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add molecular properties

This commit is contained in:
Yann Damour 2023-03-11 22:31:57 +01:00
parent 8f8001fd09
commit b16a6c7d53
10 changed files with 488 additions and 0 deletions

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[print_all_transitions]
type: logical
doc: If true, print the transition between all the states
interface: ezfio,provider,ocaml
default: false
[calc_dipole_moment]
type: logical
doc: If true, the electric dipole moment will be computed
interface: ezfio,provider,ocaml
default: false
[calc_tr_dipole_moment]
type: logical
doc: If true and N_states > 1, the transition electric dipole moment will be computed
interface: ezfio,provider,ocaml
default: false
[calc_osc_str]
type: logical
doc: If true and N_states > 1, the oscillator strength will be computed
interface: ezfio,provider,ocaml
default: false

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src/mol_properties/NEED Normal file
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determinants
davidson_undressed

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# Molecular properties
Available quantities:
- Electric dipole moment
- Electric transition dipole moment
- Oscillator strength
They are not computed by default. To compute them:
```
qp set mol_properties calc_dipole_moment true
qp set mol_properties calc_tr_dipole_moment true
qp set mol_properties calc_osc_str true
```
If you are interested in transitions between two excited states:
```
qp set mol_properties print_all_transitions true
```

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BEGIN_PROVIDER [double precision, ci_energy_no_diag, (N_states) ]
implicit none
BEGIN_DOC
! CI energy from density matrices and integrals
! Avoid the rediagonalization for ci_energy
END_DOC
ci_energy_no_diag = psi_energy + nuclear_repulsion
END_PROVIDER

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BEGIN_PROVIDER [double precision, mo_deriv_1_x , (mo_num,mo_num)]
&BEGIN_PROVIDER [double precision, mo_deriv_1_y , (mo_num,mo_num)]
&BEGIN_PROVIDER [double precision, mo_deriv_1_z , (mo_num,mo_num)]
BEGIN_DOC
! array of the integrals of MO_i * d/dx MO_j
! array of the integrals of MO_i * d/dy MO_j
! array of the integrals of MO_i * d/dz MO_j
END_DOC
implicit none
call ao_to_mo( &
ao_deriv_1_x, &
size(ao_deriv_1_x,1), &
mo_deriv_1_x, &
size(mo_deriv_1_x,1) &
)
call ao_to_mo( &
ao_deriv_1_y, &
size(ao_deriv_1_y,1), &
mo_deriv_1_y, &
size(mo_deriv_1_y,1) &
)
call ao_to_mo( &
ao_deriv_1_z, &
size(ao_deriv_1_z,1), &
mo_deriv_1_z, &
size(mo_deriv_1_z,1) &
)
END_PROVIDER

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BEGIN_PROVIDER [double precision, multi_s_deriv_1, (N_states, N_states)]
&BEGIN_PROVIDER [double precision, multi_s_x_deriv_1, (N_states, N_states)]
&BEGIN_PROVIDER [double precision, multi_s_y_deriv_1, (N_states, N_states)]
&BEGIN_PROVIDER [double precision, multi_s_z_deriv_1, (N_states, N_states)]
implicit none
BEGIN_DOC
! Providers for :
! <Psi_m|v_x|Psi_n>
! <Psi_m|v_y|Psi_n>
! <Psi_m|v_z|Psi_n>
! ||v|| = sqrt(v_x^2 + v_y^2 + v_z^2)
! v_x = d/dx
! Cf. multi_s_dipole_moment for the equations
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_deriv_1 = 0.d0
multi_s_y_deriv_1 = 0.d0
multi_s_z_deriv_1 = 0.d0
do jstate = 1, N_states
do istate = 1, N_states
do i = 1, mo_num
! Diag part
multi_s_x_deriv_1(istate,jstate) -= one_e_tr_dm_mo(i,i,istate,jstate) * mo_deriv_1_x(i,i)
multi_s_y_deriv_1(istate,jstate) -= one_e_tr_dm_mo(i,i,istate,jstate) * mo_deriv_1_y(i,i)
multi_s_z_deriv_1(istate,jstate) -= one_e_tr_dm_mo(i,i,istate,jstate) * mo_deriv_1_z(i,i)
do j = 1, mo_num
if (i == j) then
cycle
endif
! Extra diag part
multi_s_x_deriv_1(istate,jstate) -= one_e_tr_dm_mo(j,i,istate,jstate) * mo_deriv_1_x(j,i)
multi_s_y_deriv_1(istate,jstate) -= one_e_tr_dm_mo(j,i,istate,jstate) * mo_deriv_1_y(j,i)
multi_s_z_deriv_1(istate,jstate) -= one_e_tr_dm_mo(j,i,istate,jstate) * mo_deriv_1_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_deriv_1(istate,istate) += nuclei_part_x
multi_s_y_deriv_1(istate,istate) += nuclei_part_y
multi_s_z_deriv_1(istate,istate) += nuclei_part_z
enddo
! d = <Psi|r|Psi>
do jstate = 1, N_states
do istate = 1, N_states
multi_s_deriv_1(istate,jstate) = &
dsqrt(multi_s_x_deriv_1(istate,jstate)**2 &
+ multi_s_y_deriv_1(istate,jstate)**2 &
+ multi_s_z_deriv_1(istate,jstate)**2)
enddo
enddo
END_PROVIDER

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! 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

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subroutine print_mol_properties()
implicit none
BEGIN_DOC
! Run the propertie calculations
END_DOC
! Electric dipole moment
if (calc_dipole_moment) then
call print_dipole_moment
endif
! Transition electric dipole moment
if (calc_tr_dipole_moment .and. N_states > 1) then
call print_transition_dipole_moment
endif
! Oscillator strength
if (calc_osc_str .and. N_states > 1) then
call print_oscillator_strength
endif
end

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! Dipole moments
! Provided
! | N_states | integer | Number of states |
! | multi_s_x_dipole_moment(N_states,N_states) | double precision | (transition) dipole moments along x axis |
! | multi_s_y_dipole_moment(N_states,N_states) | double precision | (transition) dipole moments along y axis |
! | multi_s_z_dipole_moment(N_states,N_states) | double precision | (transition) dipole moments along z axis |
! | multi_s_dipole_moment(N_states,N_states) | double precision | Total (transition) dipole moments |
subroutine print_dipole_moment
implicit none
BEGIN_DOC
! To print the dipole moment ||<\Psi_i|µ|\Psi_i>|| and its x,y,z components
END_DOC
integer :: istate
double precision, allocatable :: d(:), d_x(:), d_y(:), d_z(:)
allocate(d(N_states),d_x(N_states),d_y(N_states),d_z(N_states))
do istate = 1, N_states
d_x(istate) = multi_s_x_dipole_moment(istate,istate)
d_y(istate) = multi_s_y_dipole_moment(istate,istate)
d_z(istate) = multi_s_z_dipole_moment(istate,istate)
d(istate) = multi_s_dipole_moment(istate,istate)
enddo
! Atomic units
print*,''
print*,'# Dipoles:'
print*,'=============================================='
print*,' Dipole moments (au)'
print*,' State X Y Z ||µ||'
do istate = 1, N_states
write(*,'(I5,4(F12.6))') (istate-1), d_x(istate), d_y(istate), d_z(istate), d(istate)
enddo
! Debye
print*,''
print*,' Dipole moments (D)'
print*,' State X Y Z ||µ||'
do istate = 1, N_states
write(*,'(I5,4(F12.6))') (istate-1), d_x(istate)*au_to_D, d_y(istate)*au_to_D, d_z(istate)*au_to_D, d(istate)*au_to_D
enddo
print*,'=============================================='
print*,''
deallocate(d,d_x,d_y,d_z)
end
! Transition dipole moments
! Provided
! | N_states | integer | Number of states |
! | multi_s_x_dipole_moment(N_states,N_states) | double precision | (transition) dipole moments along x axis |
! | multi_s_y_dipole_moment(N_states,N_states) | double precision | (transition) dipole moments along y axis |
! | multi_s_z_dipole_moment(N_states,N_states) | double precision | (transition) dipole moments along z axis |
! | multi_s_dipole_moment(N_states,N_states) | double precision | Total (transition) dipole moments |
subroutine print_transition_dipole_moment
implicit none
BEGIN_DOC
! To print the transition dipole moment ||<\Psi_i|µ|\Psi_j>|| and its components along x, y and z
END_DOC
integer :: istate,jstate, n_states_print
double precision :: f, d, d_x, d_y, d_z, dip_str
if (N_states == 1 .or. N_det == 1) then
return
endif
print*,''
print*,'# Transition dipoles:'
print*,'=============================================='
print*,' Transition dipole moments (au)'
write(*,'(A89)') ' # Transition X Y Z ||µ|| Dip. str. Osc. str.'
if (print_all_transitions) then
n_states_print = N_states
else
n_states_print = 1
endif
do jstate = 1, n_states_print !N_states
do istate = jstate + 1, N_states
d_x = multi_s_x_dipole_moment(istate,jstate)
d_y = multi_s_y_dipole_moment(istate,jstate)
d_z = multi_s_z_dipole_moment(istate,jstate)
dip_str = d_x**2 + d_y**2 + d_z**2
d = multi_s_dipole_moment(istate,jstate)
f = 2d0/3d0 * d * d * dabs(ci_energy_no_diag(istate) - ci_energy_no_diag(jstate))
write(*,'(I4,I4,A4,I3,6(F12.6))') (istate-1), (jstate-1), ' ->', (istate-1), d_x, d_y, d_z, d, dip_str, f
enddo
enddo
print*,''
print*,' Transition dipole moments (D)'
write(*,'(A89)') ' # Transition X Y Z ||µ|| Dip. str. Osc. str.'
do jstate = 1, n_states_print !N_states
do istate = jstate + 1, N_states
d_x = multi_s_x_dipole_moment(istate,jstate) * au_to_D
d_y = multi_s_y_dipole_moment(istate,jstate) * au_to_D
d_z = multi_s_z_dipole_moment(istate,jstate) * au_to_D
d = multi_s_dipole_moment(istate,jstate)
dip_str = d_x**2 + d_y**2 + d_z**2
f = 2d0/3d0 * d * d * dabs(ci_energy_no_diag(istate) - ci_energy_no_diag(jstate))
d = multi_s_dipole_moment(istate,jstate) * au_to_D
write(*,'(I4,I4,A4,I3,6(F12.6))') (istate-1), (jstate-1), ' ->', (istate-1), d_x, d_y, d_z, d, dip_str, f
enddo
enddo
print*,'=============================================='
print*,''
end
! Oscillator strengths
! Provided
! | N_states | integer | Number of states |
! | multi_s_dipole_moment(N_states,N_states) | double precision | Total (transition) dipole moments |
! | multi_s_deriv1_moment(N_states,N_states) | double precision | Total (transition) ... |
! | ci_energy_no_diag(N_states) | double precision | CI energy of each state |
! Internal
! | f_l | double precision | Oscillator strength in length gauge |
! | f_v | double precision | Oscillator strength in velocity gauge |
! | f_m | double precision | Oscillator strength in mixed gauge |
! | n_states_print | integer | Number of printed states |
subroutine print_oscillator_strength
implicit none
BEGIN_DOC
! https://doi.org/10.1016/j.cplett.2004.03.126
! Oscillator strength in:
! - length gauge, f^l_{ij} = 2/3 (E_i - E_j) <\Psi_i|r|\Psi_j> <\Psi_j|r|\Psi_i>
! - velocity gauge, f^v_{ij} = 2/3 (E_i - E_j)^(-1) <\Psi_i|v|\Psi_j> <\Psi_j|v|\Psi_i>
! - mixed gauge, f^m_{ij} = -2i/3 <\Psi_i|r|\Psi_j> <\Psi_j|v|\Psi_i>
END_DOC
integer :: istate,jstate,k, n_states_print
double precision :: f_l,f_v,f_m,d,v
if (N_states == 1 .or. N_det == 1) then
return
endif
print*,''
print*,'# Oscillator strength:'
print*,'=============================================='
if (print_all_transitions) then
n_states_print = N_states
else
n_states_print = 1
endif
write(*,'(A103)') ' Oscillator strength in length gauge (f_l), velocity gauge (f_v) and mixed length-velocity gauge (f_m)'
do jstate = 1, n_states_print !N_states
do istate = jstate + 1, N_states
d = multi_s_dipole_moment(istate,jstate)
v = multi_s_deriv_1(istate,jstate)
! Length gauge
f_l = 2d0/3d0 * d * d * dabs(ci_energy_no_diag(istate) - ci_energy_no_diag(jstate))
! Velocity gauge
f_v = 2d0/3d0 * v * v * 1d0/dabs(ci_energy_no_diag(istate) - ci_energy_no_diag(jstate))
! Mixed gauge
f_m = 2d0/3d0 * d * v
write(*,'(A19,I3,A9,F10.6,A5,F7.1,A10,F9.6,A6,F9.6,A6,F9.6,A8,F7.3)') ' # Transition n.', (istate-1), ': Excit.=', dabs((ci_energy_no_diag(istate) - ci_energy_no_diag(jstate)))*ha_to_ev, &
' eV ( ',dabs((ci_energy_no_diag(istate) - ci_energy_no_diag(jstate)))*Ha_to_nm,' nm), f_l=',f_l, ', f_v=', f_v, ', f_m=', f_m, ', <S^2>=', s2_values(istate)
!write(*,'(I4,I4,A4,I3,A6,F6.1,A6,F6.1)') (istate-1), (jstate-1), ' ->', (istate-1), ', %T1=', percent_exc(2,istate), ', %T2=',percent_exc(3,istate)
enddo
enddo
print*,'=============================================='
print*,''
end

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program mol_properties
implicit none
BEGIN_DOC
! Run the propertie calculations
END_DOC
read_wf = .True.
touch read_wf
call print_mol_properties()
end