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
given by

(337) |

For our purposes, the two contributions to are due
to the -space energy and the short-ranged, real-space energy:

(338) |

The -space contribution is given by

(339) |

The real-space contribution is given by

(340) |