.. _module_ao_basis: .. program:: ao_basis .. default-role:: option ======== ao_basis ======== This module describes the atomic orbitals basis set. An |AO| :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_factor` provider includes this normalization factor. The |AOs| are also sorted by increasing exponent to accelerate the calculation of the two electron integrals. Complex Gaussian-Type Orbitals (cGTOs) ===================================== Complex Gaussian-Type Orbitals (cGTOs) are also supported: .. math:: \chi_i(\mathbf{r}) = x^a y^b z^c \sum_k c_{ki} \left( e^{-\alpha_{ki} \mathbf{r}^2 - \imath \mathbf{k}_{ki} \cdot \mathbf{r} - \imath \phi_{ki}} + \text{C.C.} \right) where: - :math:`\alpha \in \mathbb{C}` and :math:`\Re(\alpha) > 0` (specified by ``ao_expo`` and ``ao_expo_im``), - :math:`\mathbf{k} = (k_x, k_y, k_z) \in \mathbb{R}^3` (specified by ``ao_expo_pw``), - :math:`\phi = \phi_x + \phi_y + \phi_z \in \mathbb{R}` (specified by ``ao_expo_phase``). EZFIO parameters ---------------- .. option:: ao_basis Name of the |AO| basis set .. option:: ao_num Number of |AOs| .. option:: ao_prim_num Number of primitives per |AO| .. option:: ao_prim_num_max Maximum number of primitives Default: =maxval(ao_basis.ao_prim_num) .. option:: ao_nucl Index of the nucleus on which the |AO| is centered .. option:: ao_power Powers of x, y and z for each |AO| .. option:: ao_coef Primitive coefficients, read from input. Those should not be used directly, as the MOs are expressed on the basis of **normalized** AOs. .. option:: ao_expo Exponents for each primitive of each |AO| .. option:: ao_md5 MD5 key, specific of the |AO| basis .. option:: ao_cartesian If |true|, use |AOs| in Cartesian coordinates (6d,10f,...) Default: false .. option:: ao_normalized Use normalized basis functions Default: true .. option:: primitives_normalized Use normalized primitive functions Default: true .. option:: use_cgtos If true, use cgtos for AO integrals Default: False .. option:: ao_expo_im imag part for Exponents for each primitive of each cGTOs |AO| .. option:: ao_expo_pw plane wave part for each primitive GTOs |AO| .. option:: ao_expo_phase phase shift for each primitive GTOs |AO| Providers --------- .. c:var:: ao_coef_normalization_factor File : :file:`ao_basis/aos.irp.f` .. code:: fortran double precision, allocatable :: ao_coef_normalized (ao_num,ao_prim_num_max) double precision, allocatable :: ao_coef_normalization_factor (ao_num) Coefficients including the |AO| normalization Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef` * :c:data:`ao_expo` * :c:data:`ao_normalized` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`ao_prim_num_max` * :c:data:`primitives_normalized` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered` .. c:var:: ao_coef_normalized File : :file:`ao_basis/aos.irp.f` .. code:: fortran double precision, allocatable :: ao_coef_normalized (ao_num,ao_prim_num_max) double precision, allocatable :: ao_coef_normalization_factor (ao_num) Coefficients including the |AO| normalization Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef` * :c:data:`ao_expo` * :c:data:`ao_normalized` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`ao_prim_num_max` * :c:data:`primitives_normalized` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered` .. c:var:: ao_coef_normalized_ordered File : :file:`ao_basis/aos.irp.f` .. code:: fortran double precision, allocatable :: ao_coef_normalized_ordered (ao_num,ao_prim_num_max) double precision, allocatable :: ao_expo_ordered (ao_num,ao_prim_num_max) Sorted primitives to accelerate 4 index |MO| transformation Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized` * :c:data:`ao_expo` * :c:data:`ao_num` * :c:data:`ao_prim_num` * :c:data:`ao_prim_num_max` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` .. c:var:: ao_coef_normalized_ordered_transp File : :file:`ao_basis/aos.irp.f` .. code:: fortran double precision, allocatable :: ao_coef_normalized_ordered_transp (ao_prim_num_max,ao_num) Transposed :c:data:`ao_coef_normalized_ordered` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered` * :c:data:`ao_num` * :c:data:`ao_prim_num_max` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp_per_nucl` * :c:data:`ao_deriv2_x` * :c:data:`ao_deriv_1_x` * :c:data:`ao_dipole_x` * :c:data:`ao_integrals_n_e` * :c:data:`ao_integrals_n_e_per_atom` * :c:data:`ao_integrals_pt_chrg` * :c:data:`ao_overlap` * :c:data:`ao_overlap_abs` * :c:data:`ao_pseudo_integrals_local` * :c:data:`ao_pseudo_integrals_non_local` * :c:data:`ao_spread_x` * :c:data:`ao_two_e_integral_alpha` * :c:data:`ao_two_e_integral_erf_schwartz` * :c:data:`ao_two_e_integral_schwartz` * :c:data:`ao_two_e_integrals_erf_in_map` * :c:data:`ao_two_e_integrals_in_map` * :c:data:`cholesky_ao_num` .. c:var:: ao_coef_normalized_ordered_transp_per_nucl File : :file:`ao_basis/aos_transp.irp.f` .. code:: fortran double precision, allocatable :: ao_coef_normalized_ordered_transp_per_nucl (ao_prim_num_max,N_AOs_max,nucl_num) Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_prim_num` * :c:data:`ao_prim_num_max` * :c:data:`nucl_aos_transposed` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` .. c:var:: ao_expo_ordered File : :file:`ao_basis/aos.irp.f` .. code:: fortran double precision, allocatable :: ao_coef_normalized_ordered (ao_num,ao_prim_num_max) double precision, allocatable :: ao_expo_ordered (ao_num,ao_prim_num_max) Sorted primitives to accelerate 4 index |MO| transformation Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized` * :c:data:`ao_expo` * :c:data:`ao_num` * :c:data:`ao_prim_num` * :c:data:`ao_prim_num_max` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` .. c:var:: ao_expo_ordered_transp File : :file:`ao_basis/aos.irp.f` .. code:: fortran double precision, allocatable :: ao_expo_ordered_transp (ao_prim_num_max,ao_num) Transposed :c:data:`ao_expo_ordered` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered` * :c:data:`ao_num` * :c:data:`ao_prim_num_max` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_deriv2_x` * :c:data:`ao_deriv_1_x` * :c:data:`ao_dipole_x` * :c:data:`ao_expo_ordered_transp_per_nucl` * :c:data:`ao_integrals_n_e` * :c:data:`ao_integrals_n_e_per_atom` * :c:data:`ao_integrals_pt_chrg` * :c:data:`ao_overlap` * :c:data:`ao_overlap_abs` * :c:data:`ao_pseudo_integrals_local` * :c:data:`ao_pseudo_integrals_non_local` * :c:data:`ao_spread_x` * :c:data:`ao_two_e_integral_alpha` * :c:data:`ao_two_e_integral_erf_schwartz` * :c:data:`ao_two_e_integral_schwartz` * :c:data:`ao_two_e_integrals_erf_in_map` * :c:data:`ao_two_e_integrals_in_map` * :c:data:`cholesky_ao_num` .. c:var:: ao_expo_ordered_transp_per_nucl File : :file:`ao_basis/aos_transp.irp.f` .. code:: fortran double precision, allocatable :: ao_expo_ordered_transp_per_nucl (ao_prim_num_max,N_AOs_max,nucl_num) Needs: .. hlist:: :columns: 3 * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_prim_num` * :c:data:`ao_prim_num_max` * :c:data:`nucl_aos_transposed` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` .. c:var:: ao_first_of_shell File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: ao_first_of_shell (shell_num) Index of the shell to which the AO corresponds Needs: .. hlist:: :columns: 3 * :c:data:`shell_ang_mom` * :c:data:`shell_num` .. c:var:: ao_l File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: ao_l (ao_num) integer :: ao_l_max character*(128), allocatable :: ao_l_char (ao_num) :math:`l` value of the |AO|: :math`a+b+c` in :math:`x^a y^b z^c` Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`l_to_character` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` * :c:data:`ao_l_char_space` * :c:data:`nucl_list_shell_aos` .. c:var:: ao_l_char File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: ao_l (ao_num) integer :: ao_l_max character*(128), allocatable :: ao_l_char (ao_num) :math:`l` value of the |AO|: :math`a+b+c` in :math:`x^a y^b z^c` Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`l_to_character` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` * :c:data:`ao_l_char_space` * :c:data:`nucl_list_shell_aos` .. c:var:: ao_l_char_space File : :file:`ao_basis/aos.irp.f` .. code:: fortran character*(4), allocatable :: ao_l_char_space (ao_num) Converts an l value to a string Needs: .. hlist:: :columns: 3 * :c:data:`ao_l` * :c:data:`ao_num` * :c:data:`ao_power` .. c:var:: ao_l_max File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: ao_l (ao_num) integer :: ao_l_max character*(128), allocatable :: ao_l_char (ao_num) :math:`l` value of the |AO|: :math`a+b+c` in :math:`x^a y^b z^c` Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`l_to_character` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` * :c:data:`ao_l_char_space` * :c:data:`nucl_list_shell_aos` .. c:var:: ao_power_ordered_transp_per_nucl File : :file:`ao_basis/aos_transp.irp.f` .. code:: fortran integer, allocatable :: ao_power_ordered_transp_per_nucl (3,N_AOs_max,nucl_num) Needs: .. hlist:: :columns: 3 * :c:data:`ao_power` * :c:data:`nucl_aos_transposed` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` .. c:var:: ao_prim_num_max File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer :: ao_prim_num_max Max number of primitives. Needs: .. hlist:: :columns: 3 * :c:data:`ao_prim_num` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef` * :c:data:`ao_coef_cgtos_norm_ord_transp` * :c:data:`ao_coef_norm_cgtos` * :c:data:`ao_coef_norm_cgtos_ord` * :c:data:`ao_coef_normalized` * :c:data:`ao_coef_normalized_ordered` * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_coef_normalized_ordered_transp_per_nucl` * :c:data:`ao_expo` * :c:data:`ao_expo_cgtos_ord_transp` * :c:data:`ao_expo_im` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_expo_ordered_transp_per_nucl` * :c:data:`ao_expo_phase` * :c:data:`ao_expo_pw` .. c:var:: ao_shell File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: ao_shell (ao_num) Index of the shell to which the AO corresponds Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`shell_ang_mom` * :c:data:`shell_num` .. c:var:: cart_to_sphe_0 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_0 (1,1) Spherical -> Cartesian Transformation matrix for l=0 .. c:var:: cart_to_sphe_1 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_1 (3,3) Spherical -> Cartesian Transformation matrix for l=1 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: cart_to_sphe_2 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_2 (6,5) Spherical -> Cartesian Transformation matrix for l=2 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: cart_to_sphe_3 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_3 (10,7) Spherical -> Cartesian Transformation matrix for l=3 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: cart_to_sphe_4 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_4 (15,9) Spherical -> Cartesian Transformation matrix for l=4 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: cart_to_sphe_5 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_5 (21,11) Spherical -> Cartesian Transformation matrix for l=5 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: cart_to_sphe_6 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_6 (28,13) Spherical -> Cartesian Transformation matrix for l=6 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: cart_to_sphe_7 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_7 (36,15) Spherical -> Cartesian Transformation matrix for l=7 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: cart_to_sphe_8 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_8 (45,17) Spherical -> Cartesian Transformation matrix for l=8 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: cart_to_sphe_9 File : :file:`ao_basis/spherical_to_cartesian.irp.f` .. code:: fortran double precision, allocatable :: cart_to_sphe_9 (55,19) Spherical -> Cartesian Transformation matrix for l=9 Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` .. c:var:: l_to_character File : :file:`ao_basis/aos.irp.f` .. code:: fortran character*(128), allocatable :: l_to_character (0:7) Character corresponding to the "l" value of an |AO| Needed by: .. hlist:: :columns: 3 * :c:data:`ao_l` .. c:var:: n_aos_max File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: nucl_n_aos (nucl_num) integer :: n_aos_max Number of |AOs| per atom Needs: .. hlist:: :columns: 3 * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`nucl_num` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp_per_nucl` * :c:data:`ao_expo_ordered_transp_per_nucl` * :c:data:`ao_power_ordered_transp_per_nucl` * :c:data:`nucl_aos` * :c:data:`nucl_aos_transposed` * :c:data:`nucl_list_shell_aos` .. c:var:: n_pt_max_i_x File : :file:`ao_basis/dimensions_integrals.irp.f` .. code:: fortran integer :: n_pt_max_integrals integer :: n_pt_max_i_x Number of points used in the numerical integrations. Needs: .. hlist:: :columns: 3 * :c:data:`ao_power` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_2e_cgtos_schwartz` * :c:data:`ao_integrals_n_e` * :c:data:`ao_integrals_n_e_cgtos` * :c:data:`ao_integrals_n_e_per_atom` * :c:data:`ao_integrals_pt_chrg` * :c:data:`ao_two_e_integral_alpha` * :c:data:`ao_two_e_integral_erf_schwartz` * :c:data:`ao_two_e_integral_schwartz` * :c:data:`ao_two_e_integrals_erf_in_map` * :c:data:`ao_two_e_integrals_in_map` * :c:data:`cholesky_ao_num` * :c:data:`gauleg_t2` .. c:var:: n_pt_max_integrals File : :file:`ao_basis/dimensions_integrals.irp.f` .. code:: fortran integer :: n_pt_max_integrals integer :: n_pt_max_i_x Number of points used in the numerical integrations. Needs: .. hlist:: :columns: 3 * :c:data:`ao_power` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_2e_cgtos_schwartz` * :c:data:`ao_integrals_n_e` * :c:data:`ao_integrals_n_e_cgtos` * :c:data:`ao_integrals_n_e_per_atom` * :c:data:`ao_integrals_pt_chrg` * :c:data:`ao_two_e_integral_alpha` * :c:data:`ao_two_e_integral_erf_schwartz` * :c:data:`ao_two_e_integral_schwartz` * :c:data:`ao_two_e_integrals_erf_in_map` * :c:data:`ao_two_e_integrals_in_map` * :c:data:`cholesky_ao_num` * :c:data:`gauleg_t2` .. c:var:: nucl_aos File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: nucl_aos (nucl_num,N_AOs_max) List of |AOs| centered on each atom Needs: .. hlist:: :columns: 3 * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` Needed by: .. hlist:: :columns: 3 * :c:data:`nucl_list_shell_aos` .. c:var:: nucl_aos_transposed File : :file:`ao_basis/aos_transp.irp.f` .. code:: fortran integer, allocatable :: nucl_aos_transposed (N_AOs_max,nucl_num) List of AOs attached on each atom Needs: .. hlist:: :columns: 3 * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp_per_nucl` * :c:data:`ao_expo_ordered_transp_per_nucl` * :c:data:`ao_power_ordered_transp_per_nucl` .. c:var:: nucl_list_shell_aos File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: nucl_list_shell_aos (nucl_num,N_AOs_max) integer, allocatable :: nucl_num_shell_aos (nucl_num) Index of the shell type |AOs| and of the corresponding |AOs| By convention, for p,d,f and g |AOs|, we take the index of the |AO| with the the corresponding power in the x axis Needs: .. hlist:: :columns: 3 * :c:data:`ao_l` * :c:data:`ao_power` * :c:data:`nucl_aos` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` .. c:var:: nucl_n_aos File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: nucl_n_aos (nucl_num) integer :: n_aos_max Number of |AOs| per atom Needs: .. hlist:: :columns: 3 * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`nucl_num` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp_per_nucl` * :c:data:`ao_expo_ordered_transp_per_nucl` * :c:data:`ao_power_ordered_transp_per_nucl` * :c:data:`nucl_aos` * :c:data:`nucl_aos_transposed` * :c:data:`nucl_list_shell_aos` .. c:var:: nucl_num_shell_aos File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer, allocatable :: nucl_list_shell_aos (nucl_num,N_AOs_max) integer, allocatable :: nucl_num_shell_aos (nucl_num) Index of the shell type |AOs| and of the corresponding |AOs| By convention, for p,d,f and g |AOs|, we take the index of the |AO| with the the corresponding power in the x axis Needs: .. hlist:: :columns: 3 * :c:data:`ao_l` * :c:data:`ao_power` * :c:data:`nucl_aos` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` .. c:var:: use_cgtos File : :file:`ao_basis/cgtos.irp.f` .. code:: fortran logical :: use_cgtos If true, use cgtos for AO integrals Needs: .. hlist:: :columns: 3 * :c:data:`ezfio_filename` * :c:data:`mpi_master` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_deriv2_x` * :c:data:`ao_integrals_n_e` * :c:data:`ao_overlap` * :c:data:`ao_two_e_integral_alpha` * :c:data:`ao_two_e_integral_schwartz` * :c:data:`ao_two_e_integrals_in_map` * :c:data:`cholesky_ao_num` .. c:var:: use_cosgtos File : :file:`ao_basis/cosgtos.irp.f` .. code:: fortran logical :: use_cosgtos If true, use cosgtos for AO integrals Needs: .. hlist:: :columns: 3 * :c:data:`ezfio_filename` * :c:data:`mpi_master` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_deriv2_x` * :c:data:`ao_integrals_n_e` * :c:data:`ao_overlap` * :c:data:`ao_two_e_integral_alpha` * :c:data:`ao_two_e_integral_schwartz` * :c:data:`ao_two_e_integrals_in_map` * :c:data:`cholesky_ao_num` Subroutines / functions ----------------------- .. c:function:: ao_power_index: File : :file:`ao_basis/aos.irp.f` .. code:: fortran integer function ao_power_index(nx,ny,nz) Unique index given to a triplet of powers: :math:`\frac{1}{2} (l-n_x) (l-n_x+1) + n_z + 1` .. c:function:: ao_value: File : :file:`ao_basis/aos_in_r.irp.f` .. code:: fortran double precision function ao_value(i, r) Returns the value of the i-th ao at point $\textbf{r}$ Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` .. c:function:: give_all_aos_and_grad_and_lapl_at_r: File : :file:`ao_basis/aos_in_r.irp.f` .. code:: fortran subroutine give_all_aos_and_grad_and_lapl_at_r(r, aos_array, aos_grad_array, aos_lapl_array) input : r(1) ==> r(1) = x, r(2) = y, r(3) = z output : * aos_array(i) = ao(i) evaluated at $\textbf{r}$ * aos_grad_array(1,i) = $\nabla_x$ of the ao(i) evaluated at $\textbf{r}$ Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp_per_nucl` * :c:data:`ao_expo_ordered_transp_per_nucl` * :c:data:`ao_num` * :c:data:`ao_power_ordered_transp_per_nucl` * :c:data:`ao_prim_num` * :c:data:`nucl_aos_transposed` * :c:data:`nucl_coord` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` Called by: .. hlist:: :columns: 3 * :c:func:`give_all_mos_and_grad_and_lapl_at_r` .. c:function:: give_all_aos_and_grad_at_r: File : :file:`ao_basis/aos_in_r.irp.f` .. code:: fortran subroutine give_all_aos_and_grad_at_r(r, aos_array, aos_grad_array) input : r(1) ==> r(1) = x, r(2) = y, r(3) = z output : * aos_array(i) = ao(i) evaluated at ro * aos_grad_array(1,i) = gradient X of the ao(i) evaluated at $\textbf{r}$ Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp_per_nucl` * :c:data:`ao_expo_ordered_transp_per_nucl` * :c:data:`ao_num` * :c:data:`ao_power_ordered_transp_per_nucl` * :c:data:`ao_prim_num` * :c:data:`nucl_aos_transposed` * :c:data:`nucl_coord` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` Called by: .. hlist:: :columns: 3 * :c:func:`give_all_mos_and_grad_at_r` .. c:function:: give_all_aos_at_r: File : :file:`ao_basis/aos_in_r.irp.f` .. code:: fortran subroutine give_all_aos_at_r(r, tmp_array) input : r == r(1) = x and so on output : tmp_array(i) = aos(i) evaluated in $\textbf{r}$ Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp_per_nucl` * :c:data:`ao_expo_ordered_transp_per_nucl` * :c:data:`ao_num` * :c:data:`ao_power_ordered_transp_per_nucl` * :c:data:`ao_prim_num` * :c:data:`nucl_aos_transposed` * :c:data:`nucl_coord` * :c:data:`nucl_n_aos` * :c:data:`nucl_num` Called by: .. hlist:: :columns: 3 * :c:func:`give_all_mos_at_r` .. c:function:: primitive_value: File : :file:`ao_basis/aos_in_r.irp.f` .. code:: fortran double precision function primitive_value(i, j, r) Returns the value of the j-th primitive of the i-th |AO| at point $\textbf{r} **without the coefficient** Needs: .. hlist:: :columns: 3 * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_power` * :c:data:`nucl_coord`