quack/src/GW/Bethe_Salpeter_dynamic_perturbation.f90

subroutine Bethe_Salpeter_dynamic_perturbation(BSE2,dTDA,eta,nBas,nC,nO,nV,nR,nS,eW,eGW, &
dipole_int,OmRPA,rho_RPA,OmBSE,XpY,XmY,W,A_stat)

! Compute dynamical effects via perturbation theory for BSE

  implicit none
  include 'parameters.h'

! Input variables

  logical,intent(in)            :: BSE2
  logical,intent(in)            :: dTDA 
  double precision,intent(in)   :: eta
  integer,intent(in)            :: nBas
  integer,intent(in)            :: nC
  integer,intent(in)            :: nO
  integer,intent(in)            :: nV
  integer,intent(in)            :: nR
  integer,intent(in)            :: nS

  double precision,intent(in)   :: eW(nBas)
  double precision,intent(in)   :: eGW(nBas)
  double precision,intent(in)   :: dipole_int(nBas,nBas,ncart)
  double precision,intent(in)   :: OmRPA(nS)
  double precision,intent(in)   :: rho_RPA(nBas,nBas,nS)
  double precision,intent(in)   :: OmBSE(nS)
  double precision,intent(in)   :: XpY(nS,nS)
  double precision,intent(in)   :: XmY(nS,nS)
  double precision,intent(in)   :: W(nBas,nBas,nBas,nBas)
  double precision,intent(in)   :: A_stat(nS,nS)

! Local variables

  integer                       :: ia

  integer                       :: maxS = 10
  double precision              :: gapGW

  double precision,allocatable  :: OmDyn(:)
  double precision,allocatable  :: ZDyn(:)
  double precision,allocatable  :: X(:)
  double precision,allocatable  :: Y(:)

  double precision,allocatable  ::  Ap_dyn(:,:)
  double precision,allocatable  :: ZAp_dyn(:,:)

  double precision,allocatable  ::  Bp_dyn(:,:)
  double precision,allocatable  :: ZBp_dyn(:,:)

  double precision,allocatable  ::  Am_dyn(:,:)
  double precision,allocatable  :: ZAm_dyn(:,:)

  double precision,allocatable  ::  Bm_dyn(:,:)
  double precision,allocatable  :: ZBm_dyn(:,:)

! Memory allocation

  maxS = min(nS,maxS)
  allocate(OmDyn(maxS),ZDyn(maxS),X(nS),Y(nS),Ap_dyn(nS,nS),ZAp_dyn(nS,nS))

  if(.not.dTDA) allocate(Am_dyn(nS,nS),ZAm_dyn(nS,nS),Bp_dyn(nS,nS),ZBp_dyn(nS,nS),Bm_dyn(nS,nS),ZBm_dyn(nS,nS))

  if(dTDA) then 
    write(*,*)
    write(*,*) '*** dynamical TDA activated ***'
    write(*,*)
  end if

  gapGW = eGW(nO+1) - eGW(nO) 

  write(*,*) '---------------------------------------------------------------------------------------------------'
  write(*,*) ' First-order dynamical correction to static Bethe-Salpeter excitation energies                     '
  write(*,*) '---------------------------------------------------------------------------------------------------'
  write(*,'(A57,F10.6,A3)') ' BSE neutral excitation must be lower than the GW gap = ',gapGW*HaToeV,' eV'
  write(*,*) '---------------------------------------------------------------------------------------------------'
  write(*,'(2X,A5,1X,A20,1X,A20,1X,A20,1X,A20)') '#','Static (eV)','Dynamic (eV)','Correction (eV)','Renorm. (eV)'
  write(*,*) '---------------------------------------------------------------------------------------------------'

  do ia=1,maxS

    X(:) = 0.5d0*(XpY(ia,:) + XmY(ia,:))
    Y(:) = 0.5d0*(XpY(ia,:) - XmY(ia,:))

    ! First-order correction 

    if(dTDA) then 

      ! Resonant part of the BSE correction for dynamical TDA

      call Bethe_Salpeter_A_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW,OmRPA,rho_RPA,OmBSE(ia),Ap_dyn,ZAp_dyn)

if(BSE2) call BSE2_GW_A_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,eGW,W,OmBSE(ia),Ap_dyn,ZAp_dyn,W)

      ZDyn(ia)  = dot_product(X,matmul(ZAp_dyn,X))
      OmDyn(ia) = dot_product(X,matmul( Ap_dyn - A_stat,X))

    else

      ! Resonant and anti-resonant part of the BSE correction

      call Bethe_Salpeter_AB_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW,OmRPA,rho_RPA,OmBSE(ia), &
                                            Ap_dyn,Am_dyn,Bp_dyn,Bm_dyn)

      ! Renormalization factor of the resonant and anti-resonant parts

      call Bethe_Salpeter_ZAB_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW,OmRPA,rho_RPA,OmBSE(ia), &
                                             ZAp_dyn,ZAm_dyn,ZBp_dyn,ZBm_dyn)

      ZDyn(ia)  = dot_product(X,matmul(ZAp_dyn,X)) &
                - dot_product(Y,matmul(ZAm_dyn,Y)) &
                + dot_product(X,matmul(ZBp_dyn,Y)) & 
                - dot_product(Y,matmul(ZBm_dyn,X))  

      OmDyn(ia) = dot_product(X,matmul(Ap_dyn,X)) &
                - dot_product(Y,matmul(Am_dyn,Y)) &
                + dot_product(X,matmul(Bp_dyn,Y)) & 
                - dot_product(Y,matmul(Bm_dyn,X))  

    end if

    ZDyn(ia)  = 1d0/(1d0 - ZDyn(ia))
    OmDyn(ia) = ZDyn(ia)*OmDyn(ia)

    write(*,'(2X,I5,5X,F15.6,5X,F15.6,5X,F15.6,5X,F15.6)') & 
      ia,OmBSE(ia)*HaToeV,(OmBSE(ia)+OmDyn(ia))*HaToeV,OmDyn(ia)*HaToeV,ZDyn(ia)

  end do
  write(*,*) '---------------------------------------------------------------------------------------------------'
  write(*,*) 

end subroutine Bethe_Salpeter_dynamic_perturbation