Optimum free energy in the reference functional approach for the integral equationstheory

Abstract

We investigate the question of determining the bulk properties of liquids, required as inputfor practical applications of the density functional theory of inhomogeneous systems, usingdensity functional theory itself. By considering the reference functional approach in the testparticle limit, we derive an expression of the bulk free energy that is consistent with theclosure of the Ornstein–Zernike equations in which the bridge functions are obtained fromthe reference system bridge functional. By examining the connection between the freeenergy functional and the formally exact bulk free energy, we obtain an improvedexpression of the corresponding non-local term in the standard reference hypernettedchain theory derived by Lado. In this way, we also clarify the meaning of therecently proposed criterion for determining the optimum hard-sphere diameterin the reference system. This leads to a theory in which the sole input is thereference system bridge functional both for the homogeneous system and theinhomogeneous one. The accuracy of this method is illustrated with the standardcase of the Lennard-Jones fluid and with a Yukawa fluid with very short rangeattraction.