Structure and thermodynamics of liquid alkali metals in variational modified hypernetted-chain theory

The role of the Percus-Yevick hard-sphere bridge function in the modified hypernetted-chain integral equation is examined within the context of Lados criterion [F. Lado, S. M. Foiles, and N. W. Ashcroft, Phys. Rev. A 28, 2374 (1983)]. It is found that the commonly used Lados criterion, which takes advantage of the analytical simplicity of the Percus-Yevick hard-sphere bridge function, is inadequate for determining an accurate static pair-correlation function. Following Rosenfeld [Y. Rosenfeld, Phys. Rev. A 29, 2877 (1984)], we reconsider Lados criterion in the so-called variational modified hypernetted-chain theory. The main idea is to construct a free-energy functional satisfying the virial-energy thermodynamic self-consistency. It turns out that the widely used Gibbs-Bogoliubov inequality is equivalent to this integral approach of Lados criterion. Detailed comparison between the presently obtained structural and thermodynamic quantities for liquid alkali metals and those calculated also in the modified hypernetted-chain theory but with the one-component-plasma reference system leads us to a better understanding of the universality property of the bridge function.