Correlated-particles expansion through third order: The Lennard-Jones solid

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Abstract
The correlated-particles expansion (CPE) which was described in detail in an earlier paper, is used to calculate the thermodynamic properties and mean-square displacement of an fcc nearest-neighbor Lennard-Jones solid in the classical limit. Two sets of results are presented. One is accurate through second order. The other is accurate through third order. These results are compared with those obtained with the quasiharmonic approximation (QHA), second-order perturbation theory (PT), the cell-cluster expansion (CCE), and Monte Carlo (MC) methods. When used through second order, the predictions of the CPE are significantly more accurate than those of either the QHA or PT. When used through third order, the differences between the thermodynamic properties predicted with the CPE and the MC predictions are of the order of 1% or less for all temperatures up to melting. The CCE gives results of similar accuracy.