Effects of a Volume-Dependent Potential on Equilibrium Properties of Liquid Sodium

Calculations of cohesive energy, pressure, and compressibility have been made for liquid Na at 393^. They are based on the Ashcroft form for the pseudopotential and the self-consistent dielectric function recently given by Singwi et al. , which have been found to give good agreement with the measured phonon dispersion relations in crystalline Na, and a liquid strucutre derived from a recent molecular-dynamics calculation by Rahman. The theory is formulated in terms of a volume-dependent pair potential and additional volume-dependent terms. A model which considers only volume-independent pairwise interactions gives incorrect results for the cohesive energy and pressure. It also gives a different result for the compressibility from the full theory, owing to the neglect of certain three- and four-particle interactions which are considered in the full theory; this result is, however, in reasonable agreement with experiment. The full theory gives good agreement for the cohesive energy, pressure, and compressibility if and only if an adjustment is made to the Hartree energy, similar to that made in a previous calculation for the crystal.