Nodal Expansions. Distribution Functions, Potentials of Average Force, and the Kirkwood Superposition Approximation

The customary density power series expansions of potentials of average force and distribution functions are converted into a new class of expansions, defined in terms of topological nodes. The physical meaning of the terms in the new expansions is discussed, and arguments are presented to show that the new expansions can be expected to converge considerably more rapidly than the customary density expansions. The probable occurrence of phase transitions is discussed. Possible further developments are suggested. The Kirkwood superposition approximation is shown to be valid for a large number of terms in the expansions of potentials of average force and distribution functions. The customary comparison of the exact value of the third virial coefficient with that obtained via the Kirkwood superposition approximation is shown to provide no proof of the validity or invalidity of the latter.