System-size effects in ionic fluids under periodic boundary conditions

We investigate the system-size dependence of the thermodynamic properties of ionic fluids under periodic boundary conditions. Following an approach previously developed in the context of quantum Monte Carlo simulations of many-electron systems, we show that the leading-order finite-size artifact in the Coulomb energy per particle of a classical fluid of N structureless ions at given density and temperature is simply -k_BT(2N)^-1. Analytical approximations for the periodicity-induced size dependence of the excess thermodynamic properties of the fluid in the weak-coupling regime are obtained within the linearized Debye-Hückel theory. Theoretical results are compared with published simulations of the one-component plasma and our own simulations of a primitive-model electrolyte solution. Our work is directly relevant to estimating finite-size corrections in simulations of charged fluids comprising structureless ions embedded in continuous media. We outline in the Appendix how some of our formal results may be generalized to molecular fluids with mobile ions; e.g., electrolyte solutions with explicit solvent.