Non-additive Intermolecular Potential in Gases. II. Cluster Integrals

The van der Waals interaction discussed in Part I are applied to the equation of state of rare gases. The potential energy between three identical atoms is assumed to be {aligned} U(r₁₂,r₂₃,r₃₁){=}U(r₁₂)+U(r₂₃)+U(r₃₁)+ν(r₁₂r₂₃r₃₁)⁻³(3cosθ₁cosθ₂cosθ₃+1). {aligned} Here r i j is the distance between i th and j th atoms, θ i 's are inner angles of the triangle formed by the three atoms, and {aligned} U(r){=}λ r⁻¹²-μ r⁻⁶. {aligned} Use is made of a relation proved in Part I, 4ν=3αµ, in which α is the polarizability. For this model of the intermolecular potential we have calculated the third cluster integral including quantum effect. By virtue of the non-additive part of the intermolecular potential agreement between observed and calculated values is very good.