Optimizing Working Parameters of the Smooth Particle Mesh Ewald Algorithm in Terms of Accuracy and Efficiency

We construct an accurate error estimate for the root mean square force error of the smooth particle mesh Ewald (SPME) algorithm, which is often used for molecular dynamics simulations, where charge configurations under periodic boundary conditions require considerable amounts of CPU time. The error estimates are provided for the ik- as well as analytical force differentiation schemes, and their validity is tested for a random homogeneous sample system. Finally, we demonstrate that it is possible to straightforwardly and precisely determine the SPME parameters via the error estimates prior to the simulation for a predetermined accuracy. This can save precious computer and user time and allows an easy choice of a suitable parameter set for nearly optimal speed.