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1188 lines
24 KiB
ReStructuredText
1188 lines
24 KiB
ReStructuredText
.. _module_dft_utils_one_e:
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.. program:: dft_utils_one_e
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.. default-role:: option
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===============
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dft_utils_one_e
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===============
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This module contains all the one-body related quantities needed to perform DFT or RS-DFT calculations with the LDA and PBE functionals.
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Therefore, it contains most of the properties which depends on the one-body density and density matrix.
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Some interesting quantities you might take a look at:
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* The LDA and PBE *providers* for the x/c energies in :file:`e_xc.irp.f` and :file:`sr_exc.irp.f`
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* The LDA and PBE *providers* for the x/c potentials on the AO basis in :file:`pot_ao.irp.f` and :file:`sr_pot_ao.irp.f`
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* The :math:`h_{core}` energy computed directly with the one-body density matrix in :file:`one_e_energy_dft.irp.f`
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* LDA and PBE short-range functionals *subroutines* in :file:`exc_sr_lda.irp.f` and :file:`exc_sr_pbe.irp.f`
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Providers
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---------
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.. c:var:: ao_effective_one_e_potential
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File : :file:`dft_utils_one_e/effective_pot.irp.f`
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.. code:: fortran
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double precision, allocatable :: ao_effective_one_e_potential (ao_num,ao_num,N_states)
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double precision, allocatable :: ao_effective_one_e_potential_without_kin (ao_num,ao_num,N_states)
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ao_effective_one_e_potential(i,j) = :math:`\rangle i_{AO}| v_{H}^{sr} |j_{AO}\rangle + \rangle i_{AO}| h_{core} |j_{AO}\rangle + \rangle i_{AO}|v_{xc} |j_{AO}\rangle`
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`effective_one_e_potential`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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* :c:data:`n_states`
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.. c:var:: ao_effective_one_e_potential_without_kin
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File : :file:`dft_utils_one_e/effective_pot.irp.f`
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.. code:: fortran
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double precision, allocatable :: ao_effective_one_e_potential (ao_num,ao_num,N_states)
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double precision, allocatable :: ao_effective_one_e_potential_without_kin (ao_num,ao_num,N_states)
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ao_effective_one_e_potential(i,j) = :math:`\rangle i_{AO}| v_{H}^{sr} |j_{AO}\rangle + \rangle i_{AO}| h_{core} |j_{AO}\rangle + \rangle i_{AO}|v_{xc} |j_{AO}\rangle`
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`ao_num`
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* :c:data:`effective_one_e_potential`
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* :c:data:`mo_coef`
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* :c:data:`mo_num`
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* :c:data:`n_states`
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.. c:var:: effective_one_e_potential
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File : :file:`dft_utils_one_e/effective_pot.irp.f`
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.. code:: fortran
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double precision, allocatable :: effective_one_e_potential (mo_num,mo_num,N_states)
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double precision, allocatable :: effective_one_e_potential_without_kin (mo_num,mo_num,N_states)
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Effective_one_e_potential(i,j) = :math:`\rangle i_{MO}| v_{H}^{sr} |j_{MO}\rangle + \rangle i_{MO}| h_{core} |j_{MO}\rangle + \rangle i_{MO}|v_{xc} |j_{MO}\rangle`
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on the |MO| basis
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Taking the expectation value does not provide any energy, but
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effective_one_e_potential(i,j) is the potential coupling DFT and WFT part to
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be used in any WFT calculation.
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_num`
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* :c:data:`n_states`
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* :c:data:`potential_c_alpha_mo`
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* :c:data:`potential_x_alpha_mo`
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* :c:data:`short_range_hartree_operator`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_effective_one_e_potential`
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.. c:var:: effective_one_e_potential_without_kin
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File : :file:`dft_utils_one_e/effective_pot.irp.f`
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.. code:: fortran
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double precision, allocatable :: effective_one_e_potential (mo_num,mo_num,N_states)
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double precision, allocatable :: effective_one_e_potential_without_kin (mo_num,mo_num,N_states)
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Effective_one_e_potential(i,j) = :math:`\rangle i_{MO}| v_{H}^{sr} |j_{MO}\rangle + \rangle i_{MO}| h_{core} |j_{MO}\rangle + \rangle i_{MO}|v_{xc} |j_{MO}\rangle`
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on the |MO| basis
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Taking the expectation value does not provide any energy, but
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effective_one_e_potential(i,j) is the potential coupling DFT and WFT part to
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be used in any WFT calculation.
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_num`
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* :c:data:`n_states`
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* :c:data:`potential_c_alpha_mo`
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* :c:data:`potential_x_alpha_mo`
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* :c:data:`short_range_hartree_operator`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`ao_effective_one_e_potential`
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.. c:var:: energy_sr_c_lda
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File : :file:`dft_utils_one_e/sr_exc.irp.f`
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.. code:: fortran
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double precision, allocatable :: energy_sr_x_lda (N_states)
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double precision, allocatable :: energy_sr_c_lda (N_states)
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exchange/correlation energy with the short range lda functional
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`final_grid_points`
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* :c:data:`mu_erf_dft`
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* :c:data:`n_points_final_grid`
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* :c:data:`n_states`
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* :c:data:`one_e_dm_alpha_at_r`
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.. c:var:: energy_sr_c_pbe
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File : :file:`dft_utils_one_e/sr_exc.irp.f`
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.. code:: fortran
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double precision, allocatable :: energy_sr_x_pbe (N_states)
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double precision, allocatable :: energy_sr_c_pbe (N_states)
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exchange/correlation energy with the short range pbe functional
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`final_grid_points`
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* :c:data:`mu_erf_dft`
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* :c:data:`n_points_final_grid`
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* :c:data:`n_states`
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* :c:data:`one_e_dm_and_grad_alpha_in_r`
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.. c:var:: energy_sr_x_lda
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File : :file:`dft_utils_one_e/sr_exc.irp.f`
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.. code:: fortran
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double precision, allocatable :: energy_sr_x_lda (N_states)
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double precision, allocatable :: energy_sr_c_lda (N_states)
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exchange/correlation energy with the short range lda functional
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`final_grid_points`
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* :c:data:`mu_erf_dft`
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* :c:data:`n_points_final_grid`
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* :c:data:`n_states`
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* :c:data:`one_e_dm_alpha_at_r`
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.. c:var:: energy_sr_x_pbe
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File : :file:`dft_utils_one_e/sr_exc.irp.f`
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.. code:: fortran
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double precision, allocatable :: energy_sr_x_pbe (N_states)
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double precision, allocatable :: energy_sr_c_pbe (N_states)
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exchange/correlation energy with the short range pbe functional
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`final_grid_points`
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* :c:data:`mu_erf_dft`
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* :c:data:`n_points_final_grid`
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* :c:data:`n_states`
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* :c:data:`one_e_dm_and_grad_alpha_in_r`
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.. c:function:: gga_sr_type_functionals:
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File : :file:`dft_utils_one_e/utils.irp.f`
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.. code:: fortran
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subroutine GGA_sr_type_functionals(r,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_a_b, &
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ex,vx_rho_a,vx_rho_b,vx_grad_rho_a_2,vx_grad_rho_b_2,vx_grad_rho_a_b, &
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ec,vc_rho_a,vc_rho_b,vc_grad_rho_a_2,vc_grad_rho_b_2,vc_grad_rho_a_b )
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routine that helps in building the x/c potentials on the AO basis for a GGA functional with a short-range interaction
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mu_erf_dft`
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* :c:data:`n_states`
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Called by:
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.. hlist::
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:columns: 3
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* :c:data:`aos_sr_vc_alpha_pbe_w`
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* :c:data:`aos_sr_vxc_alpha_pbe_w`
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* :c:data:`energy_sr_x_pbe`
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* :c:data:`energy_x_sr_pbe`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`ec_pbe_sr`
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* :c:func:`ex_pbe_sr`
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* :c:func:`grad_rho_ab_to_grad_rho_oc`
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* :c:func:`rho_ab_to_rho_oc`
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* :c:func:`v_grad_rho_oc_to_v_grad_rho_ab`
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* :c:func:`v_rho_oc_to_v_rho_ab`
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.. c:function:: gga_type_functionals:
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File : :file:`dft_utils_one_e/utils.irp.f`
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.. code:: fortran
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subroutine GGA_type_functionals(r,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_a_b, &
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ex,vx_rho_a,vx_rho_b,vx_grad_rho_a_2,vx_grad_rho_b_2,vx_grad_rho_a_b, &
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ec,vc_rho_a,vc_rho_b,vc_grad_rho_a_2,vc_grad_rho_b_2,vc_grad_rho_a_b )
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routine that helps in building the x/c potentials on the AO basis for a GGA functional
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_states`
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Called by:
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.. hlist::
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:columns: 3
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* :c:data:`aos_vc_alpha_pbe_w`
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* :c:data:`aos_vxc_alpha_pbe_w`
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* :c:data:`energy_c_pbe`
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* :c:data:`energy_x_pbe`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`ec_pbe_sr`
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* :c:func:`ex_pbe_sr`
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* :c:func:`grad_rho_ab_to_grad_rho_oc`
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* :c:func:`rho_ab_to_rho_oc`
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* :c:func:`v_grad_rho_oc_to_v_grad_rho_ab`
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* :c:func:`v_rho_oc_to_v_rho_ab`
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.. c:var:: mu_erf_dft
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File : :file:`dft_utils_one_e/mu_erf_dft.irp.f`
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.. code:: fortran
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double precision :: mu_erf_dft
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range separation parameter used in RS-DFT. It is set to mu_erf in order to be consistent with the two electrons integrals erf
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mu_erf`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`aos_sr_vc_alpha_lda_w`
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* :c:data:`aos_sr_vc_alpha_pbe_w`
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* :c:data:`aos_sr_vxc_alpha_lda_w`
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* :c:data:`aos_sr_vxc_alpha_pbe_w`
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* :c:data:`energy_c_sr_lda`
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* :c:data:`energy_sr_x_lda`
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* :c:data:`energy_sr_x_pbe`
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* :c:data:`energy_x_sr_lda`
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* :c:data:`energy_x_sr_pbe`
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.. c:var:: psi_dft_energy_h_core
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File : :file:`dft_utils_one_e/one_e_energy_dft.irp.f`
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.. code:: fortran
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double precision, allocatable :: psi_dft_energy_kinetic (N_states)
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double precision, allocatable :: psi_dft_energy_nuclear_elec (N_states)
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double precision, allocatable :: psi_dft_energy_h_core (N_states)
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kinetic, electron-nuclear and total h_core energy computed with the density matrix one_e_dm_mo_beta_for_dft+one_e_dm_mo_alpha_for_dft
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`elec_alpha_num`
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* :c:data:`elec_beta_num`
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_num`
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* :c:data:`n_states`
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* :c:data:`one_e_dm_mo_alpha_for_dft`
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* :c:data:`one_e_dm_mo_beta_for_dft`
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.. c:var:: psi_dft_energy_kinetic
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File : :file:`dft_utils_one_e/one_e_energy_dft.irp.f`
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.. code:: fortran
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double precision, allocatable :: psi_dft_energy_kinetic (N_states)
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double precision, allocatable :: psi_dft_energy_nuclear_elec (N_states)
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double precision, allocatable :: psi_dft_energy_h_core (N_states)
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kinetic, electron-nuclear and total h_core energy computed with the density matrix one_e_dm_mo_beta_for_dft+one_e_dm_mo_alpha_for_dft
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`elec_alpha_num`
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* :c:data:`elec_beta_num`
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_num`
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* :c:data:`n_states`
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* :c:data:`one_e_dm_mo_alpha_for_dft`
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* :c:data:`one_e_dm_mo_beta_for_dft`
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.. c:var:: psi_dft_energy_nuclear_elec
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File : :file:`dft_utils_one_e/one_e_energy_dft.irp.f`
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.. code:: fortran
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double precision, allocatable :: psi_dft_energy_kinetic (N_states)
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double precision, allocatable :: psi_dft_energy_nuclear_elec (N_states)
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double precision, allocatable :: psi_dft_energy_h_core (N_states)
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kinetic, electron-nuclear and total h_core energy computed with the density matrix one_e_dm_mo_beta_for_dft+one_e_dm_mo_alpha_for_dft
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`elec_alpha_num`
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* :c:data:`elec_beta_num`
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* :c:data:`mo_integrals_n_e`
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* :c:data:`mo_kinetic_integrals`
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* :c:data:`mo_num`
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* :c:data:`n_states`
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* :c:data:`one_e_dm_mo_alpha_for_dft`
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* :c:data:`one_e_dm_mo_beta_for_dft`
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.. c:var:: short_range_hartree
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File : :file:`dft_utils_one_e/sr_coulomb.irp.f`
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.. code:: fortran
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double precision, allocatable :: short_range_hartree_operator (mo_num,mo_num,N_states)
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double precision, allocatable :: short_range_hartree (N_states)
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short_range_Hartree_operator(i,j) = :math:`\int dr i(r)j(r) \int r' \rho(r') W_{ee}^{sr}`
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short_range_Hartree = :math:`1/2 \sum_{i,j} \rho_{ij} \mathtt{short_range_Hartree_operator}(i,j)`
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= :math:`1/2 \int dr \int r' \rho(r) \rho(r') W_{ee}^{sr}`
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`mo_integrals_erf_map`
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* :c:data:`mo_integrals_map`
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* :c:data:`mo_num`
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* :c:data:`mo_two_e_integrals_erf_in_map`
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* :c:data:`mo_two_e_integrals_in_map`
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* :c:data:`n_states`
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* :c:data:`one_e_dm_average_mo_for_dft`
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* :c:data:`one_e_dm_mo_for_dft`
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|
Needed by:
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|
.. hlist::
|
|
:columns: 3
|
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|
|
* :c:data:`effective_one_e_potential`
|
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* :c:data:`trace_v_xc`
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.. c:var:: short_range_hartree_operator
|
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File : :file:`dft_utils_one_e/sr_coulomb.irp.f`
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.. code:: fortran
|
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|
|
double precision, allocatable :: short_range_hartree_operator (mo_num,mo_num,N_states)
|
|
double precision, allocatable :: short_range_hartree (N_states)
|
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short_range_Hartree_operator(i,j) = :math:`\int dr i(r)j(r) \int r' \rho(r') W_{ee}^{sr}`
|
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|
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short_range_Hartree = :math:`1/2 \sum_{i,j} \rho_{ij} \mathtt{short_range_Hartree_operator}(i,j)`
|
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|
|
= :math:`1/2 \int dr \int r' \rho(r) \rho(r') W_{ee}^{sr}`
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|
Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`mo_integrals_erf_map`
|
|
* :c:data:`mo_integrals_map`
|
|
* :c:data:`mo_num`
|
|
* :c:data:`mo_two_e_integrals_erf_in_map`
|
|
* :c:data:`mo_two_e_integrals_in_map`
|
|
* :c:data:`n_states`
|
|
* :c:data:`one_e_dm_average_mo_for_dft`
|
|
* :c:data:`one_e_dm_mo_for_dft`
|
|
|
|
Needed by:
|
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|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`effective_one_e_potential`
|
|
* :c:data:`trace_v_xc`
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|
|
Subroutines / functions
|
|
-----------------------
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|
.. c:function:: berf:
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File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
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.. code:: fortran
|
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|
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function berf(a)
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.. c:function:: dberfda:
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File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
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|
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.. code:: fortran
|
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|
|
function dberfda(a)
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.. c:function:: dpol:
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|
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File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
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.. code:: fortran
|
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|
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double precision function dpol(rs)
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.. c:function:: dpold:
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|
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File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
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|
.. code:: fortran
|
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|
|
double precision function dpold(rs)
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.. c:function:: dpoldd:
|
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|
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File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
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|
|
.. code:: fortran
|
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|
|
double precision function dpoldd(rs)
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|
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.. c:function:: ec_lda:
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|
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File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
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|
.. code:: fortran
|
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|
|
subroutine ec_lda(rho_a,rho_b,ec,vc_a,vc_b)
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|
|
Called by:
|
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|
|
.. hlist::
|
|
:columns: 3
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|
|
* :c:func:`ec_pbe_only`
|
|
* :c:func:`ec_pbe_sr`
|
|
* :c:data:`energy_c_lda`
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ecpw`
|
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|
|
.. c:function:: ec_lda_sr:
|
|
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|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
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|
.. code:: fortran
|
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|
|
subroutine ec_lda_sr(mu,rho_a,rho_b,ec,vc_a,vc_b)
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|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`aos_sr_vc_alpha_lda_w`
|
|
* :c:data:`aos_sr_vxc_alpha_lda_w`
|
|
* :c:data:`aos_vc_alpha_lda_w`
|
|
* :c:data:`aos_vxc_alpha_lda_w`
|
|
* :c:func:`ec_pbe_only`
|
|
* :c:func:`ec_pbe_sr`
|
|
* :c:data:`energy_c_sr_lda`
|
|
* :c:data:`energy_sr_x_lda`
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ecorrlr`
|
|
* :c:func:`ecpw`
|
|
* :c:func:`vcorrlr`
|
|
|
|
|
|
.. c:function:: ec_only_lda_sr:
|
|
|
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|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine ec_only_lda_sr(mu,rho_a,rho_b,ec)
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|
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|
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|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ecorrlr`
|
|
* :c:func:`ecpw`
|
|
|
|
|
|
.. c:function:: ec_pbe_only:
|
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|
|
|
File : :file:`dft_utils_one_e/exc_sr_pbe.irp.f`
|
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|
|
.. code:: fortran
|
|
|
|
subroutine ec_pbe_only(mu,rhoc,rhoo,sigmacc,sigmaco,sigmaoo,ec)
|
|
|
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|
|
Short-range pbe correlation energy functional for erf interaction
|
|
|
|
input : ==========
|
|
|
|
mu = range separated parameter
|
|
|
|
rhoc, rhoo = total density and spin density
|
|
|
|
sigmacc = square of the gradient of the total density
|
|
|
|
sigmaco = square of the gradient of the spin density
|
|
|
|
sigmaoo = scalar product between the gradient of the total density and the one of the spin density
|
|
|
|
output: ==========
|
|
|
|
ec = correlation energy
|
|
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ec_lda`
|
|
* :c:func:`ec_lda_sr`
|
|
|
|
|
|
.. c:function:: ec_pbe_sr:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_pbe.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine ec_pbe_sr(mu,rhoc,rhoo,sigmacc,sigmaco,sigmaoo,ec,vrhoc,vrhoo,vsigmacc,vsigmaco,vsigmaoo)
|
|
|
|
|
|
Short-range pbe correlation energy functional for erf interaction
|
|
|
|
input : ==========
|
|
|
|
mu = range separated parameter
|
|
|
|
rhoc, rhoo = total density and spin density
|
|
|
|
sigmacc = square of the gradient of the total density
|
|
|
|
sigmaco = square of the gradient of the spin density
|
|
|
|
sigmaoo = scalar product between the gradient of the total density and the one of the spin density
|
|
|
|
output: ==========
|
|
|
|
ec = correlation energy
|
|
|
|
all variables v** are energy derivatives with respect to components of the density
|
|
|
|
vrhoc = derivative with respect to the total density
|
|
|
|
vrhoo = derivative with respect to spin density
|
|
|
|
vsigmacc = derivative with respect to the square of the gradient of the total density
|
|
|
|
vsigmaco = derivative with respect to scalar product between the gradients of total and spin densities
|
|
|
|
vsigmaoo = derivative with respect to the square of the gradient of the psin density
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`gga_sr_type_functionals`
|
|
* :c:func:`gga_type_functionals`
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ec_lda`
|
|
* :c:func:`ec_lda_sr`
|
|
|
|
|
|
.. c:function:: ecorrlr:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine ecorrlr(rs,z,mu,eclr)
|
|
|
|
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ec_lda_sr`
|
|
* :c:func:`ec_only_lda_sr`
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ecpw`
|
|
|
|
|
|
.. c:function:: ecpw:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine ecPW(x,y,ec,ecd,ecz,ecdd,eczd)
|
|
|
|
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ec_lda`
|
|
* :c:func:`ec_lda_sr`
|
|
* :c:func:`ec_only_lda_sr`
|
|
* :c:func:`ecorrlr`
|
|
* :c:func:`vcorrlr`
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`gpw`
|
|
|
|
|
|
.. c:function:: ex_lda:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine ex_lda(rho_a,rho_b,ex,vx_a,vx_b)
|
|
|
|
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`energy_x_lda`
|
|
|
|
|
|
.. c:function:: ex_lda_sr:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine ex_lda_sr(mu,rho_a,rho_b,ex,vx_a,vx_b)
|
|
|
|
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`aos_sr_vc_alpha_lda_w`
|
|
* :c:data:`aos_sr_vxc_alpha_lda_w`
|
|
* :c:data:`aos_vc_alpha_lda_w`
|
|
* :c:data:`aos_vxc_alpha_lda_w`
|
|
* :c:data:`energy_sr_x_lda`
|
|
* :c:data:`energy_x_sr_lda`
|
|
* :c:func:`ex_pbe_sr`
|
|
* :c:func:`ex_pbe_sr_only`
|
|
|
|
|
|
.. c:function:: ex_pbe_sr:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_pbe.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine ex_pbe_sr(mu,rho_a,rho_b,grd_rho_a_2,grd_rho_b_2,grd_rho_a_b,ex,vx_rho_a,vx_rho_b,vx_grd_rho_a_2,vx_grd_rho_b_2,vx_grd_rho_a_b)
|
|
|
|
|
|
mu = range separation parameter
|
|
rho_a = density alpha
|
|
rho_b = density beta
|
|
grd_rho_a_2 = (gradient rho_a)^2
|
|
grd_rho_b_2 = (gradient rho_b)^2
|
|
grd_rho_a_b = (gradient rho_a).(gradient rho_b)
|
|
ex = exchange energy density at the density and corresponding gradients of the density
|
|
vx_rho_a = d ex / d rho_a
|
|
vx_rho_b = d ex / d rho_b
|
|
vx_grd_rho_a_2 = d ex / d grd_rho_a_2
|
|
vx_grd_rho_b_2 = d ex / d grd_rho_b_2
|
|
vx_grd_rho_a_b = d ex / d grd_rho_a_b
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`gga_sr_type_functionals`
|
|
* :c:func:`gga_type_functionals`
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ex_lda_sr`
|
|
|
|
|
|
.. c:function:: ex_pbe_sr_only:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_pbe.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine ex_pbe_sr_only(mu,rho_a,rho_b,grd_rho_a_2,grd_rho_b_2,grd_rho_a_b,ex)
|
|
|
|
|
|
rho_a = density alpha
|
|
rho_b = density beta
|
|
grd_rho_a_2 = (gradient rho_a)^2
|
|
grd_rho_b_2 = (gradient rho_b)^2
|
|
grd_rho_a_b = (gradient rho_a).(gradient rho_b)
|
|
ex = exchange energy density at point r
|
|
|
|
Calls:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ex_lda_sr`
|
|
|
|
|
|
.. c:function:: g0d:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function g0d(rs)
|
|
|
|
|
|
|
|
|
|
.. c:function:: g0dd:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function g0dd(rs)
|
|
|
|
|
|
|
|
|
|
.. c:function:: g0f:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function g0f(x)
|
|
|
|
|
|
|
|
|
|
.. c:function:: gpw:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine GPW(x,Ac,alfa1,beta1,beta2,beta3,beta4,G,Gd,Gdd)
|
|
|
|
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`ecpw`
|
|
|
|
|
|
.. c:function:: grad_rho_ab_to_grad_rho_oc:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/rho_ab_to_rho_tot.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine grad_rho_ab_to_grad_rho_oc(grad_rho_a_2,grad_rho_b_2,grad_rho_a_b,grad_rho_o_2,grad_rho_c_2,grad_rho_o_c)
|
|
|
|
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`gga_sr_type_functionals`
|
|
* :c:func:`gga_type_functionals`
|
|
|
|
|
|
.. c:function:: qrpa:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function Qrpa(x)
|
|
|
|
|
|
|
|
|
|
.. c:function:: qrpad:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function Qrpad(x)
|
|
|
|
|
|
|
|
|
|
.. c:function:: qrpadd:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function Qrpadd(x)
|
|
|
|
|
|
|
|
|
|
.. c:function:: rho_ab_to_rho_oc:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/rho_ab_to_rho_tot.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine rho_ab_to_rho_oc(rho_a,rho_b,rho_o,rho_c)
|
|
|
|
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`gga_sr_type_functionals`
|
|
* :c:func:`gga_type_functionals`
|
|
|
|
|
|
.. c:function:: rho_oc_to_rho_ab:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/rho_ab_to_rho_tot.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine rho_oc_to_rho_ab(rho_o,rho_c,rho_a,rho_b)
|
|
|
|
|
|
|
|
|
|
.. c:function:: v_grad_rho_oc_to_v_grad_rho_ab:
|
|
|
|
|
|
File : :file:`dft_utils_one_e/rho_ab_to_rho_tot.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine v_grad_rho_oc_to_v_grad_rho_ab(v_grad_rho_o_2,v_grad_rho_c_2,v_grad_rho_o_c,v_grad_rho_a_2,v_grad_rho_b_2,v_grad_rho_a_b)
|
|
|
|
|
|
|
|
Called by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:func:`gga_sr_type_functionals`
|
|
* :c:func:`gga_type_functionals`
|
|
|
|
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.. c:function:: v_rho_ab_to_v_rho_oc:
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File : :file:`dft_utils_one_e/rho_ab_to_rho_tot.irp.f`
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.. code:: fortran
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subroutine v_rho_ab_to_v_rho_oc(v_rho_a,v_rho_b,v_rho_o,v_rho_c)
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.. c:function:: v_rho_oc_to_v_rho_ab:
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File : :file:`dft_utils_one_e/rho_ab_to_rho_tot.irp.f`
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.. code:: fortran
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subroutine v_rho_oc_to_v_rho_ab(v_rho_o,v_rho_c,v_rho_a,v_rho_b)
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`gga_sr_type_functionals`
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* :c:func:`gga_type_functionals`
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.. c:function:: vcorrlr:
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File : :file:`dft_utils_one_e/exc_sr_lda.irp.f`
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.. code:: fortran
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subroutine vcorrlr(rs,z,mu,vclrup,vclrdown,vclrupd,vclrdownd)
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Called by:
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.. hlist::
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:columns: 3
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* :c:func:`ec_lda_sr`
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Calls:
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.. hlist::
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:columns: 3
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* :c:func:`ecpw`
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