Optimized cluster theory, the Lennard-Jones fluid, and the liquid-gas phase transition

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Abstract
The optimized cluster theory is applied to the Lennard-Jones fluid. The coexistence curve obtained from the theory is presented. It represents the most accurate microscopic calculation of the liquid-gas phase diagram for a fluid with a realistic Hamiltonian. The theory is shown to be quantitatively accurate for all fluid states except those very close to the critical point. Phenomenological procedures are devised which extrapolate towards the critical point from regions in which the optimized cluster theory is accurate. The extrapolation calculations predict nonclassical values for the critical exponents which are in fairly good agreement with experiment. In addition to investigating the liquid-gas phase transition, the equilibrium pair correlation functions are calculated at several states. Further, the internal consistency of the optimized cluster theory is discussed.