Abstract
The modified Green function appropriate for solution of interior boundaryvalue problems of Laplace's equation in a three-dimensional rectangularparallelepiped, subject to periodic boundary conditions, is developed. Thisallows the determination of the potential due to an arbitrary continuouscharge distribution and its periodic replications in three dimensions.Summation of the eigenfunction expansion by application of thePoisson-Jacobi formula gives a Ewald sum, while application of the Poissonsummation formula results in a two-dimensional potential that is perturbedby a rapidly converging Fourier cosine series involving K0 Besselfunctions. The latter constitutes a generalization of formulae describedby Lekner. Numerical results show that the K0 expansion is more rapidlyconvergent than the Ewald sum, and could therefore substantially reduce thecomputational effort involved in the molecular simulation of ionic andpolar fluids. The Green function is also shown to be related to theasymptotic behaviour of lattice sums for the screened Coulomb potential, inthe limit as the screening constant tends to zero.
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