Thermodynamic limit of the energy density in a crystal

A pedagogical, semi-rigorous proof is presented for the existence of the thermodynamic (infinite-volume) limit of the energy per volume for an electrically neutral, metallic or nonmetallic crystal. The proof is based on the demonstration of the same for individual energy components, namely, the kinetic, Coulomb, and exchange contributions to the Hartree-Fock energy as well as the correlation contribution obtained by many-body perturbation or coupled-cluster theory.