On Multiple Time-step Algorithms and the Ewald Sum

Abstract

We show how standard multiple time-step algorithms devised for systems with short-range potentials can be used successfully in simulations of periodic systems with long-range (Coulombic) potentials. Three strategies for incorporating the Ewald sum into a multiple time-step algorithm are considered. These are (i) evaluation of reciprocal space terms every time-step (ii) evaluating reciprocal space terms once every n time-steps and placing these terms in with the slowly varying forces and energies (iii) a modified form of the second strategy in which primary shell (close) electrostatic interactions are evaluated directly and the more distant interactions handled by the Ewald sum (once every n time-steps). Only the first and third approaches give satisfactory thermodynamic results. The third strategy is much more efficient than the first. With the third strategy substantial savings in cpu time are acheived in both the real space and, most importantly, the reciprocal space terms of the Ewald sum. This is achieved without significant loss of accuracy or stability. Overall execution time is decreased by a factor of between 2 and 3.

Key Words:

• Molecular Dynamics Simulation
• Ewald sum
• multiple time-step