Accurate calculation of the Helmholtz free energy for simple liquid metals

The Gibbs-Bogoliubov inequality has been reexamined and put in a form more appropriate for obtaining an accurate Helmholtz free energy. Starting from this inequality, in conjunction with the classical one-component-plasma reference system, we present theoretical results of related thermodynamic quantities. By comparing the latter with available experiments, we find that (i) the calculated thermodynamic functions such as the Helmholtz free energy, the internal energy, the excess entropy, etc., are reasonably predicted and (ii) the variationally determined plasma parameters emerge naturally to values expected from liquid-structure experiments. In particular we notice that the magnitudes of the principal peaks of the liquid structure factors agree quite well with the freezing criterion of the classical one-component plasma as discussed by A. Ferraz and N. H. March [Solid State Commun. 36, 977 (1980)] in relation to liquid alkali metals.