========== AOs Module ========== This module describes the atomic orbitals basis set. An atomic orbital :math:`\chi` centered on nucleus A is represented as: .. math:: \chi_i({\bf r}) = (x-X_A)^a (y-Y_A)^b (z-Z_A)^c \sum_k c_{ki} e^{-\gamma_{ki} |{\bf r} - {\bf R}_A|^2} The AO coefficients are normalized as: .. math:: {\tilde c}_{ki} = \frac{c_{ki}}{ \int \left( (x-X_A)^a (y-Y_A)^b (z-Z_A)^c e^{-\gamma_{ki} |{\bf r} - {\bf R}_A|^2} \right)^2} dr Warning: ``ao_coef`` contains the AO coefficients given in input. These do not include the normalization constant of the AO. The ``ao_coef_normalized`` includes this normalization factor. The AOs are also sorted by increasing exponent to accelerate the calculation of the two electron integrals. Assumptions =========== * The AO coefficients in the EZFIO files are not necessarily normalized and are normalized after reading Needed Modules ============== .. Do not edit this section It was auto-generated .. by the `update_README.py` script. .. image:: tree_dependency.png * `Nuclei `_ Needed Modules ============== .. Do not edit this section It was auto-generated .. by the `update_README.py` script. .. image:: tree_dependency.png * `Nuclei `_ Documentation ============= .. Do not edit this section It was auto-generated .. by the `update_README.py` script. `ao_cartesian `_ If true, use AOs in Cartesian coordinates (6d,10f,...) `ao_coef `_ Primitive coefficients, read from input. Those should not be used directly, as the MOs are expressed on the basis of **normalized** AOs. `ao_coef_normalization_factor `_ Coefficients including the AO normalization `ao_coef_normalization_libint_factor `_ Coefficients including the AO normalization `ao_coef_normalized `_ Coefficients including the AO normalization `ao_coef_normalized_ordered `_ Sorted primitives to accelerate 4 index MO transformation `ao_coef_normalized_ordered_transp `_ Transposed ao_coef_normalized_ordered `ao_expo `_ Exponents for each primitive of each AO `ao_expo_ordered `_ Sorted primitives to accelerate 4 index MO transformation `ao_expo_ordered_transp `_ Transposed ao_expo_ordered `ao_l `_ ao_l = l value of the AO: a+b+c in x^a y^b z^c `ao_l_char `_ ao_l = l value of the AO: a+b+c in x^a y^b z^c `ao_l_char_space `_ Undocumented `ao_l_max `_ ao_l = l value of the AO: a+b+c in x^a y^b z^c `ao_md5 `_ MD5 key, specific of the AO basis `ao_nucl `_ Index of the nucleus on which the AO is centered `ao_num `_ number of AOs `ao_overlap `_ Overlap between atomic basis functions: :math:`\int \chi_i(r) \chi_j(r) dr)` `ao_overlap_abs `_ Overlap between absolute value of atomic basis functions: :math:`\int |\chi_i(r)| |\chi_j(r)| dr)` `ao_overlap_x `_ Overlap between atomic basis functions: :math:`\int \chi_i(r) \chi_j(r) dr)` `ao_overlap_y `_ Overlap between atomic basis functions: :math:`\int \chi_i(r) \chi_j(r) dr)` `ao_overlap_z `_ Overlap between atomic basis functions: :math:`\int \chi_i(r) \chi_j(r) dr)` `ao_power `_ Powers of x, y and z for each AO `ao_power_index `_ Unique index given to a triplet of powers: .br 1/2 (l-n_x)*(l-n_x+1) + n_z + 1 `ao_prim_num `_ Number of primitives per atomic orbital `ao_prim_num_max `_ max number of primitives `ao_value `_ return the value of the ith ao at point r `cart_to_sphe_0 `_ Spherical -> Cartesian Transformation matrix for l=0 `cart_to_sphe_1 `_ Spherical -> Cartesian Transformation matrix for l=1 `cart_to_sphe_2 `_ Spherical -> Cartesian Transformation matrix for l=2 `cart_to_sphe_3 `_ Spherical -> Cartesian Transformation matrix for l=3 `cart_to_sphe_4 `_ Spherical -> Cartesian Transformation matrix for l=4 `cart_to_sphe_5 `_ Spherical -> Cartesian Transformation matrix for l=5 `cart_to_sphe_6 `_ Spherical -> Cartesian Transformation matrix for l=6 `cart_to_sphe_7 `_ Spherical -> Cartesian Transformation matrix for l=7 `cart_to_sphe_8 `_ Spherical -> Cartesian Transformation matrix for l=8 `cart_to_sphe_9 `_ Spherical -> Cartesian Transformation matrix for l=9 `give_all_aos_at_r `_ gives the values of aos at a given point r `l_to_charater `_ character corresponding to the "L" value of an AO orbital `n_aos_max `_ Number of AOs per atom `n_pt_max_i_x `_ Undocumented `n_pt_max_integrals `_ Undocumented `nucl_aos `_ List of AOs attached on each atom `nucl_list_shell_aos `_ Index of the shell type Aos and of the corresponding Aos Per convention, for P,D,F and G AOs, we take the index of the AO with the the corresponding power in the "X" axis `nucl_n_aos `_ Number of AOs per atom `nucl_num_shell_aos `_ Index of the shell type Aos and of the corresponding Aos Per convention, for P,D,F and G AOs, we take the index of the AO with the the corresponding power in the "X" axis `s_half `_ S^{1/2} `s_half_inv `_ Matrix X = S^{-1/2} obtained by SVD `s_inv `_ S^-1