Quantitative comparison and optimization of methods for evaluating the chemical potential by molecular simulation

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Abstract
The precision of several methods for computing the chemical potential by molecular simulation is investigated. The study does not apply molecular simulation to the analysis but instead works with models of the simulation process. These models enable the variance of the chemical potential to be computed accurately and very quickly and thereby permits the methods (freeenergy perturbation, expanded ensembles, thermodynamic integration, and histogram-distribution methods) to be optimized and compared over a range of densities. The study focuses exclusively on the hard-sphere model. This model is simple and well characterized; yet it exhibits the essential features that make the chemical potential calculation difficult; arguments are presented to support the broader applicability of the study. The severe asymmetry of particle insertion against particle deletion is highlighted, and it is shown that any staged free-energy perturbation method with a 'deletion' component is highly prone to systematic error. More generally this implies that such methods should always be staged in the direction of decreasing entropy. Other findings show that uniform sampling is not optimal for umbrellasampling and expanded-ensemble applications, although it remains a good rule of thumb for tuning these approaches. Among the techniques we study, optimally staged insertion and the distribution–histogram methods are the most efficient and precise. The latter is effective only when used in an interpolative fashion, and we identify it as the most likely route to further progress in the field.

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