Uncorrelated-pairs approximation for the free energy of a crystal

Abstract

An approximation for estimating the anharmonic contributions to the Helmholtz free energy $F$ is derived as the lowest-order part of an expansion of $F$ in powers of the harmonic pair-pair displacement correlation function. Readily evaluated formulas that are applicable to a perfect monoatomic crystal with periodic boundary conditions are given. When applied to the special case of a linear chain with nearest-neighbor interactions, these formulas become exact. The relationship of the theory developed to the cumulant expansion for $F$, to perturbation theory, and to self-consistent phonon theory is discussed.