Perturbation Calculation of Mixed Pair Correlation Functions

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Abstract
A perturbation calculation of the change in pair correlation function (relative to some reference system) is presented for the case when the intermolecular pair potential is altered (relative to the same reference system). The analysis is developed in detail for the case of a very dilute solution of perturbing molecules in a host dense fluid, but the case of the pure fluid is also examined. Numerical calculations for a variety of inverse power potentials show that when the perturbation potential is much smaller than kT, many body interaction terms are very small and the simplest approximation, g2(R) = g20(R) exp [−βVp(R)] is valid. When Vp ∼ kT, this is no longer true; the many body effects then make an important contribution to the change in g2(R). Explicit formulas are presented for the correction terms to order β2 and general formulas valid for all β are displayed in unexpanded form.