Application of the Klein-Hanley <i>m</i> –6–8 Potential to 18 Nonpolar Gases: Correlation of Well Depths with Ab Initio Calculations and Equilibrium and Transport Properties

The four-parameter Klein-Hanley <i>m</i>-6-8 pair potential has been used to calculate simultaneously the viscosity η(<i>T</i>) and second virial coefficient (SVC) <i>B</i>(<i>T</i>) for 18 gases, including the rare gases Ne-Xe, the diatomic molecules D₂, N₂, O₂, F₂, Cl₂, and Br₂, and eight polyatomic molecules varying in complexity from CH₄ to C(CH₃)₄ over specified temperature ranges appropriate for each gas. The potential parameters <i>m</i> and γ are fully variable (in addition to ε, the well depth, and σ, the hard-sphere interaction distance) because the reduced collision integrals and SVCs, which are used to calculate η(<i>T</i>) and <i>B</i>(<i>T</i>), are expressed analytically as functions of of <i>m</i>, γ, and <i>T</i>. The four parameters are optimized by regression analysis, in which the calculated η(<i>T</i>) and <i>B</i>(<i>T</i>) are compared with the respective reference values. It is shown that, for the rare gases, N₂, O₂, F₂, CH₄, and CO₂, a linear correlation with unity slope exists between the <i>m</i>-6-8 ε parameter and <i>D</i>_<i>e</i>, the well depth obtained from ab initio calculations and from experiment, suggesting that such pair potentials should correspond with the actual depth of the isotropic potential energy curve. This relationship resolves the disparity in ε and σ values of the Lennard-Jones potential obtained from η(<i>T</i>) and <i>B</i>(<i>T</i>) data. The results of this study show that for all 18 gases, ε correlates with the exothermicity of dimer formation, calculated at a common reduced temperature of 0.7.