PowerSpectrum¶

class featomic.torch.utils.PowerSpectrum(calculator_1: CalculatorModule, calculator_2: CalculatorModule | None = None, types: List[int] | None = None)¶

Bases: Module

General power spectrum of one or of two calculators.

If calculator_2 is provided, the invariants \(p_{nl}\) are generated by taking quadratic combinations of calculator_1’s spherical expansion \(\rho_{nlm}\) and calculator_2’s spherical expansion \(\nu_{nlm}\) according to Bartók et. al.

\[p_{nl} = \rho_{nlm}^\dagger \cdot \nu_{nlm}\]

where we use the Einstein summation convention. If gradients are present the invariants of those are constructed as

\[\nabla p_{nl} = \nabla \rho_{nlm}^\dagger \cdot \nu_{nlm} + \rho_{nlm}^\dagger \cdot \nabla \nu_{nlm}\]

Note

Currently only supports gradients with respect to positions.

If calculator_2=None invariants are generated by combining the coefficients of the spherical expansion of calculator_1. The spherical expansions given as input can only be featomic.SphericalExpansion or featomic.LodeSphericalExpansion.

Parameters:

calculator_1 – first calculator
calculator_1 – second calculator
types – List of "neighbor_type" to use in the properties of the output. This option might be useful when running the calculation on subset of a whole dataset and trying to join along the sample dimension after the calculation. If None, blocks are filled with "neighbor_type" found in the systems.

Raises:

ValueError – If other calculators than featomic.SphericalExpansion or featomic.LodeSphericalExpansion are used.
ValueError – If "max_angular" of both calculators is different.

Example¶

As an example we calculate the power spectrum for a short range (sr) spherical expansion and a long-range (lr) LODE spherical expansion for a NaCl crystal.

>>> import featomic
>>> import ase

Construct the NaCl crystal

>>> atoms = ase.Atoms(
...     symbols="NaCl",
...     positions=[[0, 0, 0], [0.5, 0.5, 0.5]],
...     pbc=True,
...     cell=[1, 1, 1],
... )

Define the hyper parameters for the short-range spherical expansion

>>> sr_hypers = {
...     "cutoff": {
...         "radius": 1.0,
...         "smoothing": {"type": "ShiftedCosine", "width": 0.5},
...     },
...     "density": {
...         "type": "Gaussian",
...         "width": 0.3,
...     },
...     "basis": {
...         "type": "TensorProduct",
...         "max_angular": 2,
...         "radial": {"type": "Gto", "max_radial": 5},
...     },
... }

Define the hyper parameters for the long-range LODE spherical expansion from the hyper parameters of the short-range spherical expansion

>>> lr_hypers = {
...     "density": {
...         "type": "SmearedPowerLaw",
...         "smearing": 0.3,
...         "exponent": 1,
...     },
...     "basis": {
...         "type": "TensorProduct",
...         "max_angular": 2,
...         "radial": {"type": "Gto", "max_radial": 5, "radius": 1.0},
...     },
... }

Construct the calculators

>>> sr_calculator = featomic.SphericalExpansion(**sr_hypers)
>>> lr_calculator = featomic.LodeSphericalExpansion(**lr_hypers)

Construct the power spectrum calculators and compute the spherical expansion

>>> calculator = featomic.utils.PowerSpectrum(sr_calculator, lr_calculator)
>>> power_spectrum = calculator.compute(atoms)

The resulting invariants are stored as metatensor.TensorMap as for any other calculator

>>> power_spectrum.keys
Labels(
    center_type
        11
        17
)
>>> power_spectrum[0]
TensorBlock
    samples (1): ['system', 'atom']
    components (): []
    properties (432): ['l', 'neighbor_1_type', 'n_1', 'neighbor_2_type', 'n_2']
    gradients: None