atomic

class atomic.AtomicGrid(nrad, nang, origin, atomic_symbol, rtransform=None)

Defines a spherical grid for each center in the system.

evaluate_expansion(lmax, expansion)

Evaluate the spherical expansion for one atom (do not use with molecules):

$f(\theta, \varphi) = \sum_{\ell=0}^{\ell_{max}} \sum_{m=-\ell}^\ell f_{\ell m} \, Y_{\ell m}(\theta, \varphi)$

Parameters

• lmax (int) – Maximum $\ell$ order of the expansion.

• expansion (ndarray) – Spherical expansion array with shape (nrad, lsize), where $\ell_{size} = (\ell_{max} + 1)^2$

Returns

array with the values of the approximated $f(x)$.

Return type

output (ndarray)

integrate(*args, **kwargs)

Perform an integration of function $f$ using AtomicGrid.

Parameters

• f (ndarray) – array of $f$ computed in all grid points.

• segmented (logical) – whether to calculate the integral in a segmented way along the number of radial points.

Returns

float or array in the segmented case.

Return type

integral

spherical_average(*args)

Computes the spherical average of the product of given functions

Returns

the spherical average

Return type

output (array)

spherical_expansion(lmax, f)

Performs the spherical expansion:

$f_{\ell m}=\int_{\Omega} f(\theta,\varphi)\, Y_{\ell m}(\theta,\varphi)\,d\Omega$

Parameters

• lmax (int) – Maximum $\ell$ order of the expansion.

• f (ndarray) – Array with the values of function $f(x)$ calculated in each point of the atomic grid.

Returns

Spherical expansion array with shape (nrad, lsize), where $\ell_{size} = (\ell_{max} + 1)^2$

Return type

integral (ndarray)

property symbol

Owner of the grid