The direct determination of potential energy functions from second virial coefficients

Methods which enable the intermolecular pair potential energy curve to be determined from second virial coefficient data are critically examined. Those techniques which involve the inverse Laplace transform, though theoretically attractive, are found to be ineffective with experimental data. New approximate methods are proposed and found to be successful in characterizing both the repulsive and attractive regions of the potential energy function. The procedures were tested on simulated data calculated from a number of known potential energy functions and were shown to reproduce the original potentials with high accuracy. The techniques were then applied to experimental second virial coefficient data for argon to give the repulsive potential energy curve above 300 K and the width of the upper portion of the potential well as a function of its depth. When used in conjunction with similar techniques for the inversion of gas viscosity data, these methods enabled the potential energy curve for argon to be established over a wide range of intermolecular separation.