Colloquium: Dr. Jerome DelhommelleDr. Jerome Delhommelle Department of Chemistry University of North Dakota Grand Forks, ND
The partition function: A Concept or a Reality?
How a Random Walk can lead to the Determination of the Partition Function
Recently, a Monte Carlo algorithm, developed by Wang and Landau, was designed to perform a new kind of simulations. The idea is to directly determine the partition function of a system by carrying out a random walk in one or more thermodynamic variables. The simulation is then biased in order to perform a uniform sampling of those variables. This powerful method, known as Wang-Landau sampling, has been mainly used to determine the density of states of various systems ranging from Ising models to Lennard-Jones fluids. In this presentation, we show how this method can be extended to molecular systems and to different statistical ensembles. In particular, we will present how, (i) by combining hybrid Monte Carlo simulations in the isothermal-isobaric ensemble with the Wang–Landau sampling method, we determine the vapor-liquid equilibria of various molecular fluids such as CO2, benzene, PAHs, as well as flexible chains of n-alkanes, and (ii) by combining the Wang-Landau method with expanded grand-canonical simulations, we obtain a high-accuracy estimate for the grand-canonical partition function of adsorbed fluids in porous materials. Once the partition function is evaluated, thermodynamic properties can be calculated using the formalism of statistical mechanics. Unlike standard methods, free energies and entropy can be computed directly, allowing for a better understanding of systems exhibiting first-order or second-order phase transitions.