Molecular dynamics and higher-order perturbation-theory results for the anharmonic free energy and equation of state of a Lennard-Jones solid

The anharmonic contribution to the Helmholtz free energy (${\mathit{F}}_{\mathit{A}}$) is calculated as a function of temperature (T) and volume (V) for a fcc crystal of atoms interacting via a nearest-neighbor 6-12 Lennard-Jones potential, by the molecular-dynamics (MD) method and by perturbation theory (PT) to O(${\lambda }^2$) and O(${\lambda }^4$). The volume-dependent coefficients for the ${\mathit{T}}^2$ and ${\mathit{T}}^3$ terms of ${\mathit{F}}_{\mathit{A}}$ have been extracted from the MD results, and compared with the corresponding coefficients of ${\lambda }^2$ and ${\lambda }^4$ PT. The agreement between the results of the MD and PT methods is excellent. The coefficient of the ${\mathit{T}}^4$ term of ${\mathit{F}}_{\mathit{A}}$ is also extracted from the MD results, to give an approximation to the corresponding term in O(${\lambda }^6$) PT. Various thermodynamic properties are calculated from this approximation of PT to O(${\lambda }^6$), and are compared to exact MD results to provide a picture of the convergence properties of PT. The results suggest that ${\lambda }^6$ PT would be accurate up to approximately 60% of the melting temperature. © 1996 The American Physical Society.