Variational limits on the Helmholtz free energy of simple fluids

Accurate radial-distribution functions obtained from a thermodynamically consistent integral equation are used to calculate upper and lower bounds to the Helmholtz free energies of several inverse-power potential fluids and the Lennard-Jones fluid. Comparisons with results from Monte Carlo simulations indicate that the true free energies are tightly bracketed by the variational bounds. In addition, the simulations agree with the arithmetic mean of the limits near melt to within about 0.03NkBT for inverse power fluids and about 0.06NkBT for Lennard-Jones fluids. These results indicate that it is possible to obtain accurate free energies very efficiently by the variational method.