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qp2/docs/source/modules/mo_basis.rst
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.. _module_mo_basis:
.. program:: mo_basis
.. default-role:: option
========
mo_basis
========
Molecular orbitals are expressed as
.. math::
\phi_k({\bf r}) = \sum_i C_{ik} \chi_k({\bf r})
where :math:`\chi_k` are *normalized* atomic basis functions.
The current set of |MOs| has a label `mo_label`.
When the orbitals are modified, the label should also be updated to keep
everything consistent.
When saving the |MOs|, the :file:`mo_basis` directory of the |EZFIO| database
is copied in the :file:`save` directory, named by the current `mo_label`. All
this is done with the script named :file:`save_current_mos.sh` in the
:file:`$QP_ROOT/scripts` directory.
EZFIO parameters
----------------
.. option:: mo_num
Total number of |MOs|
.. option:: mo_coef
Coefficient of the i-th |AO| on the j-th |MO|
.. option:: mo_coef_aux
AUX Coefficient of the i-th |AO| on the j-th |MO|
.. option:: mo_coef_imag
Imaginary part of the MO coefficient of the i-th |AO| on the j-th |MO|
.. option:: mo_label
Label characterizing the MOS (Local, Canonical, Natural, *etc*)
.. option:: mo_occ
|MO| occupation numbers
.. option:: mo_symmetry
MOs with the same integer belong to the same irrep.
.. option:: mo_class
[ Core | Inactive | Active | Virtual | Deleted ], as defined by :ref:`qp_set_mo_class`
.. option:: ao_md5
MD5 checksum characterizing the |AO| basis set.
Providers
---------
.. c:var:: mo_class
File : :file:`mo_basis/mo_class.irp.f`
.. code:: fortran
character*(32), allocatable :: mo_class (mo_num)
[ Core | Inactive | Active | Virtual | Deleted ], as defined by :ref:`qp_set_mo_class`
Needs:
.. hlist::
:columns: 3
* :c:data:`ezfio_filename`
* :c:data:`mo_num`
* :c:data:`mpi_master`
Needed by:
.. hlist::
:columns: 3
* :c:data:`list_act`
* :c:data:`list_all_but_del_orb`
* :c:data:`list_core`
* :c:data:`list_del`
* :c:data:`list_inact`
* :c:data:`list_virt`
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`mo_two_e_integrals_in_map`
* :c:data:`n_act_orb`
* :c:data:`n_all_but_del_orb`
* :c:data:`n_core_orb`
* :c:data:`n_del_orb`
* :c:data:`n_inact_orb`
* :c:data:`n_virt_orb`
.. c:var:: mo_coef
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
double precision, allocatable :: mo_coef (ao_num,mo_num)
Molecular orbital coefficients on |AO| basis set
mo_coef(i,j) = coefficient of the i-th |AO| on the jth |MO|
mo_label : Label characterizing the |MOs| (local, canonical, natural, etc)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_ortho_canonical_coef`
* :c:data:`ezfio_filename`
* :c:data:`mo_num`
* :c:data:`mpi_master`
Needed by:
.. hlist::
:columns: 3
* :c:data:`attachment_orbitals`
* :c:data:`cholesky_mo_transp`
* :c:data:`d0tu_alpha_ao`
* :c:data:`eigenvectors_fock_matrix_mo`
* :c:data:`fock_matrix_mo_alpha`
* :c:data:`fock_matrix_mo_beta`
* :c:data:`fps_spf_matrix_mo`
* :c:data:`mcscf_fock_alpha_mo`
* :c:data:`mo_coef_in_ao_ortho_basis`
* :c:data:`mo_coef_transp`
* :c:data:`mo_deriv_1_x`
* :c:data:`mo_dipole_x`
* :c:data:`mo_integrals_n_e`
* :c:data:`mo_integrals_n_e_per_atom`
* :c:data:`mo_kinetic_integrals`
* :c:data:`mo_overlap`
* :c:data:`mo_pseudo_integrals`
* :c:data:`mo_pseudo_integrals_local`
* :c:data:`mo_pseudo_integrals_non_local`
* :c:data:`mo_spread_x`
* :c:data:`mo_two_e_int_erf_jj_from_ao`
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`mo_two_e_integrals_in_map`
* :c:data:`natorbsfci`
* :c:data:`one_e_dm_alpha_ao_for_dft`
* :c:data:`one_e_dm_alpha_ao_for_dft_no_core`
* :c:data:`one_e_dm_ao_alpha`
* :c:data:`one_e_dm_ao_alpha_nstates`
* :c:data:`one_e_dm_mo_alpha_for_dft`
* :c:data:`one_e_dm_mo_beta_for_dft`
* :c:data:`one_e_spin_density_ao`
* :c:data:`psi_det`
* :c:data:`s_mo_coef`
* :c:data:`scf_density_matrix_ao_alpha`
* :c:data:`scf_density_matrix_ao_beta`
.. c:var:: mo_coef_aux
File : :file:`mo_basis/mos_aux.irp.f`
.. code:: fortran
double precision, allocatable :: mo_coef_aux (ao_num,mo_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_ortho_canonical_coef`
* :c:data:`ezfio_filename`
* :c:data:`mo_num`
* :c:data:`mpi_master`
.. c:var:: mo_coef_imag
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
double precision, allocatable :: mo_coef_imag (ao_num,mo_num)
Molecular orbital coefficients on |AO| basis set
mo_coef_imag(i,j) = coefficient of the i-th |AO| on the jth |MO|
mo_label : Label characterizing the |MOs| (local, canonical, natural, etc)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ezfio_filename`
* :c:data:`mo_num`
* :c:data:`mpi_master`
.. c:var:: mo_coef_in_ao_ortho_basis
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
double precision, allocatable :: mo_coef_in_ao_ortho_basis (ao_num,mo_num)
|MO| coefficients in orthogonalized |AO| basis
:math:`C^{-1}.C_{mo}`
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_ortho_canonical_coef_inv`
* :c:data:`mo_coef`
* :c:data:`mo_num`
.. c:var:: mo_coef_transp
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
double precision, allocatable :: mo_coef_transp (mo_num,ao_num)
|MO| coefficients on |AO| basis set
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
* :c:data:`mo_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`cholesky_semi_mo_transp_simple`
* :c:data:`mo_two_e_int_erf_jj_from_ao`
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`mo_two_e_integrals_in_map`
.. c:var:: mo_label
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
character*(64) :: mo_label
|MO| coefficients on |AO| basis set
mo_coef(i,j) = coefficient of the i-th |AO| on the j-th |MO|
mo_label : Label characterizing the |MOs| (local, canonical, natural, etc)
Needs:
.. hlist::
:columns: 3
* :c:data:`ezfio_filename`
* :c:data:`mpi_master`
Needed by:
.. hlist::
:columns: 3
* :c:data:`n_det`
* :c:data:`psi_coef`
* :c:data:`psi_det`
.. c:var:: mo_num
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
integer :: mo_num
Number of MOs
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_ortho_canonical_coef`
* :c:data:`ezfio_filename`
* :c:data:`mpi_master`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_one_e_integrals_from_mo`
* :c:data:`ao_ortho_canonical_nucl_elec_integrals`
* :c:data:`ao_ortho_lowdin_nucl_elec_integrals`
* :c:data:`attachment_numbers_sorted`
* :c:data:`attachment_orbitals`
* :c:data:`banned_excitation`
* :c:data:`bielec_pqxx_array`
* :c:data:`bielec_pqxx_no_array`
* :c:data:`bielec_pxxq_array`
* :c:data:`bielec_pxxq_no_array`
* :c:data:`bielecci`
* :c:data:`bielecci_no`
* :c:data:`big_array_coulomb_integrals`
* :c:data:`cholesky_mo`
* :c:data:`cholesky_mo_transp`
* :c:data:`cholesky_no_1_idx_transp`
* :c:data:`cholesky_no_total_transp`
* :c:data:`cholesky_semi_mo_transp_simple`
* :c:data:`core_fock_operator`
* :c:data:`core_fock_operator_erf`
* :c:data:`d0tu_alpha_ao`
* :c:data:`data_one_e_dm_alpha_mo`
* :c:data:`data_one_e_dm_beta_mo`
* :c:data:`difference_dm`
* :c:data:`difference_dm_eigvect`
* :c:data:`eigenvectors_fock_matrix_mo`
* :c:data:`fapq`
* :c:data:`fipq`
* :c:data:`fock_matrix_ao`
* :c:data:`fock_matrix_mo`
* :c:data:`fock_matrix_mo_alpha`
* :c:data:`fock_matrix_mo_beta`
* :c:data:`fock_operator_closed_shell_ref_bitmask`
* :c:data:`fock_wee_closed_shell`
* :c:data:`fps_spf_matrix_mo`
* :c:data:`full_ijkl_bitmask`
* :c:data:`h_core_ri`
* :c:data:`int_erf_3_index`
* :c:data:`list_act`
* :c:data:`list_all_but_del_orb`
* :c:data:`list_core`
* :c:data:`list_core_inact`
* :c:data:`list_core_inact_act`
* :c:data:`list_del`
* :c:data:`list_inact`
* :c:data:`list_inact_act`
* :c:data:`list_virt`
* :c:data:`lowest_super_ci_coef_mo`
* :c:data:`mcscf_fock_alpha_mo`
* :c:data:`mcscf_fock_mo`
* :c:data:`mo_class`
* :c:data:`mo_coef`
* :c:data:`mo_coef_aux`
* :c:data:`mo_coef_begin_iteration`
* :c:data:`mo_coef_imag`
* :c:data:`mo_coef_in_ao_ortho_basis`
* :c:data:`mo_coef_transp`
* :c:data:`mo_deriv_1_x`
* :c:data:`mo_dipole_x`
* :c:data:`mo_integrals_cache_min`
* :c:data:`mo_integrals_erf_cache_min`
* :c:data:`mo_integrals_erf_map`
* :c:data:`mo_integrals_map`
* :c:data:`mo_integrals_n_e`
* :c:data:`mo_integrals_n_e_per_atom`
* :c:data:`mo_kinetic_integrals`
* :c:data:`mo_occ`
* :c:data:`mo_one_e_integrals`
* :c:data:`mo_overlap`
* :c:data:`mo_pseudo_integrals`
* :c:data:`mo_pseudo_integrals_local`
* :c:data:`mo_pseudo_integrals_non_local`
* :c:data:`mo_spread_centered_x`
* :c:data:`mo_spread_x`
* :c:data:`mo_two_e_int_erf_jj`
* :c:data:`mo_two_e_int_erf_jj_from_ao`
* :c:data:`mo_two_e_integrals_erf_in_map`
* :c:data:`mo_two_e_integrals_in_map`
* :c:data:`mo_two_e_integrals_jj`
* :c:data:`multi_s_deriv_1`
* :c:data:`multi_s_dipole_moment`
* :c:data:`n_act_orb`
* :c:data:`n_all_but_del_orb`
* :c:data:`n_attachment`
* :c:data:`n_core_orb`
* :c:data:`n_del_orb`
* :c:data:`n_inact_orb`
* :c:data:`n_int`
* :c:data:`n_virt_orb`
* :c:data:`natorbsci_mos`
* :c:data:`natorbsfci`
* :c:data:`neworbs`
* :c:data:`occnum`
* :c:data:`one_body_dm_mo_alpha_one_det`
* :c:data:`one_e_dm_alpha_ao_for_dft`
* :c:data:`one_e_dm_alpha_ao_for_dft_no_core`
* :c:data:`one_e_dm_ao_alpha`
* :c:data:`one_e_dm_ao_alpha_nstates`
* :c:data:`one_e_dm_average_alpha_mo_for_dft`
* :c:data:`one_e_dm_average_beta_mo_for_dft`
* :c:data:`one_e_dm_average_mo_for_dft`
* :c:data:`one_e_dm_dagger_mo_spin_index`
* :c:data:`one_e_dm_mo`
* :c:data:`one_e_dm_mo_alpha`
* :c:data:`one_e_dm_mo_alpha_average`
* :c:data:`one_e_dm_mo_alpha_for_dft`
* :c:data:`one_e_dm_mo_alpha_for_dft_no_core`
* :c:data:`one_e_dm_mo_beta_for_dft`
* :c:data:`one_e_dm_mo_beta_for_dft_no_core`
* :c:data:`one_e_dm_mo_diff`
* :c:data:`one_e_dm_mo_for_dft`
* :c:data:`one_e_dm_mo_spin_index`
* :c:data:`one_e_spin_density_ao`
* :c:data:`one_e_spin_density_mo`
* :c:data:`one_e_tr_dm_mo`
* :c:data:`one_e_tr_dm_mo_alpha`
* :c:data:`one_ints_no`
* :c:data:`ormas_n_orb`
* :c:data:`psi_energy_h_core`
* :c:data:`s_mo_coef`
* :c:data:`super_ci_dm`
* :c:data:`superci_natorb`
* :c:data:`switch_mo_coef`
* :c:data:`two_e_dm_mo`
* :c:data:`umat`
* :c:data:`v_ne_psi_energy`
* :c:data:`z_dipole_moment`
.. c:var:: mo_occ
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
double precision, allocatable :: mo_occ (mo_num)
|MO| occupation numbers
Needs:
.. hlist::
:columns: 3
* :c:data:`elec_alpha_num`
* :c:data:`elec_beta_num`
* :c:data:`ezfio_filename`
* :c:data:`mo_num`
* :c:data:`mpi_master`
Subroutines / functions
-----------------------
.. c:function:: ao_ortho_cano_to_ao:
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
subroutine ao_ortho_cano_to_ao(A_ao,LDA_ao,A,LDA)
Transform A from the |AO| basis to the orthogonal |AO| basis
$C^{-1}.A_{ao}.C^{\dagger-1}$
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_ortho_canonical_coef_inv`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemm`
.. c:function:: ao_to_mo:
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
subroutine ao_to_mo(A_ao,LDA_ao,A_mo,LDA_mo)
Transform A from the |AO| basis to the |MO| basis
$C^\dagger.A_{ao}.C$
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
* :c:data:`mo_num`
Called by:
.. hlist::
:columns: 3
* :c:data:`fock_matrix_mo_alpha`
* :c:data:`fock_matrix_mo_beta`
* :c:data:`fps_spf_matrix_mo`
* :c:data:`mcscf_fock_alpha_mo`
* :c:data:`mo_deriv_1_x`
* :c:data:`mo_dipole_x`
* :c:data:`mo_integrals_n_e`
* :c:data:`mo_integrals_n_e_per_atom`
* :c:data:`mo_kinetic_integrals`
* :c:data:`mo_pseudo_integrals`
* :c:data:`mo_pseudo_integrals_local`
* :c:data:`mo_pseudo_integrals_non_local`
* :c:data:`mo_spread_x`
* :c:data:`one_e_dm_mo_alpha_for_dft`
* :c:data:`one_e_dm_mo_beta_for_dft`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemm`
* :c:func:`restore_symmetry`
.. c:function:: give_all_mos_and_grad_and_lapl_at_r:
File : :file:`mo_basis/mos_in_r.irp.f`
.. code:: fortran
subroutine give_all_mos_and_grad_and_lapl_at_r(r,mos_array,mos_grad_array,mos_lapl_array)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
* :c:data:`mo_num`
Calls:
.. hlist::
:columns: 3
* :c:func:`give_all_aos_and_grad_and_lapl_at_r`
.. c:function:: give_all_mos_and_grad_at_r:
File : :file:`mo_basis/mos_in_r.irp.f`
.. code:: fortran
subroutine give_all_mos_and_grad_at_r(r,mos_array,mos_grad_array)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
* :c:data:`mo_num`
Calls:
.. hlist::
:columns: 3
* :c:func:`give_all_aos_and_grad_at_r`
.. c:function:: give_all_mos_at_r:
File : :file:`mo_basis/mos_in_r.irp.f`
.. code:: fortran
subroutine give_all_mos_at_r(r,mos_array)
mos_array(i) = ith MO function evaluated at "r"
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef_transp`
* :c:data:`mo_num`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemv`
* :c:func:`give_all_aos_at_r`
.. c:function:: mix_mo_jk:
File : :file:`mo_basis/mos.irp.f`
.. code:: fortran
subroutine mix_mo_jk(j,k)
Rotates the j-th |MO| with the k-th |MO| to give two new |MOs| that are
* $+ = \frac{1}{\sqrt{2}} ( | j\rangle + | k\rangle)$
* $- = \frac{1}{\sqrt{2}} ( | j\rangle - | k\rangle)$
by convention, the '+' |MO| is in the lowest index (min(j,k))
by convention, the '-' |MO| is in the highest index (max(j,k))
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
.. c:function:: mo_as_eigvectors_of_mo_matrix:
File : :file:`mo_basis/utils.irp.f`
.. code:: fortran
subroutine mo_as_eigvectors_of_mo_matrix(matrix,n,m,label,sign,output)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
* :c:data:`mo_label`
* :c:data:`mo_num`
Called by:
.. hlist::
:columns: 3
* :c:func:`create_guess`
* :c:func:`damping_scf`
* :c:func:`hcore_guess`
* :c:func:`roothaan_hall_scf`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemm`
* :c:func:`lapack_diag`
* :c:func:`write_time`
.. c:function:: mo_as_svd_vectors_of_mo_matrix:
File : :file:`mo_basis/utils.irp.f`
.. code:: fortran
subroutine mo_as_svd_vectors_of_mo_matrix(matrix,lda,m,n,label)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
* :c:data:`mo_label`
* :c:data:`mo_num`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemm`
* :c:func:`svd`
* :c:func:`write_time`
.. c:function:: mo_as_svd_vectors_of_mo_matrix_eig:
File : :file:`mo_basis/utils.irp.f`
.. code:: fortran
subroutine mo_as_svd_vectors_of_mo_matrix_eig(matrix,lda,m,n,eig,label)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
* :c:data:`mo_label`
* :c:data:`mo_num`
Called by:
.. hlist::
:columns: 3
* :c:func:`set_natorb_no_ov_rot`
* :c:func:`set_natural_mos`
* :c:func:`set_natural_mos_canon_label`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemm`
* :c:func:`svd`
* :c:func:`write_time`
.. c:function:: mo_coef_new_as_svd_vectors_of_mo_matrix_eig:
File : :file:`mo_basis/utils.irp.f`
.. code:: fortran
subroutine mo_coef_new_as_svd_vectors_of_mo_matrix_eig(matrix,lda,m,n,mo_coef_before,eig,mo_coef_new)
You enter with matrix in the MO basis defined with the mo_coef_before.
You SVD the matrix and set the eigenvectors as mo_coef_new ordered by increasing singular values
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_num`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemm`
* :c:func:`svd`
* :c:func:`write_time`
.. c:function:: save_mos:
File : :file:`mo_basis/utils.irp.f`
.. code:: fortran
subroutine save_mos
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_md5`
* :c:data:`ao_num`
* :c:data:`mo_class`
* :c:data:`mo_coef`
* :c:data:`mo_label`
* :c:data:`mo_num`
* :c:data:`mo_occ`
Called by:
.. hlist::
:columns: 3
* :c:func:`damping_scf`
* :c:func:`hcore_guess`
* :c:func:`huckel_guess`
* :c:func:`roothaan_hall_scf`
* :c:func:`run_orb_opt_trust_v2`
* :c:func:`save_natural_mos`
* :c:func:`save_natural_mos_canon_label`
* :c:func:`save_natural_mos_no_ov_rot`
Calls:
.. hlist::
:columns: 3
* :c:func:`ezfio_set_mo_basis_ao_md5`
* :c:func:`ezfio_set_mo_basis_mo_class`
* :c:func:`ezfio_set_mo_basis_mo_coef`
* :c:func:`ezfio_set_mo_basis_mo_label`
* :c:func:`ezfio_set_mo_basis_mo_num`
* :c:func:`ezfio_set_mo_basis_mo_occ`
.. c:function:: save_mos_no_occ:
File : :file:`mo_basis/utils.irp.f`
.. code:: fortran
subroutine save_mos_no_occ
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`mo_coef`
* :c:data:`mo_num`
Calls:
.. hlist::
:columns: 3
* :c:func:`ezfio_set_mo_basis_mo_coef`
.. c:function:: save_mos_truncated:
File : :file:`mo_basis/utils.irp.f`
.. code:: fortran
subroutine save_mos_truncated(n)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_md5`
* :c:data:`ao_num`
* :c:data:`mo_class`
* :c:data:`mo_coef`
* :c:data:`mo_label`
* :c:data:`mo_occ`
Calls:
.. hlist::
:columns: 3
* :c:func:`ezfio_set_mo_basis_ao_md5`
* :c:func:`ezfio_set_mo_basis_mo_class`
* :c:func:`ezfio_set_mo_basis_mo_coef`
* :c:func:`ezfio_set_mo_basis_mo_label`
* :c:func:`ezfio_set_mo_basis_mo_num`
* :c:func:`ezfio_set_mo_basis_mo_occ`
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