO, nR, nS
|
|
|
|
|
double precision, intent(in) :: lambda, eF, eta
|
|
|
|
|
double precision, intent(in) :: e(nOrb)
|
|
|
|
|
double precision, intent(in) :: ERI(nOrb,nOrb,nOrb,nOrb)
|
|
|
|
|
double precision, intent(in) :: rho(nS,nOrb,nOrb), Om(nS)
|
|
|
|
|
double precision, intent(in) :: U(nOO+nVV,n_states_diag)
|
|
|
|
|
double precision, intent(out) :: W(nOO+nVV,n_states_diag)
|
|
|
|
|
|
|
|
|
|
integer :: i, j, ij, k, l, kl
|
|
|
|
|
integer :: a, b, c, d, ab, cd
|
|
|
|
|
integer :: a0, aa, i0, ii
|
|
|
|
|
integer :: m
|
|
|
|
|
integer :: state
|
|
|
|
|
double precision :: mat_tmp, chi, eps
|
|
|
|
|
double precision :: eta2
|
|
|
|
|
double precision :: tmp_e, tmp_ab, tmp_ij
|
|
|
|
|
double precision, allocatable :: Om_tmp(:), H_mat(:,:)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
if(ispin .eq. 1) then
|
|
|
|
|
|
|
|
|
|
allocate(Om_tmp(nS))
|
|
|
|
|
|
|
|
|
|
a0 = nOrb - nR - nO
|
|
|
|
|
eta2 = eta * eta
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
Om_tmp(m) = Om(m) / (Om(m) * Om(m) + eta2)
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
allocate(H_mat(nVV,nOO+nVV))
|
|
|
|
|
|
|
|
|
|
!$OMP PARALLEL &
|
|
|
|
|
!$OMP DEFAULT(NONE) &
|
|
|
|
|
!$OMP PRIVATE(a, b, aa, ab, c, d, cd, i, j, ij, m, state, &
|
|
|
|
|
!$OMP tmp_e, tmp_ab, chi, mat_tmp) &
|
|
|
|
|
!$OMP SHARED(nC, nO, nOrb, nR, nS, n_states_diag, nVV, &
|
|
|
|
|
!$OMP nOO, a0, eF, lambda, e, Om_tmp, rho, ERI, U, &
|
|
|
|
|
!$OMP H_mat)
|
|
|
|
|
!$OMP DO SCHEDULE(GUIDED)
|
|
|
|
|
do a = nO+1, nOrb-nR
|
|
|
|
|
aa = a0 * (a - nO - 1) - (a - nO - 1) * (a - nO) / 2 - nO
|
|
|
|
|
do b = a, nOrb-nR
|
|
|
|
|
ab = aa + b
|
|
|
|
|
|
|
|
|
|
tmp_e = e(a) + e(b) - eF
|
|
|
|
|
|
|
|
|
|
tmp_ab = lambda
|
|
|
|
|
if(a .eq. b) then
|
|
|
|
|
tmp_ab = 0.7071067811865475d0 * tmp_ab
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
cd = 0
|
|
|
|
|
do c = nO+1, nOrb-nR
|
|
|
|
|
do d = c, nOrb-nR
|
|
|
|
|
cd = cd + 1
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
chi = chi - Om_tmp(m) * (rho(m,a,c) * rho(m,b,d) + rho(m,a,d) * rho(m,b,c))
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
mat_tmp = tmp_ab
|
|
|
|
|
if(c .eq. d) then
|
|
|
|
|
mat_tmp = 0.7071067811865475d0 * mat_tmp
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
mat_tmp = mat_tmp * (4.d0 * chi + ERI(c,d,a,b) + ERI(d,c,a,b))
|
|
|
|
|
if((a .eq. c) .and. (b .eq. d)) then
|
|
|
|
|
mat_tmp = mat_tmp + tmp_e
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
H_mat(ab,cd) = mat_tmp
|
|
|
|
|
enddo ! d
|
|
|
|
|
enddo ! c
|
|
|
|
|
|
|
|
|
|
ij = nVV
|
|
|
|
|
do i = nC+1, nO
|
|
|
|
|
do j = i, nO
|
|
|
|
|
ij = ij + 1
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
chi = chi - Om_tmp(m) * (rho(m,i,a) * rho(m,j,b) + rho(m,i,b) * rho(m,a,j))
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
mat_tmp = tmp_ab
|
|
|
|
|
if(i .eq. j) then
|
|
|
|
|
mat_tmp = 0.7071067811865475d0 * mat_tmp
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
mat_tmp = mat_tmp * (4.d0 * chi + ERI(i,j,a,b) + ERI(j,i,a,b))
|
|
|
|
|
|
|
|
|
|
H_mat(ab,ij) = -mat_tmp
|
|
|
|
|
enddo ! j
|
|
|
|
|
enddo ! i
|
2024-09-10 16:27:49 +02:00
|
|
|
|
|
|
|
|
enddo ! b
|
|
|
|
|
enddo ! a
|
2024-09-11 00:25:42 +02:00
|
|
|
!$OMP END DO
|
|
|
|
|
!$OMP END PARALLEL
|
|
|
|
|
|
|
|
|
|
call dgemm("N", "N", nVV, n_states_diag, nOO+nVV, 1.d0, &
|
|
|
|
|
H_mat(1,1), size(H_mat, 1), U(1,1), size(U, 1), &
|
|
|
|
|
0.d0, W(1,1), size(W, 1))
|
|
|
|
|
|
|
|
|
|
deallocate(H_mat)
|
2024-09-10 16:27:49 +02:00
|
|
|
|
|
|
|
|
! ---
|
2024-09-11 00:25:42 +02:00
|
|
|
|
|
|
|
|
allocate(H_mat(nOO,nOO+nVV))
|
|
|
|
|
|
|
|
|
|
i0 = nO - nC
|
|
|
|
|
|
|
|
|
|
!$OMP PARALLEL &
|
|
|
|
|
!$OMP DEFAULT(NONE) &
|
|
|
|
|
!$OMP PRIVATE(i, j, ii, ij, a, b, ab, k, l, kl, m, state, &
|
|
|
|
|
!$OMP tmp_e, tmp_ij, chi, mat_tmp) &
|
|
|
|
|
!$OMP SHARED(nC, nO, nOrb, nR, nS, nVV, i0, &
|
|
|
|
|
!$OMP eF, lambda, e, Om_tmp, rho, ERI, U, H_mat)
|
|
|
|
|
!$OMP DO SCHEDULE(GUIDED)
|
2024-09-10 16:27:49 +02:00
|
|
|
do i = nC+1, nO
|
2024-09-11 00:25:42 +02:00
|
|
|
ii = i0 * (i - nC - 1) - (i - nC - 1) * (i - nC) / 2 - nC
|
2024-09-10 16:27:49 +02:00
|
|
|
do j = i, nO
|
2024-09-11 00:25:42 +02:00
|
|
|
ij = ii + j
|
|
|
|
|
|
|
|
|
|
tmp_e = e(i) + e(j) - eF
|
|
|
|
|
|
|
|
|
|
tmp_ij = lambda
|
|
|
|
|
if(i .eq. j) then
|
|
|
|
|
tmp_ij = 0.7071067811865475d0 * tmp_ij
|
|
|
|
|
endif
|
2024-09-10 16:27:49 +02:00
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
ab = 0
|
|
|
|
|
do a = nO+1, nOrb-nR
|
|
|
|
|
do b = a, nOrb-nR
|
|
|
|
|
ab = ab + 1
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
chi = chi - Om_tmp(m) * (rho(m,i,a) * rho(m,j,b) + rho(m,i,b) * rho(m,a,j))
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
mat_tmp = tmp_ij
|
|
|
|
|
if(a .eq. b) then
|
|
|
|
|
mat_tmp = 0.7071067811865475d0 * mat_tmp
|
|
|
|
|
endif
|
2024-09-10 16:27:49 +02:00
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
mat_tmp = mat_tmp * (4.d0 * chi + ERI(a,b,i,j) + ERI(a,b,j,i))
|
2024-09-10 16:27:49 +02:00
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
H_mat(ij,ab) = mat_tmp
|
|
|
|
|
enddo ! b
|
|
|
|
|
enddo ! a
|
2024-09-10 16:27:49 +02:00
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
kl = nVV
|
|
|
|
|
do k = nC+1, nO
|
|
|
|
|
do l = k, nO
|
|
|
|
|
kl = kl + 1
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
chi = chi - Om_tmp(m) * (rho(m,i,k) * rho(m,j,l) + rho(m,i,l) * rho(m,j,k))
|
2024-09-10 16:27:49 +02:00
|
|
|
enddo
|
|
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
mat_tmp = tmp_ij
|
|
|
|
|
if(k .eq. l) then
|
|
|
|
|
mat_tmp = 0.7071067811865475d0 * mat_tmp
|
|
|
|
|
endif
|
2024-09-10 16:27:49 +02:00
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
mat_tmp = mat_tmp * (4.d0 * chi + ERI(i,j,k,l) + ERI(i,j,l,k))
|
2024-09-10 16:27:49 +02:00
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
if((i .eq. k) .and. (j .eq. l)) then
|
|
|
|
|
mat_tmp = mat_tmp - tmp_e
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
H_mat(ij,kl) = -mat_tmp
|
|
|
|
|
enddo ! l
|
|
|
|
|
enddo ! k
|
|
|
|
|
enddo ! j
|
|
|
|
|
enddo ! i
|
|
|
|
|
!$OMP END DO
|
|
|
|
|
!$OMP END PARALLEL
|
|
|
|
|
|
|
|
|
|
call dgemm("N", "N", nOO, n_states_diag, nOO+nVV, 1.d0, &
|
|
|
|
|
H_mat(1,1), size(H_mat, 1), U(1,1), size(U, 1), &
|
|
|
|
|
0.d0, W(nVV+1,1), size(W, 1))
|
|
|
|
|
deallocate(H_mat)
|
|
|
|
|
|
|
|
|
|
deallocate(Om_tmp)
|
|
|
|
|
|
|
|
|
|
else
|
|
|
|
|
|
|
|
|
|
print*, ' Error in ppLR_GW_HR_calc_oneshot'
|
|
|
|
|
print*, ' ispin is not supported'
|
|
|
|
|
print*, ' ispin = ', ispin
|
|
|
|
|
stop
|
|
|
|
|
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
return
|
|
|
|
|
end
|
|
|
|
|
|
|
|
|
|
! ---
|
|
|
|
|
|
|
|
|
|
subroutine ppLR_GW_HR_calc_batches(ispin, nOrb, nC, nO, nR, nOO, nVV, nS, lambda, e, eF, n_states_diag, &
|
|
|
|
|
ERI, eta, rho, Om, U, W)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
use omp_lib
|
|
|
|
|
|
|
|
|
|
implicit none
|
|
|
|
|
|
|
|
|
|
integer, intent(in) :: ispin
|
|
|
|
|
integer, intent(in) :: n_states_diag
|
|
|
|
|
integer, intent(in) :: nOO, nVV, nOrb, nC, nO, nR, nS
|
|
|
|
|
double precision, intent(in) :: lambda, eF, eta
|
|
|
|
|
double precision, intent(in) :: e(nOrb)
|
|
|
|
|
double precision, intent(in) :: ERI(nOrb,nOrb,nOrb,nOrb)
|
|
|
|
|
double precision, intent(in) :: rho(nS,nOrb,nOrb), Om(nS)
|
|
|
|
|
double precision, intent(in) :: U(nOO+nVV,n_states_diag)
|
|
|
|
|
double precision, intent(out) :: W(nOO+nVV,n_states_diag)
|
|
|
|
|
|
|
|
|
|
integer :: i, j, ij, k, l, kl
|
|
|
|
|
integer :: a, b, c, d, ab, cd
|
|
|
|
|
integer :: a0, aa, i0, ii, bb
|
|
|
|
|
integer :: m
|
|
|
|
|
integer :: state
|
|
|
|
|
double precision :: mat_tmp, chi, eps
|
|
|
|
|
double precision :: eta2
|
|
|
|
|
double precision :: tmp_e, tmp_ab, tmp_ij
|
|
|
|
|
double precision, allocatable :: Om_tmp(:), H_mat(:,:)
|
|
|
|
|
|
|
|
|
|
double precision, external :: Kronecker_delta
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
if(ispin .eq. 1) then
|
|
|
|
|
|
|
|
|
|
call omp_set_max_active_levels(1)
|
|
|
|
|
|
|
|
|
|
allocate(Om_tmp(nS))
|
|
|
|
|
|
|
|
|
|
a0 = nOrb - nR - nO
|
|
|
|
|
|
|
|
|
|
eta2 = eta * eta
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
Om_tmp(m) = Om(m) / (Om(m) * Om(m) + eta2)
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
!$OMP PARALLEL &
|
|
|
|
|
!$OMP DEFAULT(NONE) &
|
|
|
|
|
!$OMP PRIVATE(a, b, aa, ab, c, d, cd, i, j, ij, m, state, &
|
|
|
|
|
!$OMP bb, tmp_e, tmp_ab, chi, mat_tmp, H_mat) &
|
|
|
|
|
!$OMP SHARED(nC, nO, nOrb, nR, nS, n_states_diag, nVV, &
|
|
|
|
|
!$OMP nOO, a0, eF, lambda, e, Om_tmp, rho, ERI, U, W)
|
|
|
|
|
|
|
|
|
|
allocate(H_mat(nOO+nVV,a0))
|
|
|
|
|
|
|
|
|
|
!$OMP DO SCHEDULE(GUIDED)
|
|
|
|
|
do a = nO+1, nOrb-nR
|
|
|
|
|
aa = a0 * (a - nO - 1) - (a - nO - 1) * (a - nO) / 2 - nO
|
|
|
|
|
do b = a, nOrb-nR
|
|
|
|
|
ab = aa + b
|
|
|
|
|
|
|
|
|
|
bb = b - a + 1
|
|
|
|
|
|
|
|
|
|
tmp_e = e(a) + e(b) - eF
|
|
|
|
|
|
|
|
|
|
tmp_ab = lambda
|
|
|
|
|
if(a .eq. b) then
|
|
|
|
|
tmp_ab = 0.7071067811865475d0 * tmp_ab
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
cd = 0
|
|
|
|
|
do c = nO+1, nOrb-nR
|
|
|
|
|
do d = c, nOrb-nR
|
|
|
|
|
cd = cd + 1
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
chi = chi - Om_tmp(m) * (rho(m,a,c) * rho(m,b,d) + rho(m,a,d) * rho(m,b,c))
|
2024-09-10 16:27:49 +02:00
|
|
|
enddo
|
2024-09-11 00:25:42 +02:00
|
|
|
|
|
|
|
|
mat_tmp = tmp_ab
|
|
|
|
|
if(c .eq. d) then
|
|
|
|
|
mat_tmp = 0.7071067811865475d0 * mat_tmp
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
mat_tmp = mat_tmp * (4.d0 * chi + ERI(c,d,a,b) + ERI(d,c,a,b))
|
|
|
|
|
if((a .eq. c) .and. (b .eq. d)) then
|
|
|
|
|
mat_tmp = mat_tmp + tmp_e
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
H_mat(cd,bb) = mat_tmp
|
|
|
|
|
enddo ! d
|
|
|
|
|
enddo ! c
|
|
|
|
|
|
|
|
|
|
ij = nVV
|
|
|
|
|
do i = nC+1, nO
|
|
|
|
|
do j = i, nO
|
|
|
|
|
ij = ij + 1
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
chi = chi - Om_tmp(m) * (rho(m,i,a) * rho(m,j,b) + rho(m,i,b) * rho(m,a,j))
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
mat_tmp = tmp_ab
|
|
|
|
|
if(i .eq. j) then
|
|
|
|
|
mat_tmp = 0.7071067811865475d0 * mat_tmp
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
mat_tmp = mat_tmp * (4.d0 * chi + ERI(i,j,a,b) + ERI(j,i,a,b))
|
|
|
|
|
|
|
|
|
|
H_mat(ij,bb) = -mat_tmp
|
|
|
|
|
enddo ! j
|
|
|
|
|
enddo ! i
|
|
|
|
|
enddo ! b
|
|
|
|
|
|
|
|
|
|
call dgemm("T", "N", nOrb-nR-a+1, n_states_diag, nOO+nVV, 1.d0, &
|
|
|
|
|
H_mat(1,1), size(H_mat, 1), U(1,1), size(U, 1), &
|
|
|
|
|
0.d0, W(aa+a,1), size(W, 1))
|
|
|
|
|
|
|
|
|
|
enddo ! a
|
|
|
|
|
!$OMP END DO
|
|
|
|
|
|
|
|
|
|
deallocate(H_mat)
|
|
|
|
|
|
|
|
|
|
!$OMP END PARALLEL
|
|
|
|
|
|
|
|
|
|
! ---
|
|
|
|
|
|
|
|
|
|
i0 = nO - nC
|
|
|
|
|
allocate(H_mat(nOO,nOO+nVV))
|
|
|
|
|
|
|
|
|
|
!$OMP PARALLEL &
|
|
|
|
|
!$OMP DEFAULT(NONE) &
|
|
|
|
|
!$OMP PRIVATE(i, j, ii, ij, a, b, ab, k, l, kl, m, state, &
|
|
|
|
|
!$OMP tmp_e, tmp_ij, chi, mat_tmp) &
|
|
|
|
|
!$OMP SHARED(nC, nO, nOrb, nR, nS, nVV, i0, &
|
|
|
|
|
!$OMP eF, lambda, e, Om_tmp, rho, ERI, U, H_mat)
|
|
|
|
|
!$OMP DO SCHEDULE(GUIDED)
|
|
|
|
|
do i = nC+1, nO
|
|
|
|
|
ii = i0 * (i - nC - 1) - (i - nC - 1) * (i - nC) / 2 - nC
|
|
|
|
|
do j = i, nO
|
|
|
|
|
ij = ii + j
|
|
|
|
|
|
|
|
|
|
tmp_e = e(i) + e(j) - eF
|
|
|
|
|
|
|
|
|
|
tmp_ij = lambda
|
|
|
|
|
if(i .eq. j) then
|
|
|
|
|
tmp_ij = 0.7071067811865475d0 * tmp_ij
|
|
|
|
|
endif
|
2024-09-10 16:27:49 +02:00
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
ab = 0
|
|
|
|
|
do a = nO+1, nOrb-nR
|
|
|
|
|
do b = a, nOrb-nR
|
|
|
|
|
ab = ab + 1
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
chi = chi - Om_tmp(m) * (rho(m,i,a) * rho(m,j,b) + rho(m,i,b) * rho(m,a,j))
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
mat_tmp = tmp_ij
|
|
|
|
|
if(a .eq. b) then
|
|
|
|
|
mat_tmp = 0.7071067811865475d0 * mat_tmp
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
mat_tmp = mat_tmp * (4.d0 * chi + ERI(a,b,i,j) + ERI(a,b,j,i))
|
|
|
|
|
|
|
|
|
|
H_mat(ij,ab) = mat_tmp
|
|
|
|
|
enddo ! b
|
|
|
|
|
enddo ! a
|
|
|
|
|
|
|
|
|
|
kl = nVV
|
|
|
|
|
do k = nC+1, nO
|
|
|
|
|
do l = k, nO
|
|
|
|
|
kl = kl + 1
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
|
|
|
|
chi = chi - Om_tmp(m) * (rho(m,i,k) * rho(m,j,l) + rho(m,i,l) * rho(m,j,k))
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
mat_tmp = tmp_ij
|
|
|
|
|
if(k .eq. l) then
|
|
|
|
|
mat_tmp = 0.7071067811865475d0 * mat_tmp
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
mat_tmp = mat_tmp * (4.d0 * chi + ERI(i,j,k,l) + ERI(i,j,l,k))
|
|
|
|
|
|
|
|
|
|
if((i .eq. k) .and. (j .eq. l)) then
|
|
|
|
|
mat_tmp = mat_tmp - tmp_e
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
H_mat(ij,kl) = -mat_tmp
|
|
|
|
|
enddo ! l
|
|
|
|
|
enddo ! k
|
2024-09-10 16:27:49 +02:00
|
|
|
enddo ! j
|
|
|
|
|
enddo ! i
|
2024-09-11 00:25:42 +02:00
|
|
|
!$OMP END DO
|
|
|
|
|
!$OMP END PARALLEL
|
|
|
|
|
|
|
|
|
|
call dgemm("N", "N", nOO, n_states_diag, nOO+nVV, 1.d0, &
|
|
|
|
|
H_mat(1,1), size(H_mat, 1), U(1,1), size(U, 1), &
|
|
|
|
|
0.d0, W(nVV+1,1), size(W, 1))
|
|
|
|
|
deallocate(H_mat)
|
|
|
|
|
|
|
|
|
|
deallocate(Om_tmp)
|
2024-09-10 16:27:49 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
elseif(ispin .eq. 2) then
|
|
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
|
|
|
|
|
eta2 = eta * eta
|
|
|
|
|
|
2024-09-10 16:27:49 +02:00
|
|
|
ab = 0
|
|
|
|
|
do a = nO+1, nOrb-nR
|
|
|
|
|
do b = a+1, nOrb-nR
|
|
|
|
|
ab = ab + 1
|
|
|
|
|
|
|
|
|
|
do state = 1, n_states_diag
|
|
|
|
|
|
|
|
|
|
W(ab,state) = 0.d0
|
|
|
|
|
|
|
|
|
|
cd = 0
|
|
|
|
|
do c = nO+1, nOrb-nR
|
|
|
|
|
do d = c+1, nOrb-nR
|
|
|
|
|
cd = cd + 1
|
|
|
|
|
|
|
|
|
|
mat_tmp = (e(a) + e(b) - eF) * Kronecker_delta(a, c) * Kronecker_delta(b, d) &
|
|
|
|
|
+ lambda * (ERI(a,b,c,d) - ERI(a,b,d,c))
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
2024-09-11 00:25:42 +02:00
|
|
|
eps = Om(m)**2 + eta2
|
|
|
|
|
chi = chi - rho(m,a,c) * rho(m,b,d) * Om(m) / eps &
|
|
|
|
|
+ rho(m,a,d) * rho(m,b,c) * Om(m) / eps
|
2024-09-10 16:27:49 +02:00
|
|
|
enddo
|
|
|
|
|
mat_tmp = mat_tmp + 4.d0 * lambda * chi
|
|
|
|
|
|
|
|
|
|
W(ab,state) = W(ab,state) + mat_tmp * U(cd,state)
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
ij = nVV
|
|
|
|
|
do i = nC+1, nO
|
|
|
|
|
do j = i+1, nO
|
|
|
|
|
ij = ij + 1
|
|
|
|
|
|
|
|
|
|
mat_tmp = lambda * (ERI(a,b,i,j) - ERI(a,b,j,i))
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
2024-09-11 00:25:42 +02:00
|
|
|
eps = Om(m)**2 + eta2
|
|
|
|
|
chi = chi - rho(m,i,a) * rho(m,j,b) * Om(m) / eps &
|
|
|
|
|
+ rho(m,i,b) * rho(m,a,j) * Om(m) / eps
|
2024-09-10 16:27:49 +02:00
|
|
|
end do
|
|
|
|
|
mat_tmp = mat_tmp + 4.d0 * lambda * chi
|
|
|
|
|
|
|
|
|
|
W(ab,state) = W(ab,state) - mat_tmp * U(ij,state)
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
enddo ! state
|
|
|
|
|
enddo ! b
|
|
|
|
|
enddo ! a
|
|
|
|
|
|
|
|
|
|
! ---
|
|
|
|
|
|
|
|
|
|
ij = nVV
|
|
|
|
|
do i = nC+1, nO
|
|
|
|
|
do j = i+1, nO
|
|
|
|
|
ij = ij + 1
|
|
|
|
|
|
|
|
|
|
do state = 1, n_states_diag
|
|
|
|
|
|
|
|
|
|
W(ij,state) = 0.d0
|
|
|
|
|
|
|
|
|
|
ab = 0
|
|
|
|
|
do a = nO+1, nOrb-nR
|
|
|
|
|
do b = a+1, nOrb-nR
|
|
|
|
|
ab = ab + 1
|
|
|
|
|
|
|
|
|
|
mat_tmp = lambda * (ERI(a,b,i,j) - ERI(a,b,j,i))
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
2024-09-11 00:25:42 +02:00
|
|
|
eps = Om(m)**2 + eta2
|
|
|
|
|
chi = chi - rho(m,i,a) * rho(m,j,b) * Om(m) / eps &
|
|
|
|
|
+ rho(m,i,b) * rho(m,a,j) * Om(m) / eps
|
2024-09-10 16:27:49 +02:00
|
|
|
end do
|
|
|
|
|
mat_tmp = mat_tmp + 4.d0 * lambda * chi
|
|
|
|
|
|
|
|
|
|
W(ij,state) = W(ij,state) + mat_tmp * U(ab,state)
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
kl = nVV
|
|
|
|
|
do k = nC+1, nO
|
|
|
|
|
do l = k+1, nO
|
|
|
|
|
kl = kl + 1
|
|
|
|
|
|
|
|
|
|
mat_tmp = - (e(i) + e(j) - eF) * Kronecker_delta(i, k) * Kronecker_delta(j, l) &
|
|
|
|
|
+ lambda * (ERI(i,j,k,l) - ERI(i,j,l,k))
|
|
|
|
|
|
|
|
|
|
chi = 0.d0
|
|
|
|
|
do m = 1, nS
|
2024-09-11 00:25:42 +02:00
|
|
|
eps = Om(m)**2 + eta2
|
|
|
|
|
chi = chi - rho(m,i,k) * rho(m,j,l) * Om(m) / eps &
|
|
|
|
|
+ rho(m,i,l) * rho(m,j,k) * Om(m) / eps
|
2024-09-10 16:27:49 +02:00
|
|
|
enddo
|
|
|
|
|
mat_tmp = mat_tmp + 4.d0 * lambda * chi
|
|
|
|
|
|
|
|
|
|
W(ij,state) = W(ij,state) - mat_tmp * U(kl,state)
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
enddo ! state
|
|
|
|
|
enddo ! j
|
|
|
|
|
enddo ! i
|
|
|
|
|
|
|
|
|
|
else
|
|
|
|
|
|
2024-09-11 00:25:42 +02:00
|
|
|
print*, ' Error in ppLR_GW_HR_calc_batches'
|
2024-09-10 16:27:49 +02:00
|
|
|
print*, ' ispin is not supported'
|
|
|
|
|
print*, ' ispin = ', ispin
|
|
|
|
|
stop
|
|
|
|
|
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
return
|
|
|
|
|
end
|
|
|
|
|
|
|
|
|
|
! ---
|
|
|
|
|
|
