666 Energies and forces
×Mn(uz,i−kz−j 3 Nl). (B.30)Because the computational overhead of a fast Fourier transform of lengthNlscales as
O(NllogNl), andNl∝N, it follows that using the smooth particle-mesh Ewald tech-
nique to evaluate the structure factor reduces the cost of an Ewald sum toO(NlogN),
which becomes a significant computational savings in large systems.
Finally, we note that Ewald summation need not be restricted to periodic systems.
In fact, Martyna, Tuckerman, and coworkers (1999, 2004a, 2002) showed that the
Ewald summation formalism could be easily modified in a unified manner foruse in
systems with zero, one, or two periodic dimensions, correspondingto clusters, wires,
and surfaces, respectively.