EwaldCalculator

class torchpme.EwaldCalculator(potential: Potential, lr_wavelength: float, full_neighbor_list: bool = False, prefactor: float = 1.0)

Potential computed using the Ewald sum.

Scaling as \(\mathcal{O}(N^2)\) with respect to the number of particles \(N\).

For getting reasonable values for the smaring of the potential class and the lr_wavelength based on a given accuracy for a specific structure you should use torchpme.tuning.tune_ewald(). This function will also find the optimal cutoff for the neighborlist.

Hint

For a training exercise it is recommended only run a tuning procedure with torchpme.tuning.tune_ewald() for the largest system in your dataset.

For a \(\mathcal{O}(N^{1.5})\) scaling, one can set the parameters as following:

\[ \begin{align}\begin{aligned}\mathrm{smearing} &= 1.3 \cdot N^{1 / 6} / \sqrt{2}\\\mathrm{lr\_wavelength} &= 2 \pi \cdot \mathrm{smearing} / 2.2\\\mathrm{r_c} &= 2.2 \cdot \mathrm{smearing}\end{aligned}\end{align} \]

where \(N\) is the number of particles. The magic numbers \(1.3\) and \(2.2\) above result from tests on a CsCl system, whose unit cell is repeated 16 times in each direction, resulting in a system of 8192 atoms.

Parameters:

• potential (Potential) – the two-body potential that should be computed, implemented as a torchpme.potentials.Potential object. The smearing parameter of the potential determines the split between real and k-space regions. For a torchpme.CoulombPotential it corresponds to the width of the atom-centered Gaussian used to split the Coulomb potential into the short- and long-range parts. A reasonable value for most systems is to set it to 1/5 times the neighbor list cutoff.

• lr_wavelength (float) – Spatial resolution used for the long-range (reciprocal space) part of the Ewald sum. More concretely, all Fourier space vectors with a wavelength >= this value will be kept. If not set to a global value, it will be set to half the smearing parameter to ensure convergence of the long-range part to a relative precision of 1e-5.

• full_neighbor_list (bool) – If set to True, a “full” neighbor list is expected as input. This means that each atom pair appears twice. If set to False, a “half” neighbor list is expected.

• prefactor (float) – electrostatics prefactor; see Prefactors for details and common values.

forward(charges: Tensor, cell: Tensor, positions: Tensor, neighbor_indices: Tensor, neighbor_distances: Tensor)

Compute the potential “energy”.

It is calculated as

\[V_i = \frac{1}{2} \sum_{j} q_j\,v(r_{ij})\]

where \(v(r)\) is the pair potential defined by the potential parameter and \(q_j\) are atomic “charges” (corresponding to the electrostatic charge when using a Coulomb potential).

If the smearing of the potential is not set, the calculator evaluates only the real-space part of the potential. Otherwise, provided that the calculator implements a _compute_kspace method, it will also evaluate the long-range part using a Fourier-domain method.

Parameters:

• charges (Tensor) – torch.tensor of shape (n_channels, len(positions)) containaing the atomic (pseudo-)charges. n_channels is the number of charge channels the potential should be calculated. For a standard potential n_channels = 1. If more than one “channel” is provided multiple potentials for the same position are computed depending on the charges and the potentials.

• cell (Tensor) – torch.tensor of shape (3, 3), where cell[i] is the i-th basis vector of the unit cell

• positions (Tensor) – torch.tensor of shape (N, 3) containing the Cartesian coordinates of the N particles within the supercell.

• neighbor_indices (Tensor) – torch.tensor with the i,j indices of neighbors for which the potential should be computed in real space.

• neighbor_distances (Tensor) – torch.tensor with the pair distances of the neighbors for which the potential should be computed in real space.