(62a) Origins And Development Of The Gibbs Ensemble Methodology

In this presentation, I plan to review the origins of the Gibbs ensemble methodology [1,2] and its development in the intervening twenty years. The methodology was originally proposed in order to overcome limitations of methods that relied upon calculation of the chemical potential for a series of state conditions [3]. Together with Kofke's Gibbs-Duhem integration approach [4] they have allowed the relatively routine calculation of phase diagrams for model or realistic potentials. While alternative methods (e.g. histogram reweighting Monte Carlo) provide potentially greater accuracy near critical points, the Gibbs ensemble remains the method of choice for calculations such as the recent study of phase behavior of water from ab initio potentials [5].

1. A.Z. Panagiotopoulos, "Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble," Mol. Phys., 61, 813-826 (1987).

2. A. Z. Panagiotopoulos, N. Quirke, M. Stapleton and D. J. Tildesley, "Phase equilibria by simulation in the Gibbs ensemble: alternative derivation, generalization and application to mixture and membrane equilibria," Mol. Phys., 63, 527-545 (1988).

3. A.Z. Panagiotopoulos, U.W. Suter and R.C. Reid, "Phase diagrams of non-ideal fluid mixtures from Monte-Carlo simulation," Ind. Eng. Chem. Fundam., 25, 525-535 (1986).

4. D.A. Kofke, ?Direct evaluation of phase coexistence by molecular simulation via integration along the saturation curve.? J. Chem. Phys., 98, 4149 (1993).

5. M. J. McGrath, J. I. Siepmann, I. -F. W. Kuo and C. J. Mundy, ?Vapor-liquid equilibria of water from first principles: comparison of density functionals and basis sets.? Molec. Phys., 104, 3619 (2006).