CoulombPotential¶

class torchpme.CoulombPotential(smearing: float | None = None, exclusion_radius: float | None = None, dtype: dtype | None = None, device: device | None = None)[source]¶

Smoothed electrostatic Coulomb potential \(1/r\).

Here \(r\) is the inter-particle distance

It can be used to compute:

the full \(1/r\) potential
its short-range (SR) and long-range (LR) parts, the split being determined by a length-scale parameter (called “Inverse” in the code)
the Fourier transform of the LR part

Parameters:

smearing (float | None) – float or torch.Tensor containing the parameter often called “sigma” in publications, which determines the length-scale at which the short-range and long-range parts of the naive \(1/r\) potential are separated. The smearing parameter corresponds to the “width” of a Gaussian smearing of the particle density.
exclusion_radius (float | None) – A length scale that defines a local environment within which the potential should be smoothly zeroed out, as it will be described by a separate model.
dtype (dtype | None) – type used for the internal buffers and parameters
device (device | None) – device used for the internal buffers and parameters

from_dist(dist: Tensor) → Tensor[source]¶

Full \(1/r\) potential as a function of \(r\).

Parameters:: dist (Tensor) – torch.tensor containing the distances at which the potential is to be evaluated.
Return type:: Tensor

lr_from_dist(dist: Tensor) → Tensor[source]¶

Long range of the range-separated \(1/r\) potential.

Used to subtract out the interior contributions after computing the LR part in reciprocal (Fourier) space.

Parameters:: dist (Tensor) – torch.tensor containing the distances at which the potential is to be evaluated.
Return type:: Tensor

lr_from_k_sq(k_sq: Tensor) → Tensor[source]¶

Fourier transform of the LR part potential in terms of \(\mathbf{k^2}\).

Parameters:: k_sq (Tensor) – torch.tensor containing the squared lengths (2-norms) of the wave vectors k at which the Fourier-transformed potential is to be evaluated
Return type:: Tensor

self_contribution() → Tensor[source]¶

A correction that depends exclusively on the “charge” on every particle and on the range splitting parameter. Foe example, in the case of a Coulomb potential, this is the potential generated at the origin by the fictituous Gaussian charge density in order to split the potential into a SR and LR part.

Return type:: Tensor

background_correction() → Tensor[source]¶

A correction designed to compensate for the presence of divergent terms. For instance, the energy of a periodic electrostatic system is infinite when the cell is not charge-neutral. This term then implicitly assumes that a homogeneous background charge of the opposite sign is present to make the cell neutral.