xnn.common.models.electrostatics.ewald_reciprocal#

xnn.common.models.electrostatics.ewald_reciprocal(charges, pos, cell, alpha, k_cutoff, budget=100000000)[source]#

Per-atom reciprocal-space energies q_i phi_i / 2 of one periodic structure.

phi_i = (4 pi / V) sum_{k != 0} exp(-k^2 / 4 alpha^2) / k^2 [cos(k r_i) Re S(k) + sin(k r_i) Im S(k)] with the structure factor S(k) = sum_j q_j exp(i k r_j); the sum over the atoms is (2 pi / V) sum_k ... |S(k)|^2. Phases and sums are formed in float64, in blocks of lattice vectors when the phase table exceeds RECIPROCAL_BUDGET.

Parameters:

charges (Tensor) – Charges (N,).
pos (Tensor) – Positions (N, 3).
cell (Tensor) – Lattice vectors as rows (3, 3).
alpha (float) – Splitting parameter.
k_cutoff (float) – Spherical reciprocal cutoff.
budget (int, optional) – Entries of the phase table formed at once, by default RECIPROCAL_BUDGET.

Returns:

(N,) in e^2 / Angstrom, float64.

Return type:

Tensor