Relationship between Pair Potentials and Liquid Structure

Abstract

The Percus–Yevick and hypernetted chain theories are used to investigate the sensitivity of the pair potential [Formula: see text] to errors in the measured structure factor S(K) for several liquid metals and nonmetals. The linear relation between small errors, [Formula: see text], is studied by means of a generalized eigenvector analysis. Only those combinations of errors in S(K) which correspond to large eigenvalues lead to significant uncertainties in [Formula: see text]. The general form of the dominant eigenvectors was found to be the same for all liquids studied, except near the critical point. With this same exception, the following conclusions hold: Errors in S(K) for small K have by far the greatest effect on [Formula: see text]; the depth of the attractive portion of [Formula: see text] is most sensitive to errors in S(K); the repulsive core of [Formula: see text] is insensitive to errors in S(K); and the height of the main peak of S(K) has very little effect on [Formula: see text].