QuantumPackage/src/mo_optimization/org/state_average_energy.org

• State average energy

State average energy

Calculation of the state average energy from the integrals and the density matrices.

\begin{align*} E = \sum_{ij} h_{ij} \gamma_{ij} + \frac{1}{2} v_{ij}^{kl} \Gamma_{ij}^{kl} \end{align*}

$h_{ij}$: mono-electronic integral $\gamma_{ij}$: one electron density matrix $v_{ij}^{kl}$: bi-electronic integral $\Gamma_{ij}^{kl}$: two electrons density matrix

TODO: OMP version

PROVIDED:

mo_one_e_integrals	double precision	mono-electronic integrals
get_two_e_integral	double precision	bi-electronic integrals
one_e_dm_mo	double precision	one electron density matrix
two_e_dm_mo	double precision	two electrons density matrix
nuclear_repulsion	double precision	nuclear repulsion
mo_num	integer	number of MOs

Output:

energy

double precision

state average energy

Internal:

mono_e	double precision	mono-electronic energy
bi_e	double precision	bi-electronic energy
i,j,k,l	integer	indexes to loop over the MOs

subroutine state_average_energy(energy)

  implicit none

  double precision, intent(out) :: energy

  double precision :: get_two_e_integral
  double precision :: mono_e, bi_e
  integer :: i,j,k,l
  
  ! mono electronic part
  mono_e = 0d0
  do j = 1, mo_num
    do i = 1, mo_num
      mono_e =  mono_e + mo_one_e_integrals(i,j) * one_e_dm_mo(i,j)
    enddo
  enddo

  ! bi electronic part
  bi_e = 0d0
  do l = 1, mo_num
    do k = 1, mo_num
      do j = 1, mo_num
        do i = 1, mo_num
          bi_e = bi_e + get_two_e_integral(i,j,k,l,mo_integrals_map) * two_e_dm_mo(i,j,k,l)
        enddo
      enddo
    enddo
  enddo

  ! State average energy
  energy = mono_e + 0.5d0 * bi_e + nuclear_repulsion

  ! Check
  !call print_energy_components
  
  print*,'State average energy:', energy
  !print*,ci_energy

end