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https://github.com/LCPQ/quantum_package
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658 lines
12 KiB
ReStructuredText
658 lines
12 KiB
ReStructuredText
.. _ao_basis:
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.. program:: ao_basis
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.. default-role:: option
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========
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ao_basis
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========
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This module describes the atomic orbitals basis set.
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An |AO| :math:`\chi` centered on nucleus A is represented as:
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.. math::
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\chi_i({\bf r}) = (x-X_A)^a (y-Y_A)^b (z-Z_A)^c \sum_k c_{ki} e^{-\gamma_{ki} |{\bf r} - {\bf R}_A|^2}
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The |AO| coefficients are normalized as:
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.. math::
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{\tilde c}_{ki} = \frac{c_{ki}}{ \int \left( (x-X_A)^a (y-Y_A)^b (z-Z_A)^c e^{-\gamma_{ki} |{\bf r} - {\bf R}_A|^2} \right)^2 dr}
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Warning: `ao_coef` contains the |AO| coefficients given in input. These do not
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include the normalization constant of the |AO|. The `ao_coef_normalized` provider includes
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this normalization factor.
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The |AOs| are also sorted by increasing exponent to accelerate the calculation of
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the two electron integrals.
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EZFIO parameters
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----------------
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.. option:: ao_basis
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Name of the |AO| basis set
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.. option:: ao_num
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Number of |AOs|
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.. option:: ao_prim_num
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Number of primitives per |AO|
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.. option:: ao_prim_num_max
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Maximum number of primitives
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Default: =maxval(ao_basis.ao_prim_num)
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.. option:: ao_nucl
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Index of the nucleus on which the |AO| is centered
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.. option:: ao_power
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Powers of x, y and z for each |AO|
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.. option:: ao_coef
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Primitive coefficients, read from input. Those should not be used directly, as the MOs are expressed on the basis of **normalized** AOs.
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.. option:: ao_expo
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Exponents for each primitive of each |AO|
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.. option:: ao_md5
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MD5 key, specific of the |AO| basis
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.. option:: ao_cartesian
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If |true|, use |AOs| in Cartesian coordinates (6d,10f,...)
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Default: false
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Providers
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---------
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.. c:var:: ao_coef_normalization_factor
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.. code:: text
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double precision, allocatable :: ao_coef_normalized (ao_num,ao_prim_num_max)
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double precision, allocatable :: ao_coef_normalization_factor (ao_num)
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File: :file:`aos.irp.f`
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Coefficients including the |AO| normalization
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.. c:var:: ao_coef_normalization_libint_factor
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.. code:: text
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double precision, allocatable :: ao_coef_normalization_libint_factor (ao_num)
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File: :file:`aos.irp.f`
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|AO| normalization for interfacing with libint
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.. c:var:: ao_coef_normalized
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.. code:: text
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double precision, allocatable :: ao_coef_normalized (ao_num,ao_prim_num_max)
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double precision, allocatable :: ao_coef_normalization_factor (ao_num)
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File: :file:`aos.irp.f`
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Coefficients including the |AO| normalization
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.. c:var:: ao_coef_normalized_ordered
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.. code:: text
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double precision, allocatable :: ao_coef_normalized_ordered (ao_num,ao_prim_num_max)
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double precision, allocatable :: ao_expo_ordered (ao_num,ao_prim_num_max)
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File: :file:`aos.irp.f`
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Sorted primitives to accelerate 4 index |MO| transformation
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.. c:var:: ao_coef_normalized_ordered_transp
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.. code:: text
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double precision, allocatable :: ao_coef_normalized_ordered_transp (ao_prim_num_max,ao_num)
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File: :file:`aos.irp.f`
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Transposed :c:data:`ao_coef_normalized_ordered`
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.. c:var:: ao_coef_normalized_ordered_transp_per_nucl
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.. code:: text
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double precision, allocatable :: ao_coef_normalized_ordered_transp_per_nucl (ao_prim_num_max,N_AOs_max,nucl_num)
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File: :file:`aos_transp.irp.f`
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.. c:var:: ao_expo_ordered
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.. code:: text
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double precision, allocatable :: ao_coef_normalized_ordered (ao_num,ao_prim_num_max)
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double precision, allocatable :: ao_expo_ordered (ao_num,ao_prim_num_max)
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File: :file:`aos.irp.f`
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Sorted primitives to accelerate 4 index |MO| transformation
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.. c:var:: ao_expo_ordered_transp
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.. code:: text
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double precision, allocatable :: ao_expo_ordered_transp (ao_prim_num_max,ao_num)
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File: :file:`aos.irp.f`
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Transposed :c:data:`ao_expo_ordered`
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.. c:var:: ao_expo_ordered_transp_per_nucl
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.. code:: text
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double precision, allocatable :: ao_expo_ordered_transp_per_nucl (ao_prim_num_max,N_AOs_max,nucl_num)
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File: :file:`aos_transp.irp.f`
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.. c:var:: ao_l
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.. code:: text
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integer, allocatable :: ao_l (ao_num)
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integer :: ao_l_max
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character*(128), allocatable :: ao_l_char (ao_num)
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File: :file:`aos.irp.f`
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:math:`l` value of the |AO|: :math`a+b+c` in :math:`x^a y^b z^c`
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.. c:var:: ao_l_char
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.. code:: text
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integer, allocatable :: ao_l (ao_num)
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integer :: ao_l_max
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character*(128), allocatable :: ao_l_char (ao_num)
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File: :file:`aos.irp.f`
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:math:`l` value of the |AO|: :math`a+b+c` in :math:`x^a y^b z^c`
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.. c:var:: ao_l_char_space
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.. code:: text
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character*(4), allocatable :: ao_l_char_space (ao_num)
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File: :file:`aos.irp.f`
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Converts an l value to a string
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.. c:var:: ao_l_max
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.. code:: text
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integer, allocatable :: ao_l (ao_num)
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integer :: ao_l_max
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character*(128), allocatable :: ao_l_char (ao_num)
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File: :file:`aos.irp.f`
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:math:`l` value of the |AO|: :math`a+b+c` in :math:`x^a y^b z^c`
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.. c:var:: ao_power_ordered_transp_per_nucl
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.. code:: text
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integer, allocatable :: ao_power_ordered_transp_per_nucl (3,N_AOs_max,nucl_num)
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File: :file:`aos_transp.irp.f`
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.. c:var:: ao_prim_num_max
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.. code:: text
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integer :: ao_prim_num_max
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File: :file:`aos.irp.f`
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Max number of primitives.
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.. c:var:: cart_to_sphe_0
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.. code:: text
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double precision, allocatable :: cart_to_sphe_0 (1,1)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=0
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.. c:var:: cart_to_sphe_1
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.. code:: text
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double precision, allocatable :: cart_to_sphe_1 (3,3)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=1
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.. c:var:: cart_to_sphe_2
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.. code:: text
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double precision, allocatable :: cart_to_sphe_2 (6,5)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=2
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.. c:var:: cart_to_sphe_3
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.. code:: text
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double precision, allocatable :: cart_to_sphe_3 (10,7)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=3
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.. c:var:: cart_to_sphe_4
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.. code:: text
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double precision, allocatable :: cart_to_sphe_4 (15,9)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=4
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.. c:var:: cart_to_sphe_5
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.. code:: text
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double precision, allocatable :: cart_to_sphe_5 (21,11)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=5
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.. c:var:: cart_to_sphe_6
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.. code:: text
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double precision, allocatable :: cart_to_sphe_6 (28,13)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=6
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.. c:var:: cart_to_sphe_7
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.. code:: text
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double precision, allocatable :: cart_to_sphe_7 (36,15)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=7
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.. c:var:: cart_to_sphe_8
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.. code:: text
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double precision, allocatable :: cart_to_sphe_8 (45,17)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=8
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.. c:var:: cart_to_sphe_9
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.. code:: text
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double precision, allocatable :: cart_to_sphe_9 (55,19)
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File: :file:`spherical_to_cartesian.irp.f`
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Spherical -> Cartesian Transformation matrix for l=9
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.. c:var:: l_to_charater
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.. code:: text
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character*(128), allocatable :: l_to_charater (0:7)
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File: :file:`aos.irp.f`
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Character corresponding to the "l" value of an |AO|
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.. c:var:: n_aos_max
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.. code:: text
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integer, allocatable :: nucl_n_aos (nucl_num)
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integer :: n_aos_max
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File: :file:`aos.irp.f`
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Number of |AOs| per atom
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.. c:var:: n_pt_max_i_x
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.. code:: text
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integer :: n_pt_max_integrals
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integer :: n_pt_max_i_x
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File: :file:`dimensions_integrals.irp.f`
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Number of points used in the numerical integrations.
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.. c:var:: n_pt_max_integrals
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.. code:: text
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integer :: n_pt_max_integrals
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integer :: n_pt_max_i_x
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File: :file:`dimensions_integrals.irp.f`
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Number of points used in the numerical integrations.
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.. c:var:: nucl_aos
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.. code:: text
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integer, allocatable :: nucl_aos (nucl_num,N_AOs_max)
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File: :file:`aos.irp.f`
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List of |AOs| centered on each atom
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.. c:var:: nucl_aos_transposed
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.. code:: text
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integer, allocatable :: nucl_aos_transposed (N_AOs_max,nucl_num)
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File: :file:`aos_transp.irp.f`
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List of AOs attached on each atom
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.. c:var:: nucl_list_shell_aos
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.. code:: text
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integer, allocatable :: nucl_list_shell_aos (nucl_num,N_AOs_max)
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integer, allocatable :: nucl_num_shell_aos (nucl_num)
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File: :file:`aos.irp.f`
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Index of the shell type |AOs| and of the corresponding |AOs| By convention, for p,d,f and g |AOs|, we take the index of the |AO| with the the corresponding power in the x axis
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.. c:var:: nucl_n_aos
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.. code:: text
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integer, allocatable :: nucl_n_aos (nucl_num)
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integer :: n_aos_max
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File: :file:`aos.irp.f`
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Number of |AOs| per atom
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.. c:var:: nucl_num_shell_aos
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.. code:: text
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integer, allocatable :: nucl_list_shell_aos (nucl_num,N_AOs_max)
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integer, allocatable :: nucl_num_shell_aos (nucl_num)
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File: :file:`aos.irp.f`
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Index of the shell type |AOs| and of the corresponding |AOs| By convention, for p,d,f and g |AOs|, we take the index of the |AO| with the the corresponding power in the x axis
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Subroutines / functions
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-----------------------
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.. c:function:: ao_power_index
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.. code:: text
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integer function ao_power_index(nx,ny,nz)
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File: :file:`aos.irp.f`
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Unique index given to a triplet of powers:
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:math:`\frac{1}{2} (l-n_x) (l-n_x+1) + n_z + 1`
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.. c:function:: ao_value
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.. code:: text
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double precision function ao_value(i,r)
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File: :file:`aos_value.irp.f`
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return the value of the ith ao at point r
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.. c:function:: give_all_aos_and_grad_and_lapl_at_r
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.. code:: text
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subroutine give_all_aos_and_grad_and_lapl_at_r(r,aos_array,aos_grad_array,aos_lapl_array)
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File: :file:`aos_value.irp.f`
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input : r(1) ==> r(1) = x, r(2) = y, r(3) = z output : aos_array(i) = ao(i) evaluated at r : aos_grad_array(1,i) = gradient X of the ao(i) evaluated at r
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.. c:function:: give_all_aos_and_grad_at_r
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.. code:: text
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subroutine give_all_aos_and_grad_at_r(r,aos_array,aos_grad_array)
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File: :file:`aos_value.irp.f`
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input : r(1) ==> r(1) = x, r(2) = y, r(3) = z output : aos_array(i) = ao(i) evaluated at r : aos_grad_array(1,i) = gradient X of the ao(i) evaluated at r
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.. c:function:: give_all_aos_at_r
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.. code:: text
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subroutine give_all_aos_at_r(r,aos_array)
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File: :file:`aos_value.irp.f`
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input : r == r(1) = x and so on aos_array(i) = aos(i) evaluated in r
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.. c:function:: give_all_aos_at_r_old
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.. code:: text
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subroutine give_all_aos_at_r_old(r,aos_array)
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File: :file:`aos_value.irp.f`
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gives the values of aos at a given point r
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.. c:function:: primitive_value
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.. code:: text
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double precision function primitive_value(i,j,r)
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File: :file:`aos_value.irp.f`
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return the value of the jth primitive of ith ao at point r WITHOUT THE COEF
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