On the Ewald summation of Gaussian charges for the simulation of metallic surfaces

It is shown that standard three- and two-dimensional Ewald summation of point charge electrostatics is naturally extended to Gaussian charge distributions. The Gaussian nature of the charges does not affect the regularisation of the conditionally convergent sums, which are performed with spherical and cylindrical orderings, respectively. A clear connection is made between the summation of Gaussian charges and the summation of the associated point charge system. The application of these sums to a simple classical model of a metal surface is discussed. Calculations on a conducting sphere highlight the importance of the model parameterisation.