Gibbs–Bogoliubov variational procedure with the square-well reference system

Abstract

For the first time, the square-well (SW) model is used as a reference system in the thermodynamic variational calculations for liquids. The SW system is taken within the random phase approximation. To apply this approach to simple metals, the local Animalu–Heine model pseudopotential, the Vashishta–Singwi exchange-correlation function, and the Nozieres–Pines exchange-correlation energy are used. Thermodynamics and structure of liquid Na at T = 373 K are studied. We found that there are several areas of the SW parameters where the solution is stable. We chose the best of such areas in which the calculated structure factor is in good agreement with the experimental one. Then the Helmholtz free energy is minimized in this area with respect to the hard-core diameter and the SW depth at the fixed SW width. It was found that the SW variational procedure gives an upper bound of the Helmholtz free energy which is lower than that in the hard-sphere variational procedure, and that the obtained thermodynamic properties are in reasonable agreement with the experiment.