Summation of dipolar fields in simulated liquid-vapour interfaces

Abstract

Computer simulations of liquid-vapour interfaces produce configurations of some finite number of atoms or molecules within a central cell. Periodic boundary conditions repeat the central cell to infinity. To extract local fields and optical properties from these configurations it is necessary to sum over dipolar fields to infinity. For N polarizable atoms in the central simulation cell, 1 2 N( N-1) dipolar sums are required, and N simultaneous linear equations are to be solved to find the self-consistent local fields on each atom. A realistic simulation of a liquid-vapour interface requires a thousand particles or more. Hence an efficient algorithm for the dipolar sums is required. Formulae are given which convert these slowly converging sums to rapidly convergent sums requiring only a few terms. These formulae enable local fields to be computed, for each atom, as a byproduct of the computer simulation. Of particular interest are the fluctuations in the local fields.