graph2mat.core.data.basis

Utilities to describe a basis set for a point type.

Functions

get_atom_basis(atom)	For a given atom, returns the representation of its basis.
get_change_of_basis(original, target)	Change of basis matrix for the given convention.

Classes

NoBasisAtom(*args, **kwargs)	Placeholder for atoms without orbitals.
PointBasis(type, R[, basis, basis_convention])	Stores the basis set for a point type.

class graph2mat.core.data.basis.NoBasisAtom(*args, **kwargs)

Bases: Atom

Placeholder for atoms without orbitals.

This should no longer be needed once sisl allows atoms with 0 orbitals.

Atoms with no basis are for example needed for the fitting of QM/MM simulations.

property no

The number of orbitals belonging to this atom.

property q0

The initial charge of the orbitals of this atom.

class graph2mat.core.data.basis.PointBasis(type: str | int, R: float | ndarray, basis: str | Sequence[int | Tuple[int, int, int]] = (), basis_convention: str | Literal['cartesian', 'spherical', 'siesta_spherical', 'qe_spherical'] = 'spherical')

Bases: object

Stores the basis set for a point type.

Parameters:

• type (str | int) – The type ID, e.g. some meaningful name or a number.

• R (Union[float, np.ndarray]) –

  The reach of the basis. If a float, the same reach is used for all functions.

  If an array, the reach is different for each SET of functions. E.g. for a basis with 3 l=0 functions and 2 sets of l=1 functions, you must provide an array of length 5.

  The reach of the functions will determine if the point interacts with other points.

• basis (str | Sequence[int | Tuple[int, int, int]]) –

  Specification of the basis set that the point type has. It can be a list of specifications, then each item in the list can be the number of sets of functions for a given l (determined by the position of the item in the list), or a tuple specifying (n_sets, l, parity).

  It can also be a string representing the irreps of the basis in the e3nn format. E.g. “3x0e+2x1o” would mean 3 l=0 and 2 l=1 sets.

• basis_convention (str | Literal['cartesian', 'spherical', 'siesta_spherical', 'qe_spherical']) – The convention used for the basis. It can be any combination of "xyz" with optional minus signs, e.g. "xyz", "-yz-x", "z-x-y". You can also use the aliases that we provide, such as "cartesian" or "spherical".

Examples

from graph2mat import PointBasis

# Let's create a basis with 3 l=0 functions and 2 sets of l=1 functions.
# The convention for spherical harmonics will be the standard one.
# We call this type of basis set "A", and functions have a reach of 5.
basis = PointBasis("A", R=5, basis=[3, 2], basis_convention="spherical")

# Same but with a different reach for l=0 (R=5) and l=1 functions (R=3).
basis = PointBasis("A", R=np.array([5, 5, 5, 3, 3, 3, 3, 3, 3]), irreps=[3, 2], basis_convention="spherical" )

# Equivalent specification of the basis using tuples:
basis = PointBasis("A", R=5, basis=[(3, 0, 1), (2, 1, -1)], basis_convention="spherical")

R: float | ndarray

__init__(type: str | int, R: float | ndarray, basis: str | Sequence[int | Tuple[int, int, int]] = (), basis_convention: str | Literal['cartesian', 'spherical', 'siesta_spherical', 'qe_spherical'] = 'spherical') → None

basis: str | Sequence[int | Tuple[int, int, int]] = ()

basis_convention: str | Literal['cartesian', 'spherical', 'siesta_spherical', 'qe_spherical'] = 'spherical'

property basis_size: int

Returns the number of basis functions per point.

copy(**kwargs)

property e3nn_irreps

Returns the irreps in the e3nn format.

classmethod from_sisl_atom(atom: Atom, basis_convention: str | Literal['cartesian', 'spherical', 'siesta_spherical', 'qe_spherical'] = 'siesta_spherical')

Creates a point basis from a sisl atom.

Parameters:

• atom – The atom from which to create the basis.

• basis_convention – The spherical harmonics convention used for the basis.

maxR() → float

Returns the maximum reach of the basis.

property num_sets: int

Returns the number of sets of functions.

E.g. for a basis with 3 l=0 functions and 2 sets of l=1 functions, this returns 5.

to_sisl_atom(Z: int = 1) → Atom

Converts the basis to a sisl atom.

Parameters:

Z – The atomic number of the atom.

type: str | int

graph2mat.core.data.basis.get_atom_basis(atom: Atom)

For a given atom, returns the representation of its basis.

Parameters:

atom (sisl.Atom) – The atom for which we want the irreps of its basis.

Returns:

the basis representation.

Return type:

Tuple[int, int, int]

graph2mat.core.data.basis.get_change_of_basis(original: str | Literal['cartesian', 'spherical', 'siesta_spherical', 'qe_spherical'], target: str | Literal['cartesian', 'spherical', 'siesta_spherical', 'qe_spherical']) → Tuple[ndarray, ndarray]

Change of basis matrix for the given convention.

Parameters:

convention – The convention for spherical harmonics.

Returns:

• change_of_basis_matrix

• inverse_change_of_basis