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qp2/docs/source/modules/ao_one_e_ints.rst
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.. _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_integrals` which are the kinetic operator integrals on the |AO| basis
* `ao_integrals_n_e` which are the nuclear-elctron operator integrals on the |AO| basis
* `ao_one_e_integrals` which are the the h_core operator integrals on the |AO| basis
EZFIO parameters
----------------
.. option:: ao_integrals_n_e
Nucleus-electron integrals in |AO| basis set
.. option:: ao_integrals_n_e_imag
Imaginary part of the nucleus-electron integrals in |AO| basis set
.. option:: io_ao_integrals_n_e
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:: ao_integrals_kinetic_imag
Imaginary part of the 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:: ao_integrals_pseudo_imag
Imaginary part of the 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:: ao_integrals_overlap_imag
Imaginary part of the 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:: ao_one_e_integrals_imag
Imaginary part of the 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
.. option:: lin_dep_cutoff
Remove linear dependencies when the eigenvalues of the overlap matrix are below this value
Default: 1.e-6
.. option:: ao_one_e_integrals_threshold
If | (p|q) | < `ao_one_e_integrals_threshold` then (p|q) is zero
Default: 1.e-15
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:data:`lin_dep_cutoff`
.. 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_coef_cgtos_norm_ord_transp
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_cgtos_norm_ord_transp (ao_prim_num_max,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos_ord`
* :c:data:`ao_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_2e_cgtos_schwartz`
* :c:data:`ao_deriv2_cgtos_x`
* :c:data:`ao_integrals_n_e_cgtos`
* :c:data:`ao_overlap_cgtos`
.. c:var:: ao_coef_norm_cgtos
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_cgtos (ao_num,ao_prim_num_max)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef`
* :c:data:`ao_expo`
* :c:data:`ao_expo_im`
* :c:data:`ao_expo_phase`
* :c:data:`ao_expo_pw`
* :c:data:`ao_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`ao_prim_num_max`
* :c:data:`nucl_coord`
* :c:data:`primitives_normalized`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos_ord`
.. c:var:: ao_coef_norm_cgtos_ord
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_cgtos_ord (ao_num,ao_prim_num_max)
complex*16, allocatable :: ao_expo_cgtos_ord (ao_num,ao_prim_num_max)
double precision, allocatable :: ao_expo_pw_ord (4,ao_num,ao_prim_num_max)
double precision, allocatable :: ao_expo_phase_ord (4,ao_num,ao_prim_num_max)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos`
* :c:data:`ao_expo`
* :c:data:`ao_expo_im`
* :c:data:`ao_expo_phase`
* :c:data:`ao_expo_pw`
* :c:data:`ao_num`
* :c:data:`ao_prim_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_transp`
.. c:var:: ao_coef_norm_cosgtos
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_cosgtos (ao_num,ao_prim_num_max)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef`
* :c:data:`ao_expo`
* :c:data:`ao_expoim_cosgtos`
* :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_norm_ord_cosgtos`
.. c:var:: ao_coef_norm_ord_cosgtos
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_ord_cosgtos (ao_num,ao_prim_num_max)
complex*16, allocatable :: ao_expo_ord_cosgtos (ao_num,ao_prim_num_max)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cosgtos`
* :c:data:`ao_expo`
* :c:data:`ao_expoim_cosgtos`
* :c:data:`ao_num`
* :c:data:`ao_prim_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
.. c:var:: ao_coef_norm_ord_transp_cosgtos
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_ord_transp_cosgtos (ao_prim_num_max,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_cosgtos`
* :c:data:`ao_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_2e_cosgtos_schwartz`
* :c:data:`ao_deriv2_cosgtos_x`
* :c:data:`ao_integrals_n_e_cosgtos`
* :c:data:`ao_overlap_cosgtos`
.. c:var:: ao_deriv2_cgtos_x
File : :file:`ao_one_e_ints/one_e_kin_integrals_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_deriv2_cgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_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_deriv2_x`
* :c:data:`ao_kinetic_integrals_cgtos`
.. c:var:: ao_deriv2_cgtos_y
File : :file:`ao_one_e_ints/one_e_kin_integrals_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_deriv2_cgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_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_deriv2_x`
* :c:data:`ao_kinetic_integrals_cgtos`
.. c:var:: ao_deriv2_cgtos_z
File : :file:`ao_one_e_ints/one_e_kin_integrals_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_deriv2_cgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_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_deriv2_x`
* :c:data:`ao_kinetic_integrals_cgtos`
.. c:var:: ao_deriv2_cosgtos_x
File : :file:`ao_one_e_ints/one_e_kin_integrals_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_deriv2_cosgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cosgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cosgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
* :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_deriv2_x`
* :c:data:`ao_kinetic_integrals_cosgtos`
.. c:var:: ao_deriv2_cosgtos_y
File : :file:`ao_one_e_ints/one_e_kin_integrals_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_deriv2_cosgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cosgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cosgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
* :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_deriv2_x`
* :c:data:`ao_kinetic_integrals_cosgtos`
.. c:var:: ao_deriv2_cosgtos_z
File : :file:`ao_one_e_ints/one_e_kin_integrals_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_deriv2_cosgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cosgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_deriv2_cosgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
* :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_deriv2_x`
* :c:data:`ao_kinetic_integrals_cosgtos`
.. 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_deriv2_cgtos_x`
* :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:`use_cgtos`
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_deriv2_cgtos_x`
* :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:`use_cgtos`
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_deriv2_cgtos_x`
* :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:`use_cgtos`
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`
Needed by:
.. hlist::
:columns: 3
* :c:data:`mo_deriv_1_x`
.. 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`
Needed by:
.. hlist::
:columns: 3
* :c:data:`mo_deriv_1_x`
.. 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`
Needed by:
.. hlist::
:columns: 3
* :c:data:`mo_deriv_1_x`
.. 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_expo_cgtos_ord
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_cgtos_ord (ao_num,ao_prim_num_max)
complex*16, allocatable :: ao_expo_cgtos_ord (ao_num,ao_prim_num_max)
double precision, allocatable :: ao_expo_pw_ord (4,ao_num,ao_prim_num_max)
double precision, allocatable :: ao_expo_phase_ord (4,ao_num,ao_prim_num_max)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos`
* :c:data:`ao_expo`
* :c:data:`ao_expo_im`
* :c:data:`ao_expo_phase`
* :c:data:`ao_expo_pw`
* :c:data:`ao_num`
* :c:data:`ao_prim_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_transp`
.. c:var:: ao_expo_cgtos_ord_transp
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
complex*16, allocatable :: ao_expo_cgtos_ord_transp (ao_prim_num_max,ao_num)
double precision, allocatable :: ao_expo_pw_ord_transp (4,ao_prim_num_max,ao_num)
double precision, allocatable :: ao_expo_phase_ord_transp (4,ao_prim_num_max,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos_ord`
* :c:data:`ao_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_2e_cgtos_schwartz`
* :c:data:`ao_deriv2_cgtos_x`
* :c:data:`ao_integrals_n_e_cgtos`
* :c:data:`ao_overlap_cgtos`
* :c:data:`use_pw`
.. c:var:: ao_expo_ord_cosgtos
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_ord_cosgtos (ao_num,ao_prim_num_max)
complex*16, allocatable :: ao_expo_ord_cosgtos (ao_num,ao_prim_num_max)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cosgtos`
* :c:data:`ao_expo`
* :c:data:`ao_expoim_cosgtos`
* :c:data:`ao_num`
* :c:data:`ao_prim_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
.. c:var:: ao_expo_ord_transp_cosgtos
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
complex*16, allocatable :: ao_expo_ord_transp_cosgtos (ao_prim_num_max,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_cosgtos`
* :c:data:`ao_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_2e_cosgtos_schwartz`
* :c:data:`ao_deriv2_cosgtos_x`
* :c:data:`ao_integrals_n_e_cosgtos`
* :c:data:`ao_overlap_cosgtos`
.. c:var:: ao_expo_phase_ord
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_cgtos_ord (ao_num,ao_prim_num_max)
complex*16, allocatable :: ao_expo_cgtos_ord (ao_num,ao_prim_num_max)
double precision, allocatable :: ao_expo_pw_ord (4,ao_num,ao_prim_num_max)
double precision, allocatable :: ao_expo_phase_ord (4,ao_num,ao_prim_num_max)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos`
* :c:data:`ao_expo`
* :c:data:`ao_expo_im`
* :c:data:`ao_expo_phase`
* :c:data:`ao_expo_pw`
* :c:data:`ao_num`
* :c:data:`ao_prim_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_transp`
.. c:var:: ao_expo_phase_ord_transp
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
complex*16, allocatable :: ao_expo_cgtos_ord_transp (ao_prim_num_max,ao_num)
double precision, allocatable :: ao_expo_pw_ord_transp (4,ao_prim_num_max,ao_num)
double precision, allocatable :: ao_expo_phase_ord_transp (4,ao_prim_num_max,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos_ord`
* :c:data:`ao_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_2e_cgtos_schwartz`
* :c:data:`ao_deriv2_cgtos_x`
* :c:data:`ao_integrals_n_e_cgtos`
* :c:data:`ao_overlap_cgtos`
* :c:data:`use_pw`
.. c:var:: ao_expo_pw_ord
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_coef_norm_cgtos_ord (ao_num,ao_prim_num_max)
complex*16, allocatable :: ao_expo_cgtos_ord (ao_num,ao_prim_num_max)
double precision, allocatable :: ao_expo_pw_ord (4,ao_num,ao_prim_num_max)
double precision, allocatable :: ao_expo_phase_ord (4,ao_num,ao_prim_num_max)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos`
* :c:data:`ao_expo`
* :c:data:`ao_expo_im`
* :c:data:`ao_expo_phase`
* :c:data:`ao_expo_pw`
* :c:data:`ao_num`
* :c:data:`ao_prim_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_transp`
.. c:var:: ao_expo_pw_ord_transp
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
complex*16, allocatable :: ao_expo_cgtos_ord_transp (ao_prim_num_max,ao_num)
double precision, allocatable :: ao_expo_pw_ord_transp (4,ao_prim_num_max,ao_num)
double precision, allocatable :: ao_expo_phase_ord_transp (4,ao_prim_num_max,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_cgtos_ord`
* :c:data:`ao_num`
* :c:data:`ao_prim_num_max`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_2e_cgtos_schwartz`
* :c:data:`ao_deriv2_cgtos_x`
* :c:data:`ao_integrals_n_e_cgtos`
* :c:data:`ao_overlap_cgtos`
* :c:data:`use_pw`
.. 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`
These integrals also contain the pseudopotential integrals.
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp`
* :c:data:`ao_expo_ordered_transp`
* :c:data:`ao_integrals_n_e_cgtos`
* :c:data:`ao_integrals_pt_chrg`
* :c:data:`ao_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`ao_pseudo_integrals`
* :c:data:`do_pseudo`
* :c:data:`n_pt_max_integrals`
* :c:data:`nucl_charge`
* :c:data:`nucl_coord`
* :c:data:`nucl_num`
* :c:data:`point_charges`
* :c:data:`read_ao_integrals_n_e`
* :c:data:`use_cgtos`
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:`hf_kinetic_energy`
* :c:data:`mo_integrals_n_e`
.. c:var:: ao_integrals_n_e_cgtos
File : :file:`ao_one_e_ints/one_e_coul_integrals_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_integrals_n_e_cgtos (ao_num,ao_num)
Nucleus-electron interaction, in the cgtos |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_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_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:`use_pw`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_n_e`
.. c:var:: ao_integrals_n_e_cosgtos
File : :file:`ao_one_e_ints/one_e_Coul_integrals_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_integrals_n_e_cosgtos (ao_num,ao_num)
Nucleus-electron interaction, in the cosgtos |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_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
* :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`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_n_e`
.. c:var:: ao_integrals_n_e_imag
File : :file:`ao_one_e_ints/pot_ao_ints.irp.f`
.. code:: fortran
double precision, allocatable :: ao_integrals_n_e_imag (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_num`
* :c:data:`read_ao_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_integrals_pt_chrg
File : :file:`ao_one_e_ints/pot_pt_charges.irp.f`
.. code:: fortran
double precision, allocatable :: ao_integrals_pt_chrg (ao_num,ao_num)
Point charge-electron interaction, in the |AO| basis set.
:math:`\langle \chi_i | -\sum_charge charge * \frac{1}{|r-R_charge|} | \chi_j \rangle`
Notice the minus sign convention as it is supposed to be for electrons.
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:`n_pts_charge`
* :c:data:`nucl_coord`
* :c:data:`pts_charge_coord`
* :c:data:`pts_charge_z`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_integrals_n_e`
.. 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:`hf_kinetic_energy`
* :c:data:`mo_kinetic_integrals`
.. c:var:: ao_kinetic_integrals_cgtos
File : :file:`ao_one_e_ints/one_e_kin_integrals_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_kinetic_integrals_cgtos (ao_num,ao_num)
Kinetic energy integrals in the cgtos |AO| basis.
:math:`\langle \chi_i |\hat{T}| \chi_j \rangle`
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_deriv2_cgtos_x`
* :c:data:`ao_num`
.. c:var:: ao_kinetic_integrals_cosgtos
File : :file:`ao_one_e_ints/one_e_kin_integrals_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_kinetic_integrals_cosgtos (ao_num,ao_num)
Kinetic energy integrals in the cosgtos |AO| basis.
:math:`\langle \chi_i |\hat{T}| \chi_j \rangle`
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_deriv2_cosgtos_x`
* :c:data:`ao_num`
.. c:var:: ao_kinetic_integrals_imag
File : :file:`ao_one_e_ints/kin_ao_ints.irp.f`
.. code:: fortran
double precision, allocatable :: ao_kinetic_integrals_imag (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_num`
* :c:data:`read_ao_integrals_kinetic`
.. 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:`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:`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_imag
File : :file:`ao_one_e_ints/ao_one_e_ints.irp.f`
.. code:: fortran
double precision, allocatable :: ao_one_e_integrals_imag (ao_num,ao_num)
One-electron Hamiltonian in the |AO| basis.
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`read_ao_one_e_integrals`
.. 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`
* :c:data:`lin_dep_cutoff`
* :c:data:`mpi_master`
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_coef_aux`
* :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`
* :c:data:`lin_dep_cutoff`
* :c:data:`mpi_master`
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_coef_aux`
* :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_overlap_cgtos`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`nucl_coord`
* :c:data:`read_ao_integrals_overlap`
* :c:data:`use_cgtos`
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:`ao_overlap_complex`
* :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_overlap_complex`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`is_periodic`
* :c:data:`nucl_coord`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_two_e_integral_alpha`
* :c:data:`cholesky_ao_num`
.. c:var:: ao_overlap_cgtos
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_cgtos (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_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_overlap`
.. c:var:: ao_overlap_cgtos_x
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_cgtos (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_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_overlap`
.. c:var:: ao_overlap_cgtos_y
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_cgtos (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_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_overlap`
.. c:var:: ao_overlap_cgtos_z
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_cgtos (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_cgtos_norm_ord_transp`
* :c:data:`ao_expo_cgtos_ord_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_overlap`
.. c:var:: ao_overlap_complex
File : :file:`ao_one_e_ints/ao_overlap.irp.f`
.. code:: fortran
complex*16, allocatable :: ao_overlap_complex (ao_num,ao_num)
Overlap for complex AOs
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_overlap`
* :c:data:`ao_overlap_imag`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_overlap_abs`
* :c:data:`s_inv_complex`
.. c:var:: ao_overlap_cosgtos
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_cosgtos (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
* :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_overlap`
.. c:var:: ao_overlap_cosgtos_x
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_cosgtos (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
* :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_overlap`
.. c:var:: ao_overlap_cosgtos_y
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_cosgtos (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
* :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_overlap`
.. c:var:: ao_overlap_cosgtos_z
File : :file:`ao_one_e_ints/aos_cosgtos.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_cosgtos (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_x (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_y (ao_num,ao_num)
double precision, allocatable :: ao_overlap_cosgtos_z (ao_num,ao_num)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_norm_ord_transp_cosgtos`
* :c:data:`ao_expo_ord_transp_cosgtos`
* :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_overlap`
.. c:var:: ao_overlap_imag
File : :file:`ao_one_e_ints/ao_overlap.irp.f`
.. code:: fortran
double precision, allocatable :: ao_overlap_imag (ao_num,ao_num)
Imaginary part of the overlap
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_overlap_complex`
.. 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_overlap_cgtos`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`nucl_coord`
* :c:data:`read_ao_integrals_overlap`
* :c:data:`use_cgtos`
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:`ao_overlap_complex`
* :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_overlap_cgtos`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`nucl_coord`
* :c:data:`read_ao_integrals_overlap`
* :c:data:`use_cgtos`
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:`ao_overlap_complex`
* :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_overlap_cgtos`
* :c:data:`ao_power`
* :c:data:`ao_prim_num`
* :c:data:`nucl_coord`
* :c:data:`read_ao_integrals_overlap`
* :c:data:`use_cgtos`
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:`ao_overlap_complex`
* :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_integrals_n_e`
* :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_v_k_transp`
* :c:data:`pseudo_klocmax`
* :c:data:`pseudo_v_k_transp`
* :c:data:`pseudo_v_k_transp`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_pseudo_integrals`
* :c:data:`mo_pseudo_integrals_local`
.. 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_v_kl_transp`
* :c:data:`pseudo_kmax`
* :c:data:`pseudo_lmax`
* :c:data:`pseudo_v_kl_transp`
* :c:data:`pseudo_v_kl_transp`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_pseudo_integrals`
* :c:data:`mo_pseudo_integrals_non_local`
.. 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_cpolynomial_mult_center_one_e:
File : :file:`ao_one_e_ints/one_e_coul_integrals_cgtos.irp.f`
.. code:: fortran
subroutine give_cpolynomial_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_cgtos`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult_one_e_cgtos`
* :c:func:`multiply_cpoly`
.. 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_c2`
.. c:function:: i_x1_pol_mult_one_e_cgtos:
File : :file:`ao_one_e_ints/one_e_coul_integrals_cgtos.irp.f`
.. code:: fortran
recursive subroutine I_x1_pol_mult_one_e_cgtos(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_cpolynomial_mult_center_one_e`
* :c:func:`i_x1_pol_mult_one_e_cgtos`
* :c:func:`i_x2_pol_mult_one_e_cgtos`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult_one_e_cgtos`
* :c:func:`i_x2_pol_mult_one_e_cgtos`
* :c:func:`multiply_cpoly`
.. c:function:: i_x1_pol_mult_one_e_cosgtos:
File : :file:`ao_one_e_ints/one_e_Coul_integrals_cosgtos.irp.f`
.. code:: fortran
recursive subroutine I_x1_pol_mult_one_e_cosgtos(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_cpolynomial_mult_center_one_e`
* :c:func:`i_x1_pol_mult_one_e_cosgtos`
* :c:func:`i_x2_pol_mult_one_e_cosgtos`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult_one_e_cosgtos`
* :c:func:`i_x2_pol_mult_one_e_cosgtos`
* :c:func:`multiply_cpoly`
.. 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_c2`
.. c:function:: i_x2_pol_mult_one_e_cgtos:
File : :file:`ao_one_e_ints/one_e_coul_integrals_cgtos.irp.f`
.. code:: fortran
recursive subroutine I_x2_pol_mult_one_e_cgtos(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_cgtos`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult_one_e_cgtos`
* :c:func:`multiply_cpoly`
.. c:function:: i_x2_pol_mult_one_e_cosgtos:
File : :file:`ao_one_e_ints/one_e_Coul_integrals_cosgtos.irp.f`
.. code:: fortran
recursive subroutine I_x2_pol_mult_one_e_cosgtos(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_cosgtos`
Calls:
.. hlist::
:columns: 3
* :c:func:`i_x1_pol_mult_one_e_cosgtos`
* :c:func:`multiply_cpoly`
.. c:function:: nai_pol_mult_cgtos:
File : :file:`ao_one_e_ints/one_e_coul_integrals_cgtos.irp.f`
.. code:: fortran
complex*16 function NAI_pol_mult_cgtos(Ae_center, Be_center, power_A, power_B, alpha, beta, &
Ap_center, Bp_center, C_center, n_pt_in)
Computes the electron-nucleus attraction with two primitves cgtos.
:math:`\langle g_i | \frac{1}{|r-R_c|} | g_j \rangle`
Needs:
.. hlist::
:columns: 3
* :c:data:`use_pw`
Calls:
.. hlist::
:columns: 3
* :c:func:`give_cpolynomial_mult_center_one_e`
.. c:function:: nai_pol_mult_erf_with1s:
File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f`
.. code:: fortran
double precision function NAI_pol_mult_erf_with1s( A1_center, A2_center, power_A1, power_A2, alpha1, alpha2 &
, beta, B_center, C_center, n_pt_in, mu_in )
Computes the following integral :
.. math::
\int dx (x - A1_x)^a_1 (x - B1_x)^a_2 \exp(-\alpha_1 (x - A1_x)^2 - \alpha_2 (x - A2_x)^2)
\int dy (y - A1_y)^b_1 (y - B1_y)^b_2 \exp(-\alpha_1 (y - A1_y)^2 - \alpha_2 (y - A2_y)^2)
\int dz (x - A1_z)^c_1 (z - B1_z)^c_2 \exp(-\alpha_1 (z - A1_z)^2 - \alpha_2 (z - A2_z)^2)
\exp(-\beta (r - B)^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: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`
* :c:data:`lin_dep_cutoff`
.. c:var:: s_inv_complex
File : :file:`ao_one_e_ints/ao_overlap.irp.f`
.. code:: fortran
complex*16, allocatable :: s_inv_complex (ao_num,ao_num)
Inverse of the overlap matrix
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`ao_overlap_complex`
* :c:data:`lin_dep_cutoff`
.. c:var:: use_pw
File : :file:`ao_one_e_ints/aos_cgtos.irp.f`
.. code:: fortran
logical :: use_pw
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_expo_cgtos_ord_transp`
* :c:data:`ao_expo_cgtos_ord_transp`
Needed by:
.. hlist::
:columns: 3
* :c:data:`ao_2e_cgtos_schwartz`
* :c:data:`ao_integrals_n_e_cgtos`
Subroutines / functions
-----------------------
.. c:function:: ao_one_e_integral_zero:
File : :file:`ao_one_e_ints/screening.irp.f`
.. code:: fortran
logical function ao_one_e_integral_zero(i,k)
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_one_e_integrals_threshold`
* :c:data:`ao_overlap_abs`
* :c:data:`io_ao_integrals_overlap`
* :c:data:`is_periodic`
* :c:data:`use_cgtos`
.. 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:: 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, power_A, power_B, C_center, n_pt_in, d, n_pt_out, 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`
* :c:func:`nai_pol_mult_erf_v`
* :c:func:`nai_pol_mult_erf_with1s`
* :c:func:`nai_pol_mult_erf_with1s_v`
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_cosgtos:
File : :file:`ao_one_e_ints/one_e_Coul_integrals_cosgtos.irp.f`
.. code:: fortran
complex*16 function NAI_pol_mult_cosgtos(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in)
Computes the electron-nucleus attraction with two primitves cosgtos.
:math:`\langle g_i | \frac{1}{|r-R_c|} | g_j \rangle`
Calls:
.. hlist::
:columns: 3
* :c:func:`give_cpolynomial_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:`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:`n_pt_max_integrals`
* :c:data:`nucl_coord`
.. c:function:: nai_pol_mult_erf_ao_with1s:
File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f`
.. code:: fortran
double precision function NAI_pol_mult_erf_ao_with1s(i_ao, j_ao, beta, B_center, mu_in, C_center)
Computes the following integral :
$\int_{-\infty}^{infty} dr \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
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:`n_pt_max_integrals`
* :c:data:`nucl_coord`
.. c:function:: nai_pol_mult_erf_v:
File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f`
.. code:: fortran
subroutine NAI_pol_mult_erf_v(A_center, B_center, power_A, power_B, alpha, beta, C_center, LD_C, n_pt_in, mu_in, res_v, LD_resv, n_points)
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 |}$.
Calls:
.. hlist::
:columns: 3
* :c:func:`give_polynomial_mult_center_one_e_erf_opt`
.. c:function:: nai_pol_mult_erf_with1s_v:
File : :file:`ao_one_e_ints/pot_ao_erf_ints.irp.f`
.. code:: fortran
subroutine NAI_pol_mult_erf_with1s_v(A1_center, A2_center, power_A1, power_A2, alpha1, alpha2, beta, B_center, LD_B, C_center, LD_C, n_pt_in, mu_in, res_v, LD_resv, n_points)
Computes the following integral :
.. math ::
\int dx (x - A1_x)^a_1 (x - B1_x)^a_2 \exp(-\alpha_1 (x - A1_x)^2 - \alpha_2 (x - A2_x)^2)
\int dy (y - A1_y)^b_1 (y - B1_y)^b_2 \exp(-\alpha_1 (y - A1_y)^2 - \alpha_2 (y - A2_y)^2)
\int dz (x - A1_z)^c_1 (z - B1_z)^c_2 \exp(-\alpha_1 (z - A1_z)^2 - \alpha_2 (z - A2_z)^2)
\exp(-\beta (r - B)^2)
\frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
Calls:
.. hlist::
:columns: 3
* :c:func:`give_polynomial_mult_center_one_e_erf_opt`
.. c:function:: 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^2 ]
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_n_e:
File : :file:`ao_one_e_ints/pot_ao_ints.irp.f`
.. code:: fortran
double precision function V_n_e(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_n_e_cgtos:
File : :file:`ao_one_e_ints/one_e_coul_integrals_cgtos.irp.f`
.. code:: fortran
complex*16 function V_n_e_cgtos(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_n_e_cosgtos:
File : :file:`ao_one_e_ints/one_e_Coul_integrals_cosgtos.irp.f`
.. code:: fortran
complex*16 function V_n_e_cosgtos(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_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_r_cgtos:
File : :file:`ao_one_e_ints/one_e_coul_integrals_cgtos.irp.f`
.. code:: fortran
complex*16 function V_r_cgtos(n, alpha)
Computes the radial part of the nuclear attraction integral:
$\int_{0}^{\infty} r^n \exp(-\alpha r^2) dr$
.. c:function:: v_r_cosgtos:
File : :file:`ao_one_e_ints/one_e_Coul_integrals_cosgtos.irp.f`
.. code:: fortran
complex*16 function V_r_cosgtos(n, alpha)
Computes the radial part of the nuclear attraction integral:
$\int_{0}^{\infty} r^n \exp(-\alpha r^2) dr$
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