Ewald type summation method for electrostatic interactions in computer simulations of a three-dimensional system periodic in one direction

Abstract

The energy expressions for the Coulomb and dipole–dipole interactions in systems with one-dimensional periodicity are derived. In the calculations we used the integral representation of the gamma function, the one-dimensional Poisson summation formula, and two-dimensional Fourier transforms of the functions depending on position components perpendicular to the periodicity direction. In this method the reciprocal-space summation can be expressed as a sum of structure factors, containing charge or dipole positions, multiplied by coefficients depending on the reciprocal-space vector, however, in a general case two parameters must be introduced.