An Optimized Method for Treating Long-Range Potentials

✍ Scribed by Vincent Natoli; David M. Ceperley

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 318 KB
• Volume: 117
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1995.1054

✦ Synopsis

In simulations of systems with periodic boundary conditions, the Ewald image method is used to evaluate long-range potentials by constructing infinite but rapidly converging sums in both real space and reciprocal space. However, the traditional Ewald construction is not optimal for the case where the real and reciprocal space sums are truncated. We derive a criterion which is used to determine the accuracy of a given approximation and use this criterion to determine the optimal separation of a very general class of potentials, subject to cutoffs, (k_{c}) and (r_{c}), in reciprocal and real space, respectively. Using a basis of locally piecewise-quintic Hermite interpolants, we demonstrate our procedure and show that for the Coulomb potential, the error is proportional to exp( (\left.-k_{c} r_{c}\right)). At typical cutoff values we find the optimized breakup to be two orders of magnitude more accurate than the standard Ewald breakup for a given computational effort. (A) 1995 Academic Press, Inc.