iodata.basis module¶

Utility functions for working with basis sets.

class MolecularBasis(shells, conventions, primitive_normalization)[source]¶

Bases: object

A complete molecular orbital or density basis set.

shells¶: A list of objects of type Shell which can support generalized contractions.

conventions¶

A dictionary specifying the ordered basis functions for a given angular momentum and kind. The key is a tuple of angular momentum integer and kind character (‘c’ for Cartesian and ‘p’ for pure/spherical) and the value is a list of basis function strings. For example,

{
    ### Conventions for Cartesian functions
    # E.g., alphabetically ordered Cartesian functions.
    (0, 'c'): ['1'],
    (1, 'c'): ['x', 'y', 'z'],
    (2, 'c'): ['xx', 'xy', 'xz', 'yy', 'yz', 'zz'],
    ### Conventions for pure functions.
    # The notation is referring to real solid spherical harmonics.
    # See https://en.wikipedia.org/wiki/Solid_harmonics#Real_form
    # 'c{m}' = solid harmonic containing cos(m phi)
    # 's{m}' = solid harmonic containing sin(m phi)
    # where m is the magnetic quantum number and phi is the
    # azimuthal angle.
    # For example, wikipedia-ordered real spherical harmonics,
    # see https://en.wikipedia.org/wiki/Spherical_harmonics#Real_form
    (2, 'p'): ['s2', 's1', 'c0', 'c1', 'c2'],
    # Different quantum-chemistry codes may use incompatible
    # orderings and sign conventions. E.g. Molden files written
    # by ORCA use the following convention for pure f functions:
    (3, 'p'): ['c0', 'c1', 's1', 'c2', 's2', '-c3', '-s3'],
    # Note that the minus sign in the last two basis functions
    # denotes that the signs of these harmonics have been changed.
}

The basis function strings in the conventions dictionary are documented in Basis set conventions.

primitive_normalization¶: The normalization convention of primitives, which can be ‘L2’ (orbitals) or ‘L1’ (densities) normalized.

__init__(shells, conventions, primitive_normalization)¶

Method generated by attrs for class MolecularBasis.

Return type: None

conventions: Dict[str, str]¶

get_segmented()[source]¶: Unroll generalized contractions.

property nbasis¶

Number of basis functions.

Return type: int

primitive_normalization: str¶

shells: List[iodata.basis.Shell]¶

class Shell(icenter, angmoms, kinds, exponents, coeffs)[source]¶

Bases: object

A shell in a molecular basis representing (generalized) contractions with the same exponents.

icenter¶: An integer index specifying the row in the atcoords array of IOData object.

angmoms¶: An integer array of angular momentum quantum numbers, non-negative, with shape (ncon,).

kinds¶: List of strings describing the kind of contractions: ‘c’ for Cartesian and ‘p’ for pure. Pure functions are only allowed for angmom>1. The length equals the number of contractions: len(angmoms)=ncon.

exponents¶: The array containing the exponents of the primitives, with shape (nprim,).

coeffs¶: The array containing the coefficients of the normalized primitives in each contraction; shape = (nprim, ncon). These coefficients assume that the primitives are L2 (orbitals) or L1 (densities) normalized, but contractions are not necessarily normalized. (This depends on the code which generated the contractions.)

__init__(icenter, angmoms, kinds, exponents, coeffs)¶

Method generated by attrs for class Shell.

Return type: None

angmoms: List[int]¶

coeffs: numpy.ndarray¶

exponents: numpy.ndarray¶

icenter: int¶

kinds: List[str]¶

property nbasis¶

Number of basis functions (e.g. 3 for a P shell and 4 for an SP shell).

Return type: int

property ncon¶

Number of contractions. This is usually 1; e.g., it would be 2 for an SP shell.

Return type: int

property nprim¶

Number of primitives, also known as the contraction length.

Return type: int

angmom_its(angmom)[source]¶

Convert an angular momentum from integer to string representation.

Parameters: angmom (Union[int, List[int]]) – The integer representation of the angular momentum.
Returns: The string representation of the angular momentum. If a list of integer angmom is given, a list of str is returned.
Return type: char

angmom_sti(char)[source]¶

Convert an angular momentum from string to integer format.

Parameters: char (Union[str, List[str]]) – Character representation of angular momentum, (s, p, d, …)
Returns: An integer representation of the angular momentum. If a list of str char is given, a list of integers in returned.
Return type: angmom

convert_convention_shell(conv1, conv2, reverse=False)[source]¶

Return a permutation vector and sign changes to convert from 1 to 2.

The transformation from convention 1 to convention 2 can be done applying the results of this function as follows:

vector2 = vector1[permutation]*signs

When using the option reverse=True, one can use the results to convert in the opposite sense:

vector1 = vector2[permutation]*signs

Parameters

conv1 (List[str]) – Two lists, with the same strings (in different order), where each string may be prefixed with a ‘-‘.
conv2 (List[str]) – Two lists, with the same strings (in different order), where each string may be prefixed with a ‘-‘.
reverse – When, true the conversion from 2 to 1 is returned.

Return type

Tuple[ndarray, ndarray]

Returns

permutation – An integer array that permutes basis function from 1 to 2.
signs – Sign changes when going from 1 to 2, must be applied after permutation

convert_conventions(molbasis, new_conventions, reverse=False)[source]¶

Return a permutation vector and sign changes to convert from 1 to 2.

The transformation from molbasis.convention to the new convention can be done applying the results of this function as follows:

vector2 = vector1[permutation]*signs

When using the option reverse=True, one can use the results to convert in the opposite sense:

vector1 = vector2[permutation]*signs

Parameters

molbasis (MolecularBasis) – The description of a molecular basis set.
new_conventions (Dict[str, List[str]]) – The new conventions for ordering and signs, to which data for the orbital basis needs to be converted.
reverse – When, true the conversion from 2 to 1 is returned.

Return type

Tuple[ndarray, ndarray]

Returns

permutation – An integer array that permutes basis function from 1 to 2.
signs – Sign changes when going from 1 to 2, must be applied after permutation

get_default_conventions()[source]¶

Produce a conventions dictionary compatible with HORTON2.

Do not change this!!! This is also used by several file formats from other QC codes who happen to follow the same conventions.

iter_cart_alphabet(n)[source]¶

Loop over powers of Cartesian basis functions in alphabetical order.

See https://theochem.github.io/horton/2.1.1/tech_ref_gaussian_basis.html for details.

Parameters: n (int) – The angular momentum, i.e. sum of Cartesian powers in this case.
Return type: ndarray