The inversion of second virial coefficients for polyatomic molecules

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Abstract
Inversion of the second virial coefficient B(T) of a polyatomic gas yields an effective isotropic pair-potential-energy function U inv(r); the relation between this and the true anisotropic function is investigated. The existence is proved of a temperature-independent angle-average ‘well-width’ function <Δθ(φ)>, whose Laplace transform exactly specifies B(T). Although <Δθ(φ)> may be represented by an effective potential-energy function of spherical symmetry, the result generally exhibits non-analytic turning points. For a model anisotropic interaction proposed for N2, <Δθ(φ)> is found to be closely approximated by the well-width function that corresponds to U inv(r), except near the minimum energy where U inv(r) fails to show the required singularity.