Renormalized-density-functional theories for nonuniform classical fluids

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Abstract
The renormalized-density-functional theory (RDFT) proposed by Groot and Van der Eerden [Phys. Rev. A 36, 4356 (1987)] and the modified renormalized-density-functional theory (MRDFT), which is based upon a global average of the density, are considered. In the MRDFT theory, as in the RDFT theory, the weighting function and the weighted density are determined by the extremal condition of the free-energy functional with respect to the ‘‘coarse-grained’’ densities as free variables. Using an identity due to Percus [in The Equilibrium Theory of Classical Fluids, edited by H. L. Frish and J. L. Lebowitz (Benjamin, New York, 1964)], it is possible to investigate the properties of homogeneous systems in the RDFT, and in the MRDFT. The results are obtained for the RDFT theory and the MRDFT theory and are compared with each other and with those of other theories. In the RDFT theory the low-density expansion is used to calculate the fourth virial coefficient and the second-order pair-correlation function for systems with repulsive potential, in which it disagrees with the exact virial expansion of the system. The results of the RDFT theory show that the RDFT theory is less accurate than the weighted-density-approximation theory [Tarazona, Phys. Rev. A 31, 2672 (1985)] which was based upon an ad hoc form of the weighted density. The MRDFT theory leads to the usual hypernetted-chain equation of state for homogeneous systems, as does the modified weighted-density-approximation theory [Denton and Ashcroft, Phys. Rev. A 39, 4701 (1989)].