.. _module_ao_one_e_ints: .. program:: ao_one_e_ints .. default-role:: option ================== ao_one_e_integrals ================== All the one-electron integrals in the |AO| basis are here. The most important providers for usual quantum-chemistry calculation are: * `ao_kinetic_integral` which are the kinetic operator integrals on the |AO| basis (see :file:`kin_ao_ints.irp.f`) * `ao_nucl_elec_integral` which are the nuclear-elctron operator integrals on the |AO| basis (see :file:`pot_ao_ints.irp.f`) * `ao_one_e_integrals` which are the the h_core operator integrals on the |AO| basis (see :file:`ao_mono_ints.irp.f`) Note that you can find other interesting integrals related to the position operator in :file:`spread_dipole_ao.irp.f`. EZFIO parameters ---------------- .. option:: ao_integrals_e_n Nucleus-electron integrals in |AO| basis set .. option:: io_ao_integrals_e_n Read/Write |AO| nucleus-electron attraction integrals from/to disk [ Write | Read | None ] Default: None .. option:: ao_integrals_kinetic Kinetic energy integrals in |AO| basis set .. option:: io_ao_integrals_kinetic Read/Write |AO| kinetic integrals from/to disk [ Write | Read | None ] Default: None .. option:: ao_integrals_pseudo Pseudopotential integrals in |AO| basis set .. option:: io_ao_integrals_pseudo Read/Write |AO| pseudopotential integrals from/to disk [ Write | Read | None ] Default: None .. option:: ao_integrals_overlap Overlap integrals in |AO| basis set .. option:: io_ao_integrals_overlap Read/Write |AO| overlap integrals from/to disk [ Write | Read | None ] Default: None .. option:: ao_one_e_integrals Combined integrals in |AO| basis set .. option:: io_ao_one_e_integrals Read/Write |AO| one-electron integrals from/to disk [ Write | Read | None ] Default: None Providers --------- .. c:var:: ao_cart_to_sphe_coef File : :file:`ao_one_e_ints/ao_ortho_canonical.irp.f` .. code:: fortran double precision, allocatable :: ao_cart_to_sphe_coef (ao_num,ao_num) integer :: ao_cart_to_sphe_num Coefficients to go from cartesian to spherical coordinates in the current basis set Needs: .. hlist:: :columns: 3 * :c:data:`ao_l` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`cart_to_sphe_1` * :c:data:`cart_to_sphe_2` * :c:data:`cart_to_sphe_3` * :c:data:`cart_to_sphe_4` * :c:data:`cart_to_sphe_5` * :c:data:`cart_to_sphe_6` * :c:data:`cart_to_sphe_7` * :c:data:`cart_to_sphe_8` * :c:data:`cart_to_sphe_9` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_inv` * :c:data:`ao_cart_to_sphe_overlap` * :c:data:`ao_ortho_canonical_coef` .. c:var:: ao_cart_to_sphe_inv File : :file:`ao_one_e_ints/ao_ortho_canonical.irp.f` .. code:: fortran double precision, allocatable :: ao_cart_to_sphe_inv (ao_cart_to_sphe_num,ao_num) Inverse of :c:data:`ao_cart_to_sphe_coef` Needs: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` * :c:data:`ao_num` .. c:var:: ao_cart_to_sphe_num File : :file:`ao_one_e_ints/ao_ortho_canonical.irp.f` .. code:: fortran double precision, allocatable :: ao_cart_to_sphe_coef (ao_num,ao_num) integer :: ao_cart_to_sphe_num Coefficients to go from cartesian to spherical coordinates in the current basis set Needs: .. hlist:: :columns: 3 * :c:data:`ao_l` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`cart_to_sphe_1` * :c:data:`cart_to_sphe_2` * :c:data:`cart_to_sphe_3` * :c:data:`cart_to_sphe_4` * :c:data:`cart_to_sphe_5` * :c:data:`cart_to_sphe_6` * :c:data:`cart_to_sphe_7` * :c:data:`cart_to_sphe_8` * :c:data:`cart_to_sphe_9` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_inv` * :c:data:`ao_cart_to_sphe_overlap` * :c:data:`ao_ortho_canonical_coef` .. c:var:: ao_cart_to_sphe_overlap File : :file:`ao_one_e_ints/ao_ortho_canonical.irp.f` .. code:: fortran double precision, allocatable :: ao_cart_to_sphe_overlap (ao_cart_to_sphe_num,ao_cart_to_sphe_num) |AO| overlap matrix in the spherical basis set Needs: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` * :c:data:`ao_num` * :c:data:`ao_overlap` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_ortho_canonical_coef` .. c:var:: ao_deriv2_x File : :file:`ao_one_e_ints/kin_ao_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_deriv2_x (ao_num,ao_num) double precision, allocatable :: ao_deriv2_y (ao_num,ao_num) double precision, allocatable :: ao_deriv2_z (ao_num,ao_num) Second derivative matrix elements in the |AO| basis. .. math:: {\tt ao\_deriv2\_x} = \langle \chi_i(x,y,z) | \frac{\partial^2}{\partial x^2} |\chi_j (x,y,z) \rangle Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_kinetic_integrals` .. c:var:: ao_deriv2_y File : :file:`ao_one_e_ints/kin_ao_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_deriv2_x (ao_num,ao_num) double precision, allocatable :: ao_deriv2_y (ao_num,ao_num) double precision, allocatable :: ao_deriv2_z (ao_num,ao_num) Second derivative matrix elements in the |AO| basis. .. math:: {\tt ao\_deriv2\_x} = \langle \chi_i(x,y,z) | \frac{\partial^2}{\partial x^2} |\chi_j (x,y,z) \rangle Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_kinetic_integrals` .. c:var:: ao_deriv2_z File : :file:`ao_one_e_ints/kin_ao_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_deriv2_x (ao_num,ao_num) double precision, allocatable :: ao_deriv2_y (ao_num,ao_num) double precision, allocatable :: ao_deriv2_z (ao_num,ao_num) Second derivative matrix elements in the |AO| basis. .. math:: {\tt ao\_deriv2\_x} = \langle \chi_i(x,y,z) | \frac{\partial^2}{\partial x^2} |\chi_j (x,y,z) \rangle Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_kinetic_integrals` .. c:var:: ao_deriv_1_x File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_deriv_1_x (ao_num,ao_num) double precision, allocatable :: ao_deriv_1_y (ao_num,ao_num) double precision, allocatable :: ao_deriv_1_z (ao_num,ao_num) * array of the integrals of AO_i * d/dx AO_j * array of the integrals of AO_i * d/dy AO_j * array of the integrals of AO_i * d/dz AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` .. c:var:: ao_deriv_1_y File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_deriv_1_x (ao_num,ao_num) double precision, allocatable :: ao_deriv_1_y (ao_num,ao_num) double precision, allocatable :: ao_deriv_1_z (ao_num,ao_num) * array of the integrals of AO_i * d/dx AO_j * array of the integrals of AO_i * d/dy AO_j * array of the integrals of AO_i * d/dz AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` .. c:var:: ao_deriv_1_z File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_deriv_1_x (ao_num,ao_num) double precision, allocatable :: ao_deriv_1_y (ao_num,ao_num) double precision, allocatable :: ao_deriv_1_z (ao_num,ao_num) * array of the integrals of AO_i * d/dx AO_j * array of the integrals of AO_i * d/dy AO_j * array of the integrals of AO_i * d/dz AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` .. c:var:: ao_dipole_x File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_dipole_x (ao_num,ao_num) double precision, allocatable :: ao_dipole_y (ao_num,ao_num) double precision, allocatable :: ao_dipole_z (ao_num,ao_num) * array of the integrals of AO_i * x AO_j * array of the integrals of AO_i * y AO_j * array of the integrals of AO_i * z AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`mo_dipole_x` .. c:var:: ao_dipole_y File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_dipole_x (ao_num,ao_num) double precision, allocatable :: ao_dipole_y (ao_num,ao_num) double precision, allocatable :: ao_dipole_z (ao_num,ao_num) * array of the integrals of AO_i * x AO_j * array of the integrals of AO_i * y AO_j * array of the integrals of AO_i * z AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`mo_dipole_x` .. c:var:: ao_dipole_z File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_dipole_x (ao_num,ao_num) double precision, allocatable :: ao_dipole_y (ao_num,ao_num) double precision, allocatable :: ao_dipole_z (ao_num,ao_num) * array of the integrals of AO_i * x AO_j * array of the integrals of AO_i * y AO_j * array of the integrals of AO_i * z AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`mo_dipole_x` .. c:var:: ao_integrals_n_e File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_integrals_n_e (ao_num,ao_num) Nucleus-electron interaction, in the |AO| basis set. :math:`\langle \chi_i | -\sum_A \frac{1}{|r-R_A|} | \chi_j \rangle` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`n_pt_max_integrals` * :c:data:`nucl_charge` * :c:data:`nucl_coord` * :c:data:`nucl_num` * :c:data:`read_ao_integrals_e_n` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_one_e_integrals` * :c:data:`ao_ortho_canonical_nucl_elec_integrals` * :c:data:`ao_ortho_lowdin_nucl_elec_integrals` * :c:data:`mo_integrals_n_e` .. c:var:: ao_integrals_n_e_per_atom File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_integrals_n_e_per_atom (ao_num,ao_num,nucl_num) Nucleus-electron interaction in the |AO| basis set, per atom A. :math:`\langle \chi_i | -\frac{1}{|r-R_A|} | \chi_j \rangle` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`n_pt_max_integrals` * :c:data:`nucl_coord` * :c:data:`nucl_num` Needed by: .. hlist:: :columns: 3 * :c:data:`mo_integrals_n_e_per_atom` .. c:var:: ao_kinetic_integrals File : :file:`ao_one_e_ints/kin_ao_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_kinetic_integrals (ao_num,ao_num) Kinetic energy integrals in the |AO| basis. :math:`\langle \chi_i |\hat{T}| \chi_j \rangle` Needs: .. hlist:: :columns: 3 * :c:data:`ao_deriv2_x` * :c:data:`ao_num` * :c:data:`read_ao_integrals_kinetic` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_one_e_integrals` * :c:data:`mo_kinetic_integrals` .. c:var:: ao_one_e_integrals File : :file:`ao_one_e_ints/ao_one_e_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_one_e_integrals (ao_num,ao_num) double precision, allocatable :: ao_one_e_integrals_diag (ao_num) One-electron Hamiltonian in the |AO| basis. Needs: .. hlist:: :columns: 3 * :c:data:`ao_integrals_n_e` * :c:data:`ao_kinetic_integrals` * :c:data:`ao_num` * :c:data:`ao_pseudo_integrals` * :c:data:`do_pseudo` * :c:data:`read_ao_one_e_integrals` Needed by: .. hlist:: :columns: 3 * :c:data:`fock_matrix_ao_alpha` * :c:data:`hf_energy` * :c:data:`scf_energy` .. c:var:: ao_one_e_integrals_diag File : :file:`ao_one_e_ints/ao_one_e_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_one_e_integrals (ao_num,ao_num) double precision, allocatable :: ao_one_e_integrals_diag (ao_num) One-electron Hamiltonian in the |AO| basis. Needs: .. hlist:: :columns: 3 * :c:data:`ao_integrals_n_e` * :c:data:`ao_kinetic_integrals` * :c:data:`ao_num` * :c:data:`ao_pseudo_integrals` * :c:data:`do_pseudo` * :c:data:`read_ao_one_e_integrals` Needed by: .. hlist:: :columns: 3 * :c:data:`fock_matrix_ao_alpha` * :c:data:`hf_energy` * :c:data:`scf_energy` .. c:var:: ao_ortho_canonical_coef File : :file:`ao_one_e_ints/ao_ortho_canonical.irp.f` .. code:: fortran double precision, allocatable :: ao_ortho_canonical_coef (ao_num,ao_num) integer :: 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 Needs: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` * :c:data:`ao_cart_to_sphe_overlap` * :c:data:`ao_cartesian` * :c:data:`ao_num` * :c:data:`ao_overlap` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_ortho_canonical_coef_inv` * :c:data:`ao_ortho_canonical_nucl_elec_integrals` * :c:data:`ao_ortho_canonical_overlap` * :c:data:`mo_coef` * :c:data:`mo_num` .. c:var:: ao_ortho_canonical_coef_inv File : :file:`ao_one_e_ints/ao_ortho_canonical.irp.f` .. code:: fortran double precision, allocatable :: ao_ortho_canonical_coef_inv (ao_num,ao_num) ao_ortho_canonical_coef^(-1) Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_ortho_canonical_coef` Needed by: .. hlist:: :columns: 3 * :c:data:`mo_coef_in_ao_ortho_basis` .. c:var:: ao_ortho_canonical_num File : :file:`ao_one_e_ints/ao_ortho_canonical.irp.f` .. code:: fortran double precision, allocatable :: ao_ortho_canonical_coef (ao_num,ao_num) integer :: 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 Needs: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_coef` * :c:data:`ao_cart_to_sphe_overlap` * :c:data:`ao_cartesian` * :c:data:`ao_num` * :c:data:`ao_overlap` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_ortho_canonical_coef_inv` * :c:data:`ao_ortho_canonical_nucl_elec_integrals` * :c:data:`ao_ortho_canonical_overlap` * :c:data:`mo_coef` * :c:data:`mo_num` .. c:var:: ao_ortho_canonical_overlap File : :file:`ao_one_e_ints/ao_ortho_canonical.irp.f` .. code:: fortran double precision, allocatable :: ao_ortho_canonical_overlap (ao_ortho_canonical_num,ao_ortho_canonical_num) overlap matrix of the ao_ortho_canonical. Expected to be the Identity Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_ortho_canonical_coef` * :c:data:`ao_overlap` .. c:var:: ao_overlap File : :file:`ao_one_e_ints/ao_overlap.irp.f` .. code:: fortran double precision, allocatable :: ao_overlap (ao_num,ao_num) double precision, allocatable :: ao_overlap_x (ao_num,ao_num) double precision, allocatable :: ao_overlap_y (ao_num,ao_num) double precision, allocatable :: ao_overlap_z (ao_num,ao_num) Overlap between atomic basis functions: :math:`\int \chi_i(r) \chi_j(r) dr` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` * :c:data:`read_ao_integrals_overlap` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_overlap` * :c:data:`ao_ortho_canonical_coef` * :c:data:`ao_ortho_canonical_overlap` * :c:data:`ao_ortho_lowdin_coef` * :c:data:`ao_ortho_lowdin_overlap` * :c:data:`fps_spf_matrix_ao` * :c:data:`mo_overlap` * :c:data:`s_half` * :c:data:`s_half_inv` * :c:data:`s_inv` * :c:data:`s_mo_coef` .. c:var:: ao_overlap_abs File : :file:`ao_one_e_ints/ao_overlap.irp.f` .. code:: fortran double precision, allocatable :: ao_overlap_abs (ao_num,ao_num) Overlap between absolute values of atomic basis functions: :math:`\int |\chi_i(r)| |\chi_j(r)| dr` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_two_e_integral_alpha` * :c:data:`mo_two_e_int_erf_jj_from_ao` * :c:data:`mo_two_e_integral_jj_from_ao` * :c:data:`mo_two_e_integrals_vv_from_ao` .. c:var:: ao_overlap_x File : :file:`ao_one_e_ints/ao_overlap.irp.f` .. code:: fortran double precision, allocatable :: ao_overlap (ao_num,ao_num) double precision, allocatable :: ao_overlap_x (ao_num,ao_num) double precision, allocatable :: ao_overlap_y (ao_num,ao_num) double precision, allocatable :: ao_overlap_z (ao_num,ao_num) Overlap between atomic basis functions: :math:`\int \chi_i(r) \chi_j(r) dr` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` * :c:data:`read_ao_integrals_overlap` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_overlap` * :c:data:`ao_ortho_canonical_coef` * :c:data:`ao_ortho_canonical_overlap` * :c:data:`ao_ortho_lowdin_coef` * :c:data:`ao_ortho_lowdin_overlap` * :c:data:`fps_spf_matrix_ao` * :c:data:`mo_overlap` * :c:data:`s_half` * :c:data:`s_half_inv` * :c:data:`s_inv` * :c:data:`s_mo_coef` .. c:var:: ao_overlap_y File : :file:`ao_one_e_ints/ao_overlap.irp.f` .. code:: fortran double precision, allocatable :: ao_overlap (ao_num,ao_num) double precision, allocatable :: ao_overlap_x (ao_num,ao_num) double precision, allocatable :: ao_overlap_y (ao_num,ao_num) double precision, allocatable :: ao_overlap_z (ao_num,ao_num) Overlap between atomic basis functions: :math:`\int \chi_i(r) \chi_j(r) dr` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` * :c:data:`read_ao_integrals_overlap` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_overlap` * :c:data:`ao_ortho_canonical_coef` * :c:data:`ao_ortho_canonical_overlap` * :c:data:`ao_ortho_lowdin_coef` * :c:data:`ao_ortho_lowdin_overlap` * :c:data:`fps_spf_matrix_ao` * :c:data:`mo_overlap` * :c:data:`s_half` * :c:data:`s_half_inv` * :c:data:`s_inv` * :c:data:`s_mo_coef` .. c:var:: ao_overlap_z File : :file:`ao_one_e_ints/ao_overlap.irp.f` .. code:: fortran double precision, allocatable :: ao_overlap (ao_num,ao_num) double precision, allocatable :: ao_overlap_x (ao_num,ao_num) double precision, allocatable :: ao_overlap_y (ao_num,ao_num) double precision, allocatable :: ao_overlap_z (ao_num,ao_num) Overlap between atomic basis functions: :math:`\int \chi_i(r) \chi_j(r) dr` Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` * :c:data:`read_ao_integrals_overlap` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_cart_to_sphe_overlap` * :c:data:`ao_ortho_canonical_coef` * :c:data:`ao_ortho_canonical_overlap` * :c:data:`ao_ortho_lowdin_coef` * :c:data:`ao_ortho_lowdin_overlap` * :c:data:`fps_spf_matrix_ao` * :c:data:`mo_overlap` * :c:data:`s_half` * :c:data:`s_half_inv` * :c:data:`s_inv` * :c:data:`s_mo_coef` .. c:var:: ao_pseudo_integrals File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_pseudo_integrals (ao_num,ao_num) Pseudo-potential integrals in the |AO| basis set. Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_pseudo_integrals_local` * :c:data:`ao_pseudo_integrals_non_local` * :c:data:`do_pseudo` * :c:data:`pseudo_klocmax` * :c:data:`pseudo_kmax` * :c:data:`read_ao_integrals_pseudo` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_one_e_integrals` * :c:data:`mo_pseudo_integrals` .. c:var:: ao_pseudo_integrals_local File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_pseudo_integrals_local (ao_num,ao_num) Local pseudo-potential Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_charge` * :c:data:`nucl_coord` * :c:data:`nucl_num` * :c:data:`pseudo_klocmax` * :c:data:`pseudo_v_k_transp` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_pseudo_integrals` .. c:var:: ao_pseudo_integrals_non_local File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: ao_pseudo_integrals_non_local (ao_num,ao_num) Non-local pseudo-potential Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_charge` * :c:data:`nucl_coord` * :c:data:`nucl_num` * :c:data:`pseudo_kmax` * :c:data:`pseudo_lmax` * :c:data:`pseudo_v_kl_transp` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_pseudo_integrals` .. c:var:: ao_spread_x File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_spread_x (ao_num,ao_num) double precision, allocatable :: ao_spread_y (ao_num,ao_num) double precision, allocatable :: ao_spread_z (ao_num,ao_num) * array of the integrals of AO_i * x^2 AO_j * array of the integrals of AO_i * y^2 AO_j * array of the integrals of AO_i * z^2 AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`mo_spread_x` .. c:var:: ao_spread_y File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_spread_x (ao_num,ao_num) double precision, allocatable :: ao_spread_y (ao_num,ao_num) double precision, allocatable :: ao_spread_z (ao_num,ao_num) * array of the integrals of AO_i * x^2 AO_j * array of the integrals of AO_i * y^2 AO_j * array of the integrals of AO_i * z^2 AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`mo_spread_x` .. c:var:: ao_spread_z File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran double precision, allocatable :: ao_spread_x (ao_num,ao_num) double precision, allocatable :: ao_spread_y (ao_num,ao_num) double precision, allocatable :: ao_spread_z (ao_num,ao_num) * array of the integrals of AO_i * x^2 AO_j * array of the integrals of AO_i * y^2 AO_j * array of the integrals of AO_i * z^2 AO_j Needs: .. hlist:: :columns: 3 * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_nucl` * :c:data:`ao_num` * :c:data:`ao_power` * :c:data:`ao_prim_num` * :c:data:`nucl_coord` Needed by: .. hlist:: :columns: 3 * :c:data:`mo_spread_x` .. c:function:: give_polynomial_mult_center_one_e_erf: File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f` .. code:: fortran subroutine give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,& power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in) Returns the explicit polynomial in terms of the $t$ variable of the following polynomial: $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$. Calls: .. hlist:: :columns: 3 * :c:func:`i_x1_pol_mult_one_e` * :c:func:`multiply_poly` .. c:function:: give_polynomial_mult_center_one_e_erf_opt: File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f` .. code:: fortran subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,beta,& power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in,p,p_inv,p_inv_2,p_new,P_center) Returns the explicit polynomial in terms of the $t$ variable of the following polynomial: $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$. Called by: .. hlist:: :columns: 3 * :c:func:`nai_pol_mult_erf` Calls: .. hlist:: :columns: 3 * :c:func:`i_x1_pol_mult_one_e` * :c:func:`multiply_poly` .. c:function:: i_x1_pol_mult_one_e: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran recursive subroutine I_x1_pol_mult_one_e(a,c,R1x,R1xp,R2x,d,nd,n_pt_in) Recursive routine involved in the electron-nucleus potential Called by: .. hlist:: :columns: 3 * :c:func:`give_polynomial_mult_center_one_e` * :c:func:`give_polynomial_mult_center_one_e_erf` * :c:func:`give_polynomial_mult_center_one_e_erf_opt` * :c:func:`i_x1_pol_mult_one_e` * :c:func:`i_x2_pol_mult_one_e` Calls: .. hlist:: :columns: 3 * :c:func:`i_x1_pol_mult_one_e` * :c:func:`i_x2_pol_mult_one_e` * :c:func:`multiply_poly` .. c:function:: i_x2_pol_mult_one_e: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran recursive subroutine I_x2_pol_mult_one_e(c,R1x,R1xp,R2x,d,nd,dim) Recursive routine involved in the electron-nucleus potential Called by: .. hlist:: :columns: 3 * :c:func:`i_x1_pol_mult_one_e` Calls: .. hlist:: :columns: 3 * :c:func:`i_x1_pol_mult_one_e` * :c:func:`multiply_poly` .. c:var:: pseudo_dz_k_transp File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: pseudo_v_k_transp (pseudo_klocmax,nucl_num) integer, allocatable :: pseudo_n_k_transp (pseudo_klocmax,nucl_num) double precision, allocatable :: pseudo_dz_k_transp (pseudo_klocmax,nucl_num) Transposed arrays for pseudopotentials Needs: .. hlist:: :columns: 3 * :c:data:`nucl_num` * :c:data:`pseudo_dz_k` * :c:data:`pseudo_klocmax` * :c:data:`pseudo_n_k` * :c:data:`pseudo_v_k` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_pseudo_integrals_local` .. c:var:: pseudo_dz_kl_transp File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: pseudo_v_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) integer, allocatable :: pseudo_n_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) double precision, allocatable :: pseudo_dz_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) Transposed arrays for pseudopotentials Needs: .. hlist:: :columns: 3 * :c:data:`nucl_num` * :c:data:`pseudo_dz_kl` * :c:data:`pseudo_kmax` * :c:data:`pseudo_lmax` * :c:data:`pseudo_n_kl` * :c:data:`pseudo_v_kl` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_pseudo_integrals_non_local` .. c:var:: pseudo_n_k_transp File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: pseudo_v_k_transp (pseudo_klocmax,nucl_num) integer, allocatable :: pseudo_n_k_transp (pseudo_klocmax,nucl_num) double precision, allocatable :: pseudo_dz_k_transp (pseudo_klocmax,nucl_num) Transposed arrays for pseudopotentials Needs: .. hlist:: :columns: 3 * :c:data:`nucl_num` * :c:data:`pseudo_dz_k` * :c:data:`pseudo_klocmax` * :c:data:`pseudo_n_k` * :c:data:`pseudo_v_k` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_pseudo_integrals_local` .. c:var:: pseudo_n_kl_transp File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: pseudo_v_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) integer, allocatable :: pseudo_n_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) double precision, allocatable :: pseudo_dz_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) Transposed arrays for pseudopotentials Needs: .. hlist:: :columns: 3 * :c:data:`nucl_num` * :c:data:`pseudo_dz_kl` * :c:data:`pseudo_kmax` * :c:data:`pseudo_lmax` * :c:data:`pseudo_n_kl` * :c:data:`pseudo_v_kl` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_pseudo_integrals_non_local` .. c:var:: pseudo_v_k_transp File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: pseudo_v_k_transp (pseudo_klocmax,nucl_num) integer, allocatable :: pseudo_n_k_transp (pseudo_klocmax,nucl_num) double precision, allocatable :: pseudo_dz_k_transp (pseudo_klocmax,nucl_num) Transposed arrays for pseudopotentials Needs: .. hlist:: :columns: 3 * :c:data:`nucl_num` * :c:data:`pseudo_dz_k` * :c:data:`pseudo_klocmax` * :c:data:`pseudo_n_k` * :c:data:`pseudo_v_k` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_pseudo_integrals_local` .. c:var:: pseudo_v_kl_transp File : :file:`ao_one_e_ints/pot_ao_pseudo_ints.irp.f` .. code:: fortran double precision, allocatable :: pseudo_v_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) integer, allocatable :: pseudo_n_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) double precision, allocatable :: pseudo_dz_kl_transp (pseudo_kmax,0:pseudo_lmax,nucl_num) Transposed arrays for pseudopotentials Needs: .. hlist:: :columns: 3 * :c:data:`nucl_num` * :c:data:`pseudo_dz_kl` * :c:data:`pseudo_kmax` * :c:data:`pseudo_lmax` * :c:data:`pseudo_n_kl` * :c:data:`pseudo_v_kl` Needed by: .. hlist:: :columns: 3 * :c:data:`ao_pseudo_integrals_non_local` .. c:var:: s_half File : :file:`ao_one_e_ints/ao_overlap.irp.f` .. code:: fortran double precision, allocatable :: s_half (ao_num,ao_num) :math:`S^{1/2}` Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_overlap` .. c:var:: s_half_inv File : :file:`ao_one_e_ints/ao_overlap.irp.f` .. code:: fortran double precision, allocatable :: s_half_inv (AO_num,AO_num) :math:`X = S^{-1/2}` obtained by SVD Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_overlap` Needed by: .. hlist:: :columns: 3 * :c:data:`eigenvalues_fock_matrix_ao` .. c:var:: s_inv File : :file:`ao_one_e_ints/ao_overlap.irp.f` .. code:: fortran double precision, allocatable :: s_inv (ao_num,ao_num) Inverse of the overlap matrix Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` * :c:data:`ao_overlap` Subroutines / functions ----------------------- .. c:function:: give_all_erf_kl_ao: File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f` .. code:: fortran subroutine give_all_erf_kl_ao(integrals_ao,mu_in,C_center) Subroutine that returns all integrals over $r$ of type $\frac{ \erf(\mu * | r - R_C | ) }{ | r - R_C | }$ Needs: .. hlist:: :columns: 3 * :c:data:`ao_num` .. c:function:: give_polynomial_mult_center_one_e: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran subroutine give_polynomial_mult_center_one_e(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out) Returns the explicit polynomial in terms of the "t" variable of the following $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$. Called by: .. hlist:: :columns: 3 * :c:func:`nai_pol_mult` Calls: .. hlist:: :columns: 3 * :c:func:`i_x1_pol_mult_one_e` * :c:func:`multiply_poly` .. c:function:: int_gaus_pol: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision function int_gaus_pol(alpha,n) Computes the integral: $\int_{-\infty}^{\infty} x^n \exp(-\alpha x^2) dx$. .. c:function:: nai_pol_mult: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision function NAI_pol_mult(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in) Computes the electron-nucleus attraction with two primitves. :math:`\langle g_i | \frac{1}{|r-R_c|} | g_j \rangle` Calls: .. hlist:: :columns: 3 * :c:func:`give_polynomial_mult_center_one_e` .. c:function:: nai_pol_mult_erf: File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f` .. code:: fortran double precision function NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in) Computes the following integral : .. math:: \int dr (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 ) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$. Calls: .. hlist:: :columns: 3 * :c:func:`give_polynomial_mult_center_one_e_erf_opt` .. c:function:: nai_pol_mult_erf_ao: File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f` .. code:: fortran double precision function NAI_pol_mult_erf_ao(i_ao,j_ao,mu_in,C_center) Computes the following integral : $\int_{-\infty}^{infty} dr \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$. Needs: .. hlist:: :columns: 3 * :c:data:`n_pt_max_integrals` * :c:data:`ao_coef_normalized_ordered_transp` * :c:data:`ao_power` * :c:data:`ao_expo_ordered_transp` * :c:data:`ao_prim_num` * :c:data:`ao_nucl` * :c:data:`nucl_coord` .. c:function:: overlap_bourrin_deriv_x: File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran subroutine overlap_bourrin_deriv_x(i_component,A_center,B_center,alpha,beta,power_A,power_B,dx,lower_exp_val,overlap_x,nx) Called by: .. hlist:: :columns: 3 * :c:data:`ao_deriv_1_x` Calls: .. hlist:: :columns: 3 * :c:func:`overlap_bourrin_x` .. c:function:: overlap_bourrin_dipole: File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran subroutine overlap_bourrin_dipole(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,lower_exp_val,dx,nx) Called by: .. hlist:: :columns: 3 * :c:data:`ao_dipole_x` .. c:function:: overlap_bourrin_spread: File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran subroutine overlap_bourrin_spread(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,lower_exp_val,dx,nx) Computes the following integral : int [-infty ; +infty] of [(x-A_center)^(power_A) * (x-B_center)^power_B * exp(-alpha(x-A_center)^2) * exp(-beta(x-B_center)^2) * x ] needed for the dipole and those things Called by: .. hlist:: :columns: 3 * :c:data:`ao_spread_x` .. c:function:: overlap_bourrin_x: File : :file:`ao_one_e_ints/spread_dipole_ao.irp.f` .. code:: fortran subroutine overlap_bourrin_x(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,lower_exp_val,dx,nx) Called by: .. hlist:: :columns: 3 * :c:func:`overlap_bourrin_deriv_x` .. c:function:: v_e_n: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision function V_e_n(a_x,a_y,a_z,b_x,b_y,b_z,alpha,beta) Primitve nuclear attraction between the two primitves centered on the same atom. $p_1 = x^{a_x} y^{a_y} z^{a_z} \exp(-\alpha r^2)$ $p_2 = x^{b_x} y^{b_y} z^{b_z} \exp(-\beta r^2)$ .. c:function:: v_phi: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision function V_phi(n,m) Computes the angular $\phi$ part of the nuclear attraction integral: $\int_{0}^{2 \pi} \cos(\phi)^n \sin(\phi)^m d\phi$. .. c:function:: v_r: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision function V_r(n,alpha) Computes the radial part of the nuclear attraction integral: $\int_{0}^{\infty} r^n \exp(-\alpha r^2) dr$ .. c:function:: v_theta: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision function V_theta(n,m) Computes the angular $\theta$ part of the nuclear attraction integral: $\int_{0}^{\pi} \cos(\theta)^n \sin(\theta)^m d\theta$ .. c:function:: wallis: File : :file:`ao_one_e_ints/pot_ao_ints.irp.f` .. code:: fortran double precision function Wallis(n) Wallis integral: $\int_{0}^{\pi} \cos(\theta)^n d\theta$.