Perturbation theory for the thermodynamic properties of liquid nitrogen using model potentials

Abstract

A statistical mechanical perturbation theory due to Fischer has been used to calculate thermodynamic properties of liquid nitrogen for model intermolecular potentials due to Cheung and Powles (CP), Raich and Gillis (RG), and Berns and van der Avoird (BV). Refinements in the numerical implementation of the Fischer theory are described. Results for the CP potential agree well with both simulation and experimental data except at high density and high temperature. Differences between theory and experiment are usually comparable to the differences between two sets of experimental data for the CP potential but are generally larger for the other two potentials. For both BV and RG potentials the excess Helmholtz energies and excess internal energies are up to 15 and 10 per cent higher, respectively, than experimental values whereas the predicted pressures are low by 100-200 bar for RG and 50-100 bar for BV. The BV potential is slightly more satisfactory than the RG potential overall. Results for spherical harmonic components of the radial correlation function for the CP potential calculated using zeroth and first order approximations in the Fischer theory and also in the RAM theory are also compared with results from molecular dynamics simulations.

An efficient algorithm for the solution of the correlation function for soft spherical repulsions

“…Therefore, the method can now he used to derive a number of thermodynamic properties. The calculated values for the configurational free energy for a moderately soft potential are in excellent agreement with those of Watanabe et al [20] and Fischer [3] as shown in table 1. Also, the calculated values for the excess specific heat at the constant volume are almost identical with those given by Fischer et al [6] (see Table 2.…”

“…Results of the perturbation theory for diatomic molecules for L = 0.3292 (corresponding to a moderately soft potential) at T* = kT/e = 2.0 where e is the depth of the potential well of Lennard-Jones type. Perturbation theory values for the reduced configurational free energy Ar at densities (/90 "3) obtained in the present study are compared with those of Watanabe et al[20] and Fischer[3].…”

The importance of accurate numerical integration in perturbation theories of molecular liquids

“…For diatomic molecules, the nonspherical perturbation approach initiated by Fischer [11 is the most successful of the perturbation theories, and has already achieved much success in predicting the thermodynamic properties for liquids and liquid mixtures [2-51. In view of the importance of the diatomic molecules with two centre Lennard-Jones potential (2CLJ), several refinements [2,3] have already been proposed for the numerical calculation following Fischer's theory. In order to increase the precision further, we have now introduced another important refinement which will be reported in this note.…”