THE BRIDGE FUNCTION EXPANSION AND THE SELF-CONSISTENCY PROBLEM OF THEORNSTEIN-ZERNIKE EQUATION SOLUTION

We propose self-consistent solutions to the Ornstein-Zemike equation w here the approximate closure is replaced by a bridge function expansio n, whose main advantage is the improvement of correlation functions. U nknown coefficients of this expansion are found from the principle of total thermodynamic consistency. The latter includes not only the conv entional pressure-compressibility equation but also the relation betwe en internal energy and pressure. We show that utilizing only the first equation one may face a nonunique partially consistent solution condi tioned by noncomplete formulation of the consistency problem. At the s ame time the suggested set of equations is sufficient to determine a t rue and unique physical solution regardless of the number of unknown c oefficients. In this paper we expand the bridge function in powers of potential of mean force and perform the example of building the approx imate self-consistent closure. Moreover, the approach via total thermo dynamic consistency introduces the value of residual inconsistency as the internal criterion of accuracy, which is equal to zero only for th e exact closure relation and the corresponding solution. This value is found to be in agreement with the deviation of thermodynamic quantiti es from numeric simulation data. The proposed method is tested on the classical model of a Lennard-Jones fluid in a wide range of temperatur es and high densities.