A smooth particle mesh Ewald method

TLDR

The reformulation extends the particle mesh Ewald method to potentials of the form 1/r^p with p≥1. The method is reformulated using efficient B‑spline interpolation of structure factors, which also enables efficient calculation of the virial tensor. Replacing Lagrange interpolation with B‑splines yields analytic gradients and markedly improves accuracy; arbitrary precision is attainable regardless of system size at N log N cost, permitting biomolecular systems with thousands of atoms to employ Ewald summation at a cost comparable to a simple 10 Å truncation.

Abstract

The previously developed particle mesh Ewald method is reformulated in terms of efficient B-spline interpolation of the structure factors. This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1. Furthermore, efficient calculation of the virial tensor follows. Use of B-splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy. We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N). For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 Å or less.