========== MOs Module ========== 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 set. The current set of molecular orbitals 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 ``mo_basis`` directory of the EZFIO file is copied in the ``save`` directory, named by the current ``mo_label``. All this is done with the script named ``save_current_mos.sh`` in the ``scripts`` directory. Assumptions =========== .. Do not edit this section. It was auto-generated from the .. NEEDED_MODULES_CHILDREN file by the `update_README.py` script. ASSUMPTONS ========== * The AO basis functions are normalized. Needed Modules ============== .. Do not edit this section It was auto-generated .. by the `update_README.py` script. .. image:: tree_dependency.png * `AO_Basis `_ * `Electrons `_ Needed Modules ============== .. Do not edit this section It was auto-generated .. by the `update_README.py` script. .. image:: tree_dependency.png * `AO_Basis `_ * `Electrons `_ Documentation ============= .. Do not edit this section It was auto-generated .. by the `update_README.py` script. `ao_cart_to_sphe_coef `_ matrix of the coefficients of the mos generated by the orthonormalization by the S^{-1/2} canonical transformation of the aos ao_cart_to_sphe_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital `ao_cart_to_sphe_inv `_ AO_cart_to_sphe_coef^(-1) `ao_cart_to_sphe_num `_ matrix of the coefficients of the mos generated by the orthonormalization by the S^{-1/2} canonical transformation of the aos ao_cart_to_sphe_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital `ao_cart_to_sphe_overlap `_ AO overlap matrix in the spherical basis set `ao_ortho_cano_to_ao `_ Transform A from the AO basis to the orthogonal AO basis .br C^(-1).A_ao.Ct^(-1) `ao_ortho_canonical_coef `_ matrix of the coefficients of the mos generated by the orthonormalization by the S^{-1/2} canonical transformation of the aos ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital `ao_ortho_canonical_coef_inv `_ ao_ortho_canonical_coef^(-1) `ao_ortho_canonical_num `_ matrix of the coefficients of the mos generated by the orthonormalization by the S^{-1/2} canonical transformation of the aos ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital `ao_ortho_canonical_overlap `_ overlap matrix of the ao_ortho_canonical. Expected to be the Identity `ao_to_mo `_ Transform A from the AO basis to the MO basis .br Ct.A_ao.C `cholesky_mo `_ Cholesky decomposition of AO Density matrix .br n : Number of AOs m : Number of MOs .br P(LDP,n) : Density matrix in AO basis .br C(LDC,m) : MOs .br tol_in : tolerance .br rank : Nomber of local MOs (output) .br `give_all_mos_at_r `_ Undocumented `give_specific_mos_at_r `_ Undocumented `mix_mo_jk `_ subroutine that rotates the jth MO with the kth MO to give two new MO's that are '+' = 1/sqrt(2) (|j> + |k>) '-' = 1/sqrt(2) (|j> - |k>) by convention, the '+' MO is in the lower index (min(j,k)) by convention, the '-' MO is in the greater index (max(j,k)) `mo_as_eigvectors_of_mo_matrix `_ Undocumented `mo_as_eigvectors_of_mo_matrix_sort_by_observable `_ Undocumented `mo_as_svd_vectors_of_mo_matrix `_ Undocumented `mo_class `_ Core|Inactive|Active|Virtual|Deleted `mo_coef `_ Molecular orbital coefficients on AO basis set mo_coef(i,j) = coefficient of the ith ao on the jth mo mo_label : Label characterizing the MOS (local, canonical, natural, etc) `mo_coef_in_ao_ortho_basis `_ MO coefficients in orthogonalized AO basis .br C^(-1).C_mo `mo_coef_transp `_ Molecular orbital coefficients on AO basis set `mo_label `_ Molecular orbital coefficients on AO basis set mo_coef(i,j) = coefficient of the ith ao on the jth mo mo_label : Label characterizing the MOS (local, canonical, natural, etc) `mo_num `_ mo_tot_num without the highest deleted MOs `mo_occ `_ MO occupation numbers `mo_overlap `_ Undocumented `mo_sort_by_observable `_ Undocumented `mo_to_ao `_ Transform A from the MO basis to the AO basis .br (S.C).A_mo.(S.C)t `mo_to_ao_no_overlap `_ Transform A from the MO basis to the S^-1 AO basis Useful for density matrix `mo_tot_num `_ Number of MOs `permut_mos `_ Undocumented `s_mo_coef `_ Product S.C where S is the overlap matrix in the AO basis and C the mo_coef matrix. `save_mos `_ Undocumented `save_mos_truncated `_ Undocumented `svd_mo `_ Singular value decomposition of the AO Density matrix .br n : Number of AOs m : Number of MOs .br P(LDP,n) : Density matrix in AO basis .br C(LDC,m) : MOs .br tol_in : tolerance .br rank : Nomber of local MOs (output) .br `swap_mos `_ Undocumented