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