# 3.4.2. horton.gbasis.gobasis – Gaussian orbital basis set module.¶

class horton.gbasis.gobasis.GOBasisDesc(default, element_map=None, index_map=None, pure=True)

Bases: object

Arguments:

default
The default basis set applied to each atom.

Optional arguments:

element_map
A dictionary with element names or numbers as keys, and basis sets as values. These specs override the default basis
index_map
A dictionary with atomic indexes (based on the order of the atoms) as keys and basis sets as values
pure
By default pure basis functions are used. Set this to false to switch to Cartesian basis functions.

In the argument default, element_map and index_map, basis may either refer to None, a string representation like "STO-3G", a GOBasisFamily instance or a GOBasisAtom instance.

__init__(default, element_map=None, index_map=None, pure=True)

Arguments:

default
The default basis set applied to each atom.

Optional arguments:

element_map
A dictionary with element names or numbers as keys, and basis sets as values. These specs override the default basis
index_map
A dictionary with atomic indexes (based on the order of the atoms) as keys and basis sets as values
pure
By default pure basis functions are used. Set this to false to switch to Cartesian basis functions.

In the argument default, element_map and index_map, basis may either refer to None, a string representation like "STO-3G", a GOBasisFamily instance or a GOBasisAtom instance.

apply_to(coordinates, numbers)

Construct a GOBasis object for the given molecular geometry

Arguments:

coordinates
A (N, 3) float numpy array with Cartesian coordinates of the atoms.
numbers
A (N,) numpy vector with the atomic numbers.

Note that the geometry specified by the arguments may also contain ghost atoms.

class horton.gbasis.gobasis.GOBasisFamily(name, basis_atom_map=None, filename=None)

Bases: object

Arguments:

name
The name of the basis set family, e.g. ‘STO-3G’.

Optional Arguments:

basis_atom_map
A dictionary with atomic numbers as values and GOBasisAtom instances as keys.
filename
A file to load the basis set from when needed.

Either one of the two optional arguments must be provided. The first allows the user to craft his/her own basis set family. The second can be used to refer to a file that contains the basis set family. This file is only loaded when a basis set is requested for a given atom, in order to avoid slow startup times. The format of the basis set filename is deduced from the extension.

__init__(name, basis_atom_map=None, filename=None)

Arguments:

name
The name of the basis set family, e.g. ‘STO-3G’.

Optional Arguments:

basis_atom_map
A dictionary with atomic numbers as values and GOBasisAtom instances as keys.
filename
A file to load the basis set from when needed.

Either one of the two optional arguments must be provided. The first allows the user to craft his/her own basis set family. The second can be used to refer to a file that contains the basis set family. This file is only loaded when a basis set is requested for a given atom, in order to avoid slow startup times. The format of the basis set filename is deduced from the extension.

get(number)

Return the GOBasisAtom instance for the given number.

load()

Load the basis set from file.

class horton.gbasis.gobasis.GOBasisAtom(bcs)

Bases: object

Arguments:

bcs
A list of GOBasisContraction instances.
__init__(bcs)

Arguments:

bcs
A list of GOBasisContraction instances.
extend(i, shell_map, nprims, shell_types, alphas, con_coeffs, pure=True)

Extend the lists with basis functions for this atom.

Arguments:

i
The index of the center of this atom.
shell_map, nprims, shell_types, alphas, con_coeffs
These are all output arguments that must be extended with the basis set parameters for this atom. The meaning of each argument is defined in the documentation for constructor of the GOBasis class.

Optional argument:

pure
By default pure basis functions are used. Set this to False to switch to Cartesian basis functions.
class horton.gbasis.gobasis.GOBasisContraction(shell_type, alphas, con_coeffs)

Bases: object

Arguments:

shell_type
The angular quantum numbers of the shell. (0=s, 1=p, 2=d, …)
alphas
1D array with exponents of the primitives.
con_coeffs
the linear coefficients of the contraction. In the case of a segmented basis set, this is just a 1D array with the same size as alphas. In the case of a generalized contraction, this is a 2D numpy array, where each row corresponds to a primitive and the columns correspond to different contractions.

It is possible to construct this object with lists instead of arrays as arguments. Just call the to_arrays method once the lists are completed. (This is convenient when loading basis sets from a file.)

__init__(shell_type, alphas, con_coeffs)

Arguments:

shell_type
The angular quantum numbers of the shell. (0=s, 1=p, 2=d, …)
alphas
1D array with exponents of the primitives.
con_coeffs
the linear coefficients of the contraction. In the case of a segmented basis set, this is just a 1D array with the same size as alphas. In the case of a generalized contraction, this is a 2D numpy array, where each row corresponds to a primitive and the columns correspond to different contractions.

It is possible to construct this object with lists instead of arrays as arguments. Just call the to_arrays method once the lists are completed. (This is convenient when loading basis sets from a file.)

get_segmented_bcs()

Return a list of segmented contractions.

is_generalized()

Return True if this is a generalized contraction.

normalize(*args, **kwargs)

Normalize the contraction.

to_arrays()

Convert the alphas and con_coeffs attributes to numpy arrays.

horton.gbasis.gobasis.get_gobasis(coordinates, numbers, default, element_map=None, index_map=None, pure=True)

Return GOBasis for a given molecule

Arguments:

coordinates
A (N, 3) float numpy array with Cartesian coordinates of the atoms.
numbers
A (N,) numpy vector with the atomic numbers.
default
The default basis set applied to each atom.

Optional arguments:

element_map
A dictionary with element names or numbers as keys, and basis sets as values. These specs override the default basis
index_map
A dictionary with atomic indexes (based on the order of the atoms) as keys and basis sets as values
pure
By default pure basis functions are used. Set this to false to switch to Cartesian basis functions.

Returns: a GOBasis instance

In the argument default, element_map and index_map, basis may either refer to None, a string representation like "STO-3G", a GOBasisFamily instance or a GOBasisAtom instance.

Note that the geometry specified by the arguments can also contain ghost atoms.