subroutine UGW_phACFDT(exchange_kernel,doXBS,TDA_W,TDA,spin_conserved,spin_flip,eta, & nBas,nC,nO,nV,nR,nS,ERI_aaaa,ERI_aabb,ERI_bbbb,eW,eGW,EcAC) ! Compute the correlation energy via the adiabatic connection fluctuation dissipation theorem implicit none include 'parameters.h' include 'quadrature.h' ! Input variables logical,intent(in) :: doXBS logical,intent(in) :: TDA_W logical,intent(in) :: TDA logical,intent(in) :: exchange_kernel logical,intent(in) :: spin_conserved logical,intent(in) :: spin_flip double precision,intent(in) :: eta 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) :: nS(nspin) double precision,intent(in) :: eW(nBas,nspin) 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) ! Local variables logical :: dRPA = .false. logical :: dRPA_W = .true. integer :: ispin integer :: isp_W integer :: iAC double precision :: lambda double precision,allocatable :: Ec(:,:) double precision,allocatable :: Aph(:,:) double precision,allocatable :: Bph(:,:) double precision,allocatable :: KA(:,:) double precision,allocatable :: KB(:,:) double precision :: EcRPA double precision,allocatable :: OmRPA(:) double precision,allocatable :: XpY_RPA(:,:) double precision,allocatable :: XmY_RPA(:,:) double precision,allocatable :: rho_RPA(:,:,:,:) integer :: nS_aa,nS_bb,nS_sc integer :: nS_ab,nS_ba,nS_sf double precision,allocatable :: Om(:) double precision,allocatable :: XpY(:,:) double precision,allocatable :: XmY(:,:) ! Output variables double precision,intent(out) :: EcAC(nspin) ! Memory allocation allocate(Ec(nAC,nspin)) ! Hello World write(*,*) '-----------------------------------------------------------' write(*,*) ' Adiabatic connection version of BSE@GW correlation energy ' write(*,*) '-----------------------------------------------------------' write(*,*) ! eXtended BSE if(doXBS) then write(*,*) '*** scaled screening version (XBS) ***' write(*,*) end if ! Antisymmetrized kernel version if(exchange_kernel) then write(*,*) write(*,*) '*** Exchange kernel version ***' write(*,*) end if EcAC(:) = 0d0 Ec(:,:) = 0d0 ! Compute (singlet) RPA screening isp_W = 1 EcRPA = 0d0 ! Memory allocation nS_aa = nS(1) nS_bb = nS(2) nS_sc = nS_aa + nS_bb nS_ab = (nO(1) - nC(1))*(nV(2) - nR(2)) nS_ba = (nO(2) - nC(2))*(nV(1) - nR(1)) nS_sf = nS_ab + nS_ba allocate(OmRPA(nS_sc),XpY_RPA(nS_sc,nS_sc),XmY_RPA(nS_sc,nS_sc),rho_RPA(nBas,nBas,nS_sc,nspin)) allocate(Aph(nS_sc,nS_sc),Bph(nS_sc,nS_sc),KA(nS_sc,nS_sc),KB(nS_sc,nS_sc)) call phULR_A(isp_W,dRPA_W,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,1d0,eW,ERI_aaaa,ERI_aabb,ERI_bbbb,Aph) if(.not.TDA_W) call phULR_B(isp_W,dRPA_W,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,1d0,ERI_aaaa,ERI_aabb,ERI_bbbb,Bph) call phULR(TDA_W,nS_aa,nS_bb,nS_sc,Aph,Bph,EcRPA,OmRPA,XpY_RPA,XmY_RPA) call UGW_excitation_density(nBas,nC,nO,nR,nS_aa,nS_bb,nS_sc,ERI_aaaa,ERI_aabb,ERI_bbbb,XpY_RPA,rho_RPA) call UGW_phBSE_static_kernel_A(ispin,eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,nS_sc,1d0,OmRPA,rho_RPA,KA) if(.not.TDA) call UGW_phBSE_static_kernel_B(ispin,eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,nS_sc,1d0,OmRPA,rho_RPA,KB) ! Spin-conserved manifold if(spin_conserved) then ispin = 1 allocate(Om(nS_sc),XpY(nS_sc,nS_sc),XmY(nS_sc,nS_sc)) write(*,*) '------------------------' write(*,*) 'Spin-conserved manifold ' write(*,*) '------------------------' write(*,*) write(*,*) '-----------------------------------------------------------------------------------' write(*,'(2X,A15,1X,A30,1X,A30)') 'lambda','Ec(lambda)','Tr(K x P_lambda)' write(*,*) '-----------------------------------------------------------------------------------' do iAC=1,nAC lambda = rAC(iAC) if(doXBS) then call phULR_A(isp_W,dRPA_W,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,lambda,eW,ERI_aaaa,ERI_aabb,ERI_bbbb,Aph) if(.not.TDA_W) call phULR_B(isp_W,dRPA_W,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,lambda,ERI_aaaa,ERI_aabb,ERI_bbbb,Bph) call phULR(TDA_W,nS_aa,nS_bb,nS_sc,Aph,Bph,EcRPA,OmRPA,XpY_RPA,XmY_RPA) call UGW_excitation_density(nBas,nC,nO,nR,nS_aa,nS_bb,nS_sc,ERI_aaaa,ERI_aabb,ERI_bbbb,XpY_RPA,rho_RPA) call UGW_phBSE_static_kernel_A(ispin,eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,nS_sc,lambda,OmRPA,rho_RPA,KA) if(.not.TDA) call UGW_phBSE_static_kernel_B(ispin,eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,nS_sc,lambda,OmRPA,rho_RPA,KB) end if call phULR_A(ispin,dRPA,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,lambda,eW,ERI_aaaa,ERI_aabb,ERI_bbbb,Aph) if(.not.TDA) call phULR_B(ispin,dRPA,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,lambda,ERI_aaaa,ERI_aabb,ERI_bbbb,Bph) Aph(:,:) = Aph(:,:) + KA(:,:) if(.not.TDA) Bph(:,:) = Bph(:,:) + KB(:,:) call phULR(TDA,nS_aa,nS_bb,nS_sc,Aph,Bph,EcAC(ispin),Om,XpY,XmY) call phUACFDT_correlation_energy(ispin,exchange_kernel,nBas,nC,nO,nV,nR,nS,nS_aa,nS_bb,nS_sc, & ERI_aaaa,ERI_aabb,ERI_bbbb,XpY,XmY,Ec(iAC,ispin)) write(*,'(2X,F15.6,1X,F30.15,1X,F30.15)') lambda,EcAC(ispin),Ec(iAC,ispin) end do EcAC(ispin) = 0.5d0*dot_product(wAC,Ec(:,ispin)) if(exchange_kernel) EcAC(ispin) = 0.5d0*EcAC(ispin) write(*,*) '-----------------------------------------------------------------------------------' write(*,'(2X,A50,1X,F15.6)') ' Ec(AC) via Gauss-Legendre quadrature:',EcAC(ispin) write(*,*) '-----------------------------------------------------------------------------------' write(*,*) deallocate(Om,XpY,XmY) end if ! spin-flip manifold if(spin_flip) then ispin = 2 ! Memory allocation allocate(Om(nS_sf),XpY(nS_sf,nS_sf),XmY(nS_sf,nS_sf)) write(*,*) '--------------------' write(*,*) ' Spin-flip manifold ' write(*,*) '--------------------' write(*,*) write(*,*) '-----------------------------------------------------------------------------------' write(*,'(2X,A15,1X,A30,1X,A30)') 'lambda','Ec(lambda)','Tr(K x P_lambda)' write(*,*) '-----------------------------------------------------------------------------------' do iAC=1,nAC lambda = rAC(iAC) if(doXBS) then call phULR_A(isp_W,dRPA_W,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,lambda,eW,ERI_aaaa,ERI_aabb,ERI_bbbb,Aph) if(.not.TDA_W) call phULR_B(isp_W,dRPA_W,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,lambda,ERI_aaaa,ERI_aabb,ERI_bbbb,Bph) call phULR(TDA_W,nS_aa,nS_bb,nS_sc,Aph,Bph,EcRPA,OmRPA,XpY_RPA,XmY_RPA) call UGW_excitation_density(nBas,nC,nO,nR,nS_aa,nS_bb,nS_sc,ERI_aaaa,ERI_aabb,ERI_bbbb,XpY_RPA,rho_RPA) call UGW_phBSE_static_kernel_A(ispin,eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,nS_sc,lambda,OmRPA,rho_RPA,KA) if(.not.TDA) call UGW_phBSE_static_kernel_B(ispin,eta,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sc,nS_sc,lambda,OmRPA,rho_RPA,KB) end if call phULR_A(ispin,dRPA,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sf,lambda,eW,ERI_aaaa,ERI_aabb,ERI_bbbb,Aph) if(.not.TDA) call phULR_B(ispin,dRPA,nBas,nC,nO,nV,nR,nS_aa,nS_bb,nS_sf,lambda,ERI_aaaa,ERI_aabb,ERI_bbbb,Bph) Aph(:,:) = Aph(:,:) + KA(:,:) if(.not.TDA) Bph(:,:) = Bph(:,:) + KB(:,:) call phULR(TDA,nS_aa,nS_bb,nS_sf,Aph,Bph,EcAC(ispin),Om,XpY,XmY) call phUACFDT_correlation_energy(ispin,exchange_kernel,nBas,nC,nO,nV,nR,nS,nS_ab,nS_ba,nS_sf, & ERI_aaaa,ERI_aabb,ERI_bbbb,XpY,XmY,Ec(iAC,ispin)) write(*,'(2X,F15.6,1X,F30.15,1X,F30.15)') lambda,EcAC(ispin),Ec(iAC,ispin) end do EcAC(ispin) = 0.5d0*dot_product(wAC,Ec(:,ispin)) if(exchange_kernel) EcAC(ispin) = 0.5d0*EcAC(ispin) write(*,*) '-----------------------------------------------------------------------------------' write(*,'(2X,A50,1X,F15.6)') ' Ec(AC) via Gauss-Legendre quadrature:',EcAC(ispin) write(*,*) '-----------------------------------------------------------------------------------' write(*,*) deallocate(Om,XpY,XmY) end if end subroutine