quantum_package/src/Perturbation/epstein_nesbet.irp.f

subroutine pt2_epstein_nesbet(det_pert,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st)
  use bitmasks
  implicit none
  integer, intent(in)            :: Nint,ndet,N_st
  integer(bit_kind), intent(in)  :: det_pert(Nint,2)
  double precision , intent(out) :: c_pert(N_st),e_2_pert(N_st),H_pert_diag(N_st)
  double precision               :: i_H_psi_array(N_st)
  
  BEGIN_DOC
  ! compute the standard Epstein-Nesbet perturbative first order coefficient and second order energetic contribution
  !
  ! for the various N_st states.
  !
  ! c_pert(i) = <psi(i)|H|det_pert>/( E(i) - <det_pert|H|det_pert> )
  !
  ! e_2_pert(i) = <psi(i)|H|det_pert>^2/( E(i) - <det_pert|H|det_pert> )
  !
  END_DOC
  
  integer                        :: i,j
  double precision               :: diag_H_mat_elem, h
  PROVIDE  selection_criterion

  ASSERT (Nint == N_int)
  ASSERT (Nint > 0)
  call i_H_psi(det_pert,psi_selectors,psi_selectors_coef,Nint,N_det_selectors,psi_selectors_size,N_st,i_H_psi_array)
  h = diag_H_mat_elem(det_pert,Nint)
  do i =1,N_st
    if(CI_electronic_energy(i)>h.and.CI_electronic_energy(i).ne.0.d0)then
      c_pert(i) = -1.d0
      e_2_pert(i) = selection_criterion*selection_criterion_factor*2.d0
    else if  (dabs(CI_electronic_energy(i) - h) > 1.d-6) then
        c_pert(i) = i_H_psi_array(i) / (CI_electronic_energy(i) - h)
        H_pert_diag(i) = h*c_pert(i)*c_pert(i)
        e_2_pert(i) = c_pert(i) * i_H_psi_array(i)
    else
      c_pert(i) = -1.d0
      e_2_pert(i) = -dabs(i_H_psi_array(i))
      H_pert_diag(i) = h
    endif
  enddo
  
end

subroutine pt2_epstein_nesbet_2x2(det_pert,c_pert,e_2_pert,H_pert_diag,Nint,ndet,N_st)
  use bitmasks
  implicit none
  integer, intent(in)            :: Nint,ndet,N_st
  integer(bit_kind), intent(in)  :: det_pert(Nint,2)
  double precision , intent(out) :: c_pert(N_st),e_2_pert(N_st),H_pert_diag(N_st)
  double precision               :: i_H_psi_array(N_st)
  
  BEGIN_DOC
  ! compute the Epstein-Nesbet 2x2 diagonalization coefficient and energetic contribution
  !
  ! for the various N_st states.
  !
  ! e_2_pert(i) = 0.5 * (( <det_pert|H|det_pert> -  E(i) )  - sqrt( ( <det_pert|H|det_pert> -  E(i)) ^2 + 4 <psi(i)|H|det_pert>^2  )
  !
  ! c_pert(i) = e_2_pert(i)/ <psi(i)|H|det_pert>
  !
  END_DOC
  
  integer                        :: i,j
  double precision               :: diag_H_mat_elem,delta_e, h
  ASSERT (Nint == N_int)
  ASSERT (Nint > 0)
  PROVIDE CI_electronic_energy

  call i_H_psi(det_pert,psi_selectors,psi_selectors_coef,Nint,N_det_selectors,psi_selectors_size,N_st,i_H_psi_array)
  h = diag_H_mat_elem(det_pert,Nint)
  do i =1,N_st
    if (i_H_psi_array(i) /= 0.d0) then
      delta_e = h - CI_electronic_energy(i)
      if (delta_e > 0.d0) then
        e_2_pert(i) = 0.5d0 * (delta_e - dsqrt(delta_e * delta_e + 4.d0 * i_H_psi_array(i) * i_H_psi_array(i)))
      else
        e_2_pert(i) = 0.5d0 * (delta_e + dsqrt(delta_e * delta_e + 4.d0 * i_H_psi_array(i) * i_H_psi_array(i)))
      endif
      if (dabs(i_H_psi_array(i)) > 1.d-6) then
        c_pert(i) = e_2_pert(i)/i_H_psi_array(i)
      else
        c_pert(i) = 0.d0
      endif
      H_pert_diag(i) = h*c_pert(i)*c_pert(i)
    else
      e_2_pert(i) = 0.d0
      c_pert(i) = 0.d0
      H_pert_diag(i) = 0.d0
    endif
  enddo

end