Now, we can use Eq. 334 in a Monte Carlo simulation of a system of charges, provided that periodic boundary conditions are used and the domain is cubic. (Extensions to non-cubic boxes and slab geometries are discussed to a limited extent in F&S.) We can also use the Ewald technique to calculate forces for use in molecular dynamics simulations.
The force on particle due to the charges in the system is
For our purposes, the two contributions to are due
to the -space energy and the short-ranged, real-space energy:
The -space contribution is given by
The real-space contribution is given by