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qp2/src/mol_properties/multi_s_dipole_moment.irp.f
2023-06-29 18:31:48 +02:00

94 lines
3.1 KiB
Fortran

! Providers for the dipole moments along x,y,z and the total dipole
! moments.
! The dipole moment along the x axis is:
! \begin{align*}
! \mu_x = < \Psi_m | \sum_i x_i + \sum_A Z_A R_A | \Psi_n >
! \end{align*}
! where $i$ is used for the electrons and $A$ for the nuclei.
! $Z_A$ the charge of the nucleus $A$ and $R_A$ its position in the
! space.
! And it can be computed using the (transition, if n /= m) density
! matrix as a expectation value
! \begin{align*}
! <\Psi_n|x| \Psi_m > = \sum_p \gamma_{pp}^{nm} < \phi_p | x | \phi_p >
! + \sum_{pq, p \neq q} \gamma_{pq}^{nm} < \phi_p |x | \phi_q > + < \Psi_m | \sum_A Z_A R_A | \Psi_n >
! \end{align*}
BEGIN_PROVIDER [double precision, multi_s_dipole_moment, (N_states, N_states)]
&BEGIN_PROVIDER [double precision, multi_s_x_dipole_moment, (N_states, N_states)]
&BEGIN_PROVIDER [double precision, multi_s_y_dipole_moment, (N_states, N_states)]
&BEGIN_PROVIDER [double precision, multi_s_z_dipole_moment, (N_states, N_states)]
implicit none
BEGIN_DOC
! Providers for :
! <\Psi_m|\mu_x|\Psi_n>
! <\Psi_m|\mu_y|\Psi_n>
! <\Psi_m|\mu_z|\Psi_n>
! ||\mu|| = \sqrt{\mu_x^2 + \mu_y^2 + \mu_z^2}
!
! <\Psi_n|x| \Psi_m > = \sum_p \gamma_{pp}^{nm} \bra{\phi_p} x \ket{\phi_p}
! + \sum_{pq, p \neq q} \gamma_{pq}^{nm} \bra{\phi_p} x \ket{\phi_q}
! \Psi: wf
! n,m indexes for the states
! p,q: general spatial MOs
! gamma^{nm}: density matrix \bra{\Psi^n} a^{\dagger}_a a_i \ket{\Psi^m}
END_DOC
integer :: istate,jstate ! States
integer :: i,j ! general spatial MOs
double precision :: nuclei_part_x, nuclei_part_y, nuclei_part_z
multi_s_x_dipole_moment = 0.d0
multi_s_y_dipole_moment = 0.d0
multi_s_z_dipole_moment = 0.d0
do jstate = 1, N_states
do istate = 1, N_states
do i = 1, mo_num
do j = 1, mo_num
multi_s_x_dipole_moment(istate,jstate) -= one_e_tr_dm_mo(j,i,istate,jstate) * mo_dipole_x(j,i)
multi_s_y_dipole_moment(istate,jstate) -= one_e_tr_dm_mo(j,i,istate,jstate) * mo_dipole_y(j,i)
multi_s_z_dipole_moment(istate,jstate) -= one_e_tr_dm_mo(j,i,istate,jstate) * mo_dipole_z(j,i)
enddo
enddo
enddo
enddo
! Nuclei part
nuclei_part_x = 0.d0
nuclei_part_y = 0.d0
nuclei_part_z = 0.d0
do i = 1,nucl_num
nuclei_part_x += nucl_charge(i) * nucl_coord(i,1)
nuclei_part_y += nucl_charge(i) * nucl_coord(i,2)
nuclei_part_z += nucl_charge(i) * nucl_coord(i,3)
enddo
! Only if istate = jstate, otherwise 0 by the orthogonality of the states
do istate = 1, N_states
multi_s_x_dipole_moment(istate,istate) += nuclei_part_x
multi_s_y_dipole_moment(istate,istate) += nuclei_part_y
multi_s_z_dipole_moment(istate,istate) += nuclei_part_z
enddo
! d = <Psi|r|Psi>
do jstate = 1, N_states
do istate = 1, N_states
multi_s_dipole_moment(istate,jstate) = &
dsqrt(multi_s_x_dipole_moment(istate,jstate)**2 &
+ multi_s_y_dipole_moment(istate,jstate)**2 &
+ multi_s_z_dipole_moment(istate,jstate)**2)
enddo
enddo
END_PROVIDER