CONSISTENT INTEGRAL-EQUATIONS FOR 2-BODY-FORCE AND 3-BODY-FORCE MODELS - APPLICATION TO A MODEL OF SILICON

Functional differentiation of systematic expansions for the entropy, i n the grand ensemble [B. B. Laird and A. D. J. Haymet, Phys. Rev. A 45 , 5680 (1992)], leads directly to consistent integral equations for cl assical systems interacting via two-body, three-body, and even higher- order forces. This method is both a concise method for organizing exis ting published results and for deriving previously unpublished higher- order integral equations. The equations are automatically consistent i n the sense that all thermodynamic quantities may be derived from a mi nimum on an approximate free-energy surface, without the need to intro duce weighting functions or numerically determined crossover functions . A number of existing approximate theories are recovered by making ad ditional approximations to the equations. For example, the Kirkwood su perposition approximation is shown to arise from a particular approxim ation to the entropy. The lowest-order theory is then used to obtain i ntegral-equation predictions for the well-known Stillinger-Weber model for silicon, with encouraging results. Further connections are made w ith increasingly popular density-functional methods in classical stati stical mechanics.