Effect of asymmetric isotopic substitution on atom–diatom potentials

Abstract

A simple and accurate method is proposed for transforming the Legendre expansion of an atom–diatom potential about the diatom center of mass into a new Legendre expansion about a shifted (by isotope substitution) diatom center of mass. It is found that a simple quadrature procedure yields accurate results throughout the range of intermolecular separation of physical interest, while a previously proposed Taylor series expansion procedure gives comparable accuracy only for intermolecular separations greater than the equilibrium separation. Numerical tests of the method are performed for three model atom‐plus‐rigid diatom systems H₂(HD) –He, HCl(DCl) –Ar, and ³⁵ClF(³⁷ClF) –Kr. adequate to determine the residual energy and entropy as well as their volume derivatives. The temperature dependence of the derivatives of the energy and entropy supports the contention that the equation of state is that for segments having a steep repulsive potential of the form ε (σ/r)ⁿ with a mean field containing the attractive potential. The independently measured heat capacity combined with (δS/δlnV)_T predict the exponent n and this value is corroborated by the internal scaling of the latter derivative. Scaling between compounds of pressure (δS/δV)_T and (δU/δV)_T is achieved by a two‐parameter corresponding‐states relation.