SUMMATION OF COULOMB FIELDS IN COMPUTER-SIMULATED DISORDERED-SYSTEMS

Formulae are derived for the sums over Coulomb forces exerted on a charged particle by other charged particles, the central cell system being repeated to infinity by periodic boundary conditions. Such sums are needed in molecular dynamics simulations involving either ions or neutral molecules represented as bound conglomerates of charges, and in astrophysical simulations of gravitating masses. The derived sums are rapidly convergent, being expressed in terms of Bessel functions K(v)(z), which decrease exponentially with z. The force expressions are integrated analytically to give the potential function, which may be used in Monte Carlo simulations. The geometries considered are: (i) systems confined between two parallel walls, and (ii) unconfined three-dimensional systems.