subroutine ACFDT(exchange_kernel,doXBS,dRPA,TDA_W,TDA,BSE,singlet,triplet,eta,nBas,nC,nO,nV,nR,nS,ERI,eW,e,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) :: exchange_kernel logical,intent(in) :: dRPA logical,intent(in) :: TDA_W logical,intent(in) :: TDA logical,intent(in) :: BSE logical,intent(in) :: singlet logical,intent(in) :: triplet double precision,intent(in) :: eta integer,intent(in) :: nBas,nC,nO,nV,nR,nS double precision,intent(in) :: eW(nBas) double precision,intent(in) :: e(nBas) double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas) ! Local variables integer :: ispin integer :: isp_W integer :: iAC double precision :: lambda double precision,allocatable :: Ec(:,:) double precision :: EcRPA double precision,allocatable :: WA(:,:) double precision,allocatable :: WB(:,:) double precision,allocatable :: OmRPA(:) double precision,allocatable :: XpY_RPA(:,:) double precision,allocatable :: XmY_RPA(:,:) double precision,allocatable :: rho_RPA(:,:,:) double precision,allocatable :: Omega(:,:) double precision,allocatable :: XpY(:,:,:) double precision,allocatable :: XmY(:,:,:) ! Output variables double precision,intent(out) :: EcAC(nspin) ! Memory allocation allocate(Ec(nAC,nspin)) allocate(WA(nS,nS),WB(nS,nS),OmRPA(nS),XpY_RPA(nS,nS),XmY_RPA(nS,nS),rho_RPA(nBas,nBas,nS)) allocate(Omega(nS,nspin),XpY(nS,nS,nspin),XmY(nS,nS,nspin)) ! 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 call linear_response(isp_W,.true.,TDA_W,eta,nBas,nC,nO,nV,nR,nS,1d0,eW,ERI, & EcRPA,OmRPA,XpY_RPA,XmY_RPA) call GW_excitation_density(nBas,nC,nO,nR,nS,ERI,XpY_RPA,rho_RPA) call BSE_static_kernel_KA(eta,nBas,nC,nO,nV,nR,nS,1d0,ERI,OmRPA,rho_RPA,WA) call BSE_static_kernel_KB(eta,nBas,nC,nO,nV,nR,nS,1d0,ERI,OmRPA,rho_RPA,WB) ! Singlet manifold if(singlet) then ispin = 1 write(*,*) '--------------' write(*,*) 'Singlet states' 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 linear_response(isp_W,.true.,TDA_W,eta,nBas,nC,nO,nV,nR,nS,lambda,eW,ERI, & EcRPA,OmRPA,XpY_RPA,XmY_RPA) call GW_excitation_density(nBas,nC,nO,nR,nS,ERI,XpY_RPA,rho_RPA) ! call print_excitation('W^lambda: ',isp_W,nS,OmRPA) call BSE_static_kernel_KA(eta,nBas,nC,nO,nV,nR,nS,lambda,ERI,OmRPA,rho_RPA,WA) call BSE_static_kernel_KB(eta,nBas,nC,nO,nV,nR,nS,lambda,ERI,OmRPA,rho_RPA,WB) end if call linear_response_BSE(ispin,dRPA,TDA,BSE,eta,nBas,nC,nO,nV,nR,nS,lambda,e,ERI,WA,WB, & EcAC(ispin),Omega(:,ispin),XpY(:,:,ispin),XmY(:,:,ispin)) call ACFDT_correlation_energy(ispin,exchange_kernel,nBas,nC,nO,nV,nR,nS, & ERI,XpY(:,:,ispin),XmY(:,:,ispin),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(*,*) end if ! Triplet manifold if(triplet) then ispin = 2 write(*,*) '--------------' write(*,*) 'Triplet states' 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 linear_response(isp_W,.true.,TDA_W,eta,nBas,nC,nO,nV,nR,nS,lambda,eW,ERI, & EcRPA,OmRPA,XpY_RPA,XmY_RPA) call GW_excitation_density(nBas,nC,nO,nR,nS,ERI,XpY_RPA,rho_RPA) call BSE_static_kernel_KA(eta,nBas,nC,nO,nV,nR,nS,lambda,ERI,OmRPA,rho_RPA,WA) call BSE_static_kernel_KB(eta,nBas,nC,nO,nV,nR,nS,lambda,ERI,OmRPA,rho_RPA,WB) end if call linear_response_BSE(ispin,dRPA,TDA,BSE,eta,nBas,nC,nO,nV,nR,nS,lambda,e,ERI,WA,WB, & EcAC(ispin),Omega(:,ispin),XpY(:,:,ispin),XmY(:,:,ispin)) call ACFDT_correlation_energy(ispin,exchange_kernel,nBas,nC,nO,nV,nR,nS,ERI,XpY(:,:,ispin),XmY(:,:,ispin),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) = 1.5d0*EcAC(ispin) write(*,*) '-----------------------------------------------------------------------------------' write(*,'(2X,A50,1X,F15.6)') ' Ec(AC) via Gauss-Legendre quadrature:',EcAC(ispin) write(*,*) '-----------------------------------------------------------------------------------' write(*,*) end if end subroutine ACFDT