quack/src/QuAcK/G0W0.f90

subroutine G0W0(doACFDT,exchange_kernel,doXBS,COHSEX,SOSEX,BSE,TDA_W,TDA,        & 
                dBSE,dTDA,evDyn,singlet_manifold,triplet_manifold,linearize,eta, & 
                nBas,nC,nO,nV,nR,nS,ENuc,ERHF,Hc,H,ERI,PHF,cHF,eHF,eGW)

! Perform G0W0 calculation

  implicit none
  include 'parameters.h'
  include 'quadrature.h'

! Input variables

  logical,intent(in)            :: doACFDT
  logical,intent(in)            :: exchange_kernel
  logical,intent(in)            :: doXBS
  logical,intent(in)            :: COHSEX
  logical,intent(in)            :: SOSEX
  logical,intent(in)            :: BSE
  logical,intent(in)            :: TDA_W
  logical,intent(in)            :: TDA
  logical,intent(in)            :: dBSE
  logical,intent(in)            :: dTDA
  logical,intent(in)            :: evDyn
  logical,intent(in)            :: singlet_manifold
  logical,intent(in)            :: triplet_manifold
  logical,intent(in)            :: linearize
  double precision,intent(in)   :: eta

  integer,intent(in)            :: nBas,nC,nO,nV,nR,nS
  double precision,intent(in)   :: ENuc
  double precision,intent(in)   :: ERHF
  double precision,intent(in)   :: eHF(nBas)
  double precision,intent(in)   :: cHF(nBas,nBas)
  double precision,intent(in)   :: PHF(nBas,nBas)
  double precision,intent(in)   :: Hc(nBas,nBas)
  double precision,intent(in)   :: H(nBas,nBas)
  double precision,intent(in)   :: ERI(nBas,nBas,nBas,nBas)

! Local variables

  logical                       :: print_W = .true.
  integer                       :: ispin
  double precision              :: EcRPA(nspin)
  double precision              :: EcBSE(nspin)
  double precision              :: EcAC(nspin)
  double precision              :: EcGM
  double precision,allocatable  :: SigC(:)
  double precision,allocatable  :: Z(:)
  double precision,allocatable  :: Omega(:,:)
  double precision,allocatable  :: XpY(:,:,:)
  double precision,allocatable  :: XmY(:,:,:)
  double precision,allocatable  :: rho(:,:,:,:)
  double precision,allocatable  :: rhox(:,:,:,:)

  double precision,allocatable  :: eGWlin(:)

! Output variables

  double precision              :: eGW(nBas)

! Hello world

  write(*,*)
  write(*,*)'************************************************'
  write(*,*)'|          One-shot G0W0 calculation           |'
  write(*,*)'************************************************'
  write(*,*)

! Initialization

  EcRPA(:) = 0d0

! SOSEX correction

  if(SOSEX) write(*,*) 'SOSEX correction activated!'
  write(*,*)

! COHSEX approximation

  if(COHSEX) write(*,*) 'COHSEX approximation activated!'
  write(*,*)

! TDA for W

  if(TDA_W) write(*,*) 'Tamm-Dancoff approximation for dynamic screening!'
  write(*,*)

! TDA 

  if(TDA) write(*,*) 'Tamm-Dancoff approximation activated!'
  write(*,*)

! Spin manifold 

  ispin = 1

! Memory allocation

  allocate(SigC(nBas),Z(nBas),Omega(nS,nspin),XpY(nS,nS,nspin),XmY(nS,nS,nspin),  & 
           rho(nBas,nBas,nS,nspin),rhox(nBas,nBas,nS,nspin),eGWlin(nBas))

! Compute linear response

  call linear_response(ispin,.true.,TDA_W,.false.,eta,nBas,nC,nO,nV,nR,nS,1d0,eHF,ERI, & 
                       rho(:,:,:,ispin),EcRPA(ispin),Omega(:,ispin),XpY(:,:,ispin),XmY(:,:,ispin))

! Compute correlation part of the self-energy 

  call excitation_density(nBas,nC,nO,nR,nS,ERI,XpY(:,:,ispin),rho(:,:,:,ispin))

  if(SOSEX) call excitation_density_SOSEX(nBas,nC,nO,nR,nS,ERI,XpY(:,:,ispin),rhox(:,:,:,ispin))

  call self_energy_correlation_diag(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eHF, & 
                                    Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),EcGM,SigC)

! Compute renormalization factor

  call renormalization_factor(COHSEX,SOSEX,eta,nBas,nC,nO,nV,nR,nS,eHF, & 
                              Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin),Z(:))

! Solve the quasi-particle equation

  eGWlin(:) = eHF(:) + Z(:)*SigC(:)

  if(linearize) then 
 
    write(*,*) ' *** Quasiparticle energies obtained by linearization *** '
    write(*,*)

    eGW(:) = eGWlin(:)

! Find all the roots of the QP equation if necessary

! call QP_roots(nBas,nC,nO,nV,nR,nS,eta,eHF,Omega,rho,eGWlin)

  else 
  
  ! Find graphical solution of the QP equation

  call QP_graph(nBas,nC,nO,nV,nR,nS,eta,eHF,Omega,rho,eGWlin,eGW)
 
  end if

! Dump results

  if(print_W) call print_excitation('RPA@G0W0    ',ispin,nS,Omega(:,ispin))

  call print_G0W0(nBas,nO,eHF,ENuc,ERHF,SigC,Z,eGW,EcRPA(ispin),EcGM)

! Compute the RPA correlation energy

  call linear_response(ispin,.true.,TDA_W,.false.,eta,nBas,nC,nO,nV,nR,nS,1d0,eGW,ERI, & 
                       rho(:,:,:,ispin),EcRPA(ispin),Omega(:,ispin),XpY(:,:,ispin),XmY(:,:,ispin))

  write(*,*)
  write(*,*)'-------------------------------------------------------------------------------'
  write(*,'(2X,A50,F20.10)') 'Tr@RPA@G0W0 correlation energy (singlet) =',EcRPA(1)
  write(*,'(2X,A50,F20.10)') 'Tr@RPA@G0W0 correlation energy (triplet) =',EcRPA(2)
  write(*,'(2X,A50,F20.10)') 'Tr@RPA@G0W0 correlation energy           =',EcRPA(1) + EcRPA(2)
  write(*,'(2X,A50,F20.10)') 'Tr@RPA@G0W0 total energy                 =',ENuc + ERHF + EcRPA(1) + EcRPA(2)
  write(*,*)'-------------------------------------------------------------------------------'
  write(*,*)

! Plot stuff

! call plot_GW(nBas,nC,nO,nV,nR,nS,eHF,eGW,Omega(:,ispin),rho(:,:,:,ispin),rhox(:,:,:,ispin))

! Perform BSE calculation

  if(BSE) then

    call Bethe_Salpeter(TDA_W,TDA,dBSE,dTDA,evDyn,singlet_manifold,triplet_manifold,eta, &
                        nBas,nC,nO,nV,nR,nS,ERI,eHF,eGW,Omega,XpY,XmY,rho,EcRPA,EcBSE)

    if(exchange_kernel) then
 
      EcRPA(1) = 0.5d0*EcRPA(1)
      EcRPA(2) = 1.5d0*EcRPA(1)
 
    end if

    write(*,*)
    write(*,*)'-------------------------------------------------------------------------------'
    write(*,'(2X,A50,F20.10)') 'Tr@BSE@G0W0 correlation energy (singlet) =',EcBSE(1)
    write(*,'(2X,A50,F20.10)') 'Tr@BSE@G0W0 correlation energy (triplet) =',EcBSE(2)
    write(*,'(2X,A50,F20.10)') 'Tr@BSE@G0W0 correlation energy           =',EcBSE(1) + EcBSE(2)
    write(*,'(2X,A50,F20.10)') 'Tr@BSE@G0W0 total energy                 =',ENuc + ERHF + EcBSE(1) + EcBSE(2)
    write(*,*)'-------------------------------------------------------------------------------'
    write(*,*)

!   Compute the BSE correlation energy via the adiabatic connection 

    if(doACFDT) then

      write(*,*) '------------------------------------------------------'
      write(*,*) 'Adiabatic connection version of BSE correlation energy'
      write(*,*) '------------------------------------------------------'
      write(*,*) 

      if(doXBS) then 

        write(*,*) '*** scaled screening version (XBS) ***'
        write(*,*)

      end if

      call ACFDT(exchange_kernel,doXBS,.true.,TDA_W,TDA,BSE,singlet_manifold,triplet_manifold,eta, & 
                 nBas,nC,nO,nV,nR,nS,ERI,eHF,eGW,Omega,XpY,XmY,rho,EcAC)

      if(exchange_kernel) then
  
        EcAC(1) = 0.5d0*EcAC(1)
        EcAC(2) = 1.5d0*EcAC(1)
  
      end if

      write(*,*)
      write(*,*)'-------------------------------------------------------------------------------'
      write(*,'(2X,A50,F20.10)') 'AC@BSE@G0W0 correlation energy (singlet) =',EcAC(1)
      write(*,'(2X,A50,F20.10)') 'AC@BSE@G0W0 correlation energy (triplet) =',EcAC(2)
      write(*,'(2X,A50,F20.10)') 'AC@BSE@G0W0 correlation energy           =',EcAC(1) + EcAC(2)
      write(*,'(2X,A50,F20.10)') 'AC@BSE@G0W0 total energy                 =',ENuc + ERHF + EcAC(1) + EcAC(2)
      write(*,*)'-------------------------------------------------------------------------------'
      write(*,*)

    end if

  end if

end subroutine G0W0