Lattice integrals for the energy of disordered solids with long-range interparticle interactions

Abstract

We introduce a model hard-sphere solid with correlation functions in excellent agreement with hard-sphere solid correlation functions calculated from simulations. The model solid is of independently distributed Gaussian particles centred at the points of a face-centred cubic lattice. We generalize the model to any lattice and use it to calculate contributions to the internal energy due to long-ranged potentials.