The approximate method to treat the practical quantum anharmonic solids proposed by Hardy. Lacks and Shukla is reformulated with explicit physical meanings. It is shown that the quantum effect is important at low temperature, it at be treated in the harmonic framework; and the anharmonic effect is important at high temperature and tends to zero at low temperature, it can be treated by using a classical approximation. The alternative formulation is easier for various applications, and is applied to a Debye-Gruneisen aolid with the generalized Lennard-Jones intermolecular interaction. The expressions for the Debye temperature and Grunelsen parameter as a function of volume are analytically derived. The analytic equation of state is applied to predict the thermodynamic properties of solid xenon at normal pressure with the nearest-neighbour Lennard-Jones interaction, and is further applied to research the properties of solid xenon and krypton at high pressure by using an all-neighbour Lennard-Jones interaction. The theoretical results are in agreement with the experiments.

The analytic equations of state for the double Yukawa fluids with (GHCDY) and without (SDY) hard-core repulsion have been derived based on the Barker–Henderson and Ross perturbation theories, respectively, and the analytic expression of HS-RDF previously developed. The comparison of the numerical results with computer simulation data shows that the GHCDY potential should be divided into three types in terms of the values of parameters in GHCDY potential function. The first type is hard-core plus pure attraction. Second type is hard-core plus small part soft-repulsion and attraction. Third type is hard-core plus large part softrepulsion and attraction. The BH theory is applicable to first and second types but not to third type. The simple fluid is one of the most important prototypes of GHCDY fluid, and it belongs to second type. The charged protein molecules is another one, it belongs to third type. The GHCDY potential being appropriate to charged protein molecules is very similar to the SDY potential, and its thermodynamic properties can be alternatively described by using the Ross variational perturbation theory. © 2004 Elsevier B. V. All rights reserved.

In this letter, it is pointed out that an ideal universal equation of state (EOS) of solids should have four merits. The EOS corresponding to the generalized Lennard-Jones (GLJ) potential is derived. It is pointed out that the GLJ EOS is not volume analytic, as the exponents contained in the potential function take arbitrary values. On making the exponents satisfy a relationship, the GLJ EOS becomes volume analytic with two parameters (mGLJ EOS), and has all four merits. By applying six EOSs in investigating 50 materials, it is shown that the mGLJ EOS gives the best results.

A fitting procedure is proposed to establish two analytic approximate expressions for the complicated Rarker-Henderson (BH) diameter with Lennard-Joues potential in two temperature ranges. Considering that the differentiation is a process enlarging the errors and the integration decreasing the errors and that the derivative of BH diameter is important in the calculation of in ternal energy, we propose to tit the derivative directly, instead of usually fitting the original function and subsequently deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively used expressions in literature. The one with following form only has an average fitting 0.0063% in the reduced temperature range (0.4≤Kt/S≤15), and can be extrapolated to a wider temperature range (0.4≤Kt/S≤50) with an average error 0.13%, which is d/ơ=1.1755+0.02878 In T -0.2072T1/4+0.00643T3/4.

A simple method is proposed to dispose the quantum effect and anharmonic effect at the same time. Considering the quantum effect is remarkable only at low temperature, and tends to zero at high temperature, the potential energy of an atom is expanded harmonically to consider the quantum effect of solids within the harmonic oscillator framework. The anharmonic effect is remarkable only at high temperature, and tends to zero at low temperature, it was disposed by using a classical approximation. The universal formalism is applied to the generalized Lennard-Jones solid. The comparison shows that the results with and without anharmonic effect are in agreement with cach other at some low temperature, to which the Einstein model is applicable. The results without anharmonic effect become divergent at slightly higher temperatures; however, the results including anharmonic effect are in good agreement with the experimental data of solid xenon. The method proposed in this paper can be extended on other potentials to develop practical molecular thermodynamic equations of state for solids.