Frank H. Stillinger†,* and Salvatore Torquato†,‡,§ †Department of Chemistry, Princeton University, Princeton, NJ 08544, USA; ‡PRISM, Princeton University, Princeton, NJ 08544, USA; §Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544. Received 31 March 2005; in final form 21 April 2005. *Frank H. Stillinger is in the Department of Chemistry, Princeton University, Princeton, NJ 08544, USA. Email: fhs@princeton.edu. The authors gratefully acknowledge the support of the Office of Basic Energy Sciences, DOE, under Grant No. DE-FG02-04ER46108. Molecular Physics, Vol. 103, Nos. 21–23, 10 November–10 December 2005, 2943–2949

Abstract

Iso-g(2) processes in the equilibrium regime concern density-dependent interactions that identically cancel the usual density variation of many-body pair correlation functions. This paper considers the formal density expansion for effective pair potentials with this iso-g(2) property, showing how successive terms in that expansion can be determined iteratively. Explicit results through second density order have been obtained for two types of ‘target’ pair correlation functions: (a) a unit step function (hard core), and (b) unity augmented by an origin-centred Gaussian profile with numerical multiplier A. For the unit step function and the -1=A<0 Gaussian cases, realizability appears to be attainable up to a finite terminal density. However, when the Gaussian A>0, the terminal density diverges to infinity while the effective pair interaction series is non-convergent, though possibly valid as an asymptotic expansion.