Computer simulation and the dielectric constant at finite wavelength

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Abstract
In computer simulations the wavevector-dependent dielectric constant ϵ(k) may be calculated from the equilibrium fluctuations of the spatial Fourier components of the instantaneous polarization of the sample. It is shown that this relationship depends on the boundary conditions/dipolar interactions used in the simulation, not only at infinite but also at finite wavelength, and explicit expressions are given for all simulation techniques currently used. By means of these fluctuation formulas it is now possible to calculate the entire k-dependent dielectric constant from simulations with arbitrary boundary conditions. The formulas also permit a general discussion of the relative merits of various simulation techniques as well as of some quantitative aspects of the Ewald sum in particular. Longitudinal and transverse components of ϵ(k) have been obtained from a reaction field simulation of a Stockmayer system, and these results are used to calculate the k-dependent polarization fluctuations for various other boundary conditions. The predictions are found to be consistent with the behaviour in actual simulations. Finally it is pointed out that, once the dielectric constant is known from any type of simulation, the orientational structure of the infinite system can be obtained by exploiting the relationship between ϵ(k) and the pair correlation function. It is shown that for the Stockmayer system this route is feasible in practice.