quack/src/GW/Sangalli_dynamic_perturbation.f90

subroutine Sangalli_dynamic_perturbation(dTDA,eta,nBas,nC,nO,nV,nR,nS,eGW,OmRPA,OmBSE,XpY,XmY,rho)

! Compute dynamical effects via perturbation theory for Sangalli's kernel

  implicit none
  include 'parameters.h'

! Input variables

  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)   :: eGW(nBas)
  double precision,intent(in)   :: OmRPA(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)   :: rho(nBas,nBas,nS)

! Local variables

  integer                       :: ia

  integer,parameter             :: 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

  allocate(OmDyn(nS),ZDyn(nS),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))

! Print main components of transition vectors

  call print_transition_vectors(nBas,nC,nO,nV,nR,nS,OmBSE,XpY,XmY)

  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 BSE excitation energies with Sangalli kernel           '
  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,min(nS,maxS)

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

    if(dTDA) then 

!     call Sangalli_A_matrix_dynamic (eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),+OmBSE(ia),rho(:,:,:),Ap_dyn(:,:))
!     call Sangalli_ZA_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),-OmBSE(ia),rho(:,:,:),ZAp_dyn(:,:))
     
      ZDyn(ia)  = dot_product(X(:),matmul(ZAp_dyn(:,:),X(:)))
      OmDyn(ia) = dot_product(X(:),matmul(Ap_dyn(:,:),X(:)))

    else

!     call Sangalli_A_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),+OmBSE(ia),rho(:,:,:),Ap_dyn(:,:))
!     call Sangalli_A_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),-OmBSE(ia),rho(:,:,:),Am_dyn(:,:))

!     call Sangalli_B_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),+OmBSE(ia),rho(:,:,:),Bp_dyn(:,:))
!     call Sangalli_B_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),-OmBSE(ia),rho(:,:,:),Bm_dyn(:,:))

!     call Sangalli_ZA_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),+OmBSE(ia),rho(:,:,:),ZAp_dyn(:,:))
!     call Sangalli_ZA_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),-OmBSE(ia),rho(:,:,:),ZAm_dyn(:,:))
!     call Sangalli_ZB_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),+OmBSE(ia),rho(:,:,:),ZBp_dyn(:,))
!     call Sangalli_ZB_matrix_dynamic(eta,nBas,nC,nO,nV,nR,nS,1d0,eGW(:),OmRPA(:),-OmBSE(ia),rho(:,:,:),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 Sangalli_dynamic_perturbation