Ewald type summations of Coulomb interactions in computer simulations of a system with one-dimensional periodic boundary conditions

The Ewald type method (EW1D), its modified version (EW1DM) and the three-dimensional Ewald method with correction term (EW3DC) that properly treat long-range electrostatic interactions in a system with one-dimensional periodic boundary conditions are presented. The methods are tested in molecular dynamics simulations of liquid acetone in various cylindrical pores, when number of acetone molecules is increasing from 58 to 464. For the smallest system the EW1D method leads to the fastest calculations, but computational time scales approximately as N-2 (N is number of charges), and with increasing N the efficiency of the method becomes worse than that of the EW1DM method when computational time grows like N-3/2. Computational efficiency of the EW3DC method depends on ratio of pore diameter to the simulation box length. When this ratio is large, the method is inefficient, and for its value smaller than 0.05 efficiency of the method is similar to that of the EW1DM method. (C) 2004 Elsevier B.V. All rights reserved.