Effective pair potentials in fluids in the presence of three-body forces

Abstract

The physical properties of a fluid in which there is only a two-body potential, uαβ , can be expressed in terms of the total correlation function, h 12, which is a sum of all connected graphs with root-points on molecules 1 and 2, whose links are f bonds, where fαβ = exp (-uαβ/κT) - 1. It is shown that the total correlation function in the presence of a weak three-body potential, uαβγ , is h 12*, where h 12* is the sum of all two-body connected graphs in which each f bond is replaced in turn by an f* bond, where and where ✶ is a sub-set of the elementary graphs each of which contains one fαβγ link. We call this sub-set the line-irreducible graphs, and its leading term is a graph discussed by Rushbrooke and Silbert. The three-body potential is set equal to the dipole-dipole-dipole potential of Axilrod and Teller, and the analytic properties and numerical values of the first term ✶1 examined in detail. Other effective potentials have been defined and the relations between them are elucidated. In particular ...