QuAcK/src/GW/ufG0W0.f90

subroutine ufG0W0(nBas,nC,nO,nV,nR,nS,ENuc,ERHF,ERI,eHF,TDA_W)

! Unfold G0W0 equations

  implicit none
  include 'parameters.h'

! Input variables

  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)   :: ENuc
  double precision,intent(in)   :: ERHF
  double precision,intent(in)   :: ERI(nBas,nBas,nBas,nBas)
  double precision,intent(in)   :: eHF(nBas)
  logical,intent(in)            :: TDA_W

! Local variables

  integer                       :: p
  integer                       :: s
  integer                       :: i,j,k,l
  integer                       :: a,b,c,d
  integer                       :: jb,kc,ia,ja
  integer                       :: klc,kcd,ija,ijb,iab,jab

  integer                       :: ispin
  double precision              :: EcRPA
  integer                       :: n2h1p,n2p1h,nH
  double precision,external     :: Kronecker_delta
  double precision,allocatable  :: H(:,:)
  double precision,allocatable  :: cGW(:,:)
  double precision,allocatable  :: eGW(:)
  double precision,allocatable  :: Z(:)
  double precision,allocatable  :: OmRPA(:)
  double precision,allocatable  :: XpY_RPA(:,:)
  double precision,allocatable  :: XmY_RPA(:,:)
  double precision,allocatable  :: rho_RPA(:,:,:)

  logical                       :: verbose = .true.
  double precision,parameter    :: cutoff1 = 0.0d0
  double precision,parameter    :: cutoff2 = 0.01d0

! Output variables

! Hello world

  write(*,*)
  write(*,*)'**********************************************'
  write(*,*)'|        Unfolded G0W0 calculation           |'
  write(*,*)'**********************************************'
  write(*,*)

  ! Dimension of the supermatrix

  write(*,*) 'Tamm-Dancoff approximation for dynamic screening by default!'
  write(*,*)

! Dimension of the supermatrix

  n2h1p = nO*nO*nV
  n2p1h = nV*nV*nO
  nH = 1 + n2h1p + n2p1h

  ! Memory allocation

  allocate(H(nH,nH),cGW(nH,nH),eGW(nH),Z(nH))

  ! Initialization

  H(:,:) = 0d0

  p=nO !Compute only the HOMO!

  if (TDA_W) then

     ! TDA for W

     write(*,*) 'Tamm-Dancoff approximation'
     write(*,*) 'No need to compute RPA quantities first'
     write(*,*)

     !---------------------------!
     !  Compute GW supermatrix   !
     !---------------------------!
     !                           !
     !     |   F   V2h1p V2p1h | ! 
     !     |                   | ! 
     ! H = | V2h1p C2h1p     0 | ! 
     !     |                   | ! 
     !     | V2p1h   0   C2p1h | ! 
     !                           !
     !---------------------------!
     !-------------!
     ! Block C2h1p !
     !-------------!

     ija = 0
     do i=nC+1,nO
        do j=nC+1,nO
           do a=nO+1,nBas-nR
              ija = ija + 1
              
              klc = 0
              do k=nC+1,nO
                 do l=nC+1,nO
                    do c=nO+1,nBas-nR
                       klc = klc + 1
                       
                       H(1+ija,1+klc) & 
                            = ((eHF(i) + eHF(j) - eHF(a))*Kronecker_delta(j,l)*Kronecker_delta(a,c) & 
                            - 2d0*ERI(j,c,a,l))*Kronecker_delta(i,k)
                       
                    end do
                 end do
              end do

           end do
        end do
     end do

     !-------------!
     ! Block C2p1h !
     !-------------!
     
     iab = 0
     do i=nC+1,nO
        do a=nO+1,nBas-nR
           do b=nO+1,nBas-nR
              iab = iab + 1
              
              kcd = 0
              do k=nC+1,nO
                 do c=nO+1,nBas-nR
                    do d=nO+1,nBas-nR
                       kcd = kcd + 1
                       
                       H(1+n2h1p+iab,1+n2h1p+kcd) &
                            = ((eHF(a) + eHF(b) - eHF(i))*Kronecker_delta(i,k)*Kronecker_delta(a,c) & 
                            + 2d0*ERI(a,k,i,c))*Kronecker_delta(b,d)
                       
                    end do
                 end do
              end do
       
           end do
        end do
     end do

     !---------!
     ! Block F !
     !---------!
     
     H(1,1) = eHF(p)
     
     !-------------!
     ! Block V2h1p !
     !-------------!
     klc = 0
     do k=nC+1,nO
        do l=nC+1,nO
           do c=nO+1,nBas-nR
              klc = klc + 1
              
              H(1       ,1+klc) = sqrt(2d0)*ERI(p,c,k,l)
              H(1+klc,1       ) = sqrt(2d0)*ERI(p,c,k,l)

           end do
        end do
     end do

     !-------------!
     ! Block V2p1h !
     !-------------!     
     kcd = 0
     do k=nC+1,nO
        do c=nO+1,nBas-nR
           do d=nO+1,nBas-nR
              
              kcd = kcd + 1   
              H(1              ,1+n2h1p+kcd) = sqrt(2d0)*ERI(p,k,d,c)
              H(1+n2h1p+kcd,1              ) = sqrt(2d0)*ERI(p,k,d,c)
              
           end do
        end do
     end do
     
  else

     ! No TDA for W

     write(*,*) 'NO Tamm-Dancoff approximation'
     write(*,*) 'A prior RPA calculation will be done'
     write(*,*)

     !---------------------------!
     !  Compute GW supermatrix   !
     !---------------------------!
     !                           !
     !     |   F   W2h1p W2p1h | ! 
     !     |                   | ! 
     ! H = | W2h1p D2h1p     0 | ! 
     !     |                   | ! 
     !     | W2p1h   0   D2p1h | ! 
     !                           !
     !---------------------------!

     ! Memory allocation !
     allocate(OmRPA(nS),XpY_RPA(nS,nS),XmY_RPA(nS,nS),rho_RPA(nBas,nBas,nS))

     ! Spin manifold 
     ispin = 1
     !-------------------!
     ! Compute screening !
     !-------------------!
     call linear_response(ispin,.true.,TDA_W,0d0,nBas,nC,nO,nV,nR,nS,1d0, & 
          eHF,ERI,EcRPA,OmRPA,XpY_RPA,XmY_RPA)
     !--------------------------!
     ! Compute spectral weights !
     !--------------------------!
     call GW_excitation_density(nBas,nC,nO,nR,nS,ERI,XpY_RPA,rho_RPA)

     !---------!
     ! Block F !
     !---------!
     H(1,1) = eHF(p)

     !-------------!
     ! Block D2h1p !
     !-------------!
     ija = 0
     do i=nC+1,nO
        do ja=1,nS
           ija = ija + 1
           H(1+ija,1+ija) = eHF(i) - OmRPA(ja) 
        end do
     end do

     !-------------!
     ! Block W2h1p !
     !-------------!
     ija = 0
     do i=nC+1,nO
        do ja=1,nS
           ija = ija + 1
           H(1    ,1+ija) = sqrt(2d0)*rho_RPA(p,i,ja)
           H(1+ija,1    ) = sqrt(2d0)*rho_RPA(p,i,ja)
        end do
     end do

     !-------------!
     ! Block D2h1p !
     !-------------!
     iab = 0
     do b=nO+1,nBas-nR
        ia = 0
        do i=nC+1,nO
           do a=nO+1,nBas-nR
              ia = ia + 1
              iab = iab + 1
              H(1+n2h1p+iab,1+n2h1p+iab) = eHF(b) + OmRPA(ia)
           end do
        end do
     end do

     !-------------!
     ! Block W2p1h !
     !-------------!
     iab = 0
     do b=nO+1,nBas-nR
        ia = 0
        do i=nC+1,nO
           do a=nO+1,nBas-nR
              ia = ia + 1
              iab = iab + 1
              H(1          ,1+n2h1p+iab) = sqrt(2d0)*rho_RPA(p,b,ia)
              H(1+n2h1p+iab,1          ) = sqrt(2d0)*rho_RPA(p,b,ia)
           end do
        end do
     end do
     
  end if
  
  !-------------------------!
  ! Diagonalize supermatrix !
  !-------------------------!

   cGW(:,:) = H(:,:)
   call diagonalize_matrix(nH,cGW,eGW)

  !-----------------!
  ! Compute weights !
  !-----------------!

    do s=1,nH
      Z(s) = cGW(1,s)**2
    end do

  !--------------!
  ! Dump results !
  !--------------!

    write(*,*)'-------------------------------------------'
    write(*,'(A35,I3)')' G0W0 energies (eV) for orbital ',p
    write(*,*)'-------------------------------------------'
    write(*,'(1X,A1,1X,A3,1X,A1,1X,A15,1X,A1,1X,A15,1X,A1,1X,A15,1X)') &
              '|','#','|','e_QP (eV)','|','Z','|'
    write(*,*)'-------------------------------------------'
 
    do s=1,nH
      write(*,'(1X,A1,1X,I3,1X,A1,1X,F15.6,1X,A1,1X,F15.6,1X,A1,1X)') &
      '|',s,'|',eGW(s)*HaToeV,'|',Z(s),'|'
    enddo
 
    write(*,*)'-------------------------------------------'
    write(*,*)

    if(verbose) then 

      do s=1,nH

        if(Z(s) > cutoff1) then

          write(*,*)'*************************************************************'
          write(*,'(1X,A20,I3,A6,I3)')'Vector for orbital ',p,' and #',s
          write(*,'(1X,A7,F10.6,A13,F10.6,1X)')' e_QP = ',eGW(s)*HaToeV,' eV and Z = ',Z(s)
          write(*,*)'*************************************************************'
          write(*,'(1X,A20,1X,A20,1X,A15,1X)') &
                    ' Configuration ',' Coefficient ',' Weight ' 
          write(*,*)'*************************************************************'
         
          if(p <= nO) & 
            write(*,'(1X,A7,I3,A16,1X,F15.6,1X,F15.6)') &
            '      (',p,')               ',cGW(1,s),cGW(1,s)**2
          if(p > nO) & 
            write(*,'(1X,A16,I3,A7,1X,F15.6,1X,F15.6)') &
            '               (',p,')      ',cGW(1,s),cGW(1,s)**2
         
          klc = 0
          do k=nC+1,nO
            do l=nC+1,nO
              do c=nO+1,nBas-nR
         
                klc = klc + 1

                if(abs(cGW(1+klc,s)) > cutoff2)               &
                write(*,'(1X,A3,I3,A1,I3,A6,I3,A7,1X,F15.6,1X,F15.6)') &
                '  (',k,',',l,') -> (',c,')      ',cGW(1+klc,s),cGW(1+klc,s)**2
         
              end do
            end do
          end do
         
          kcd = 0
          do k=nC+1,nO
            do c=nO+1,nBas-nR
              do d=nO+1,nBas-nR
         
                kcd = kcd + 1
                if(abs(cGW(1+n2h1p+kcd,s)) > cutoff2)           &
                  write(*,'(1X,A7,I3,A6,I3,A1,I3,A3,1X,F15.6,1X,F15.6)') &
                  '      (',k,') -> (',c,',',d,')  ',cGW(1+n2h1p+kcd,s),cGW(1+n2h1p+kcd,s)**2
                
              end do
            end do
          end do
 
          write(*,*)'*************************************************************'
          write(*,*)

        end if

      end do

    end if


end subroutine ufG0W0