On the convergence of multi-scale free energy simulations

In this work, we employ simple model systems to evaluate the relative performance of two of the most important free energy methods: The Zwanzig equation (also known as Free energy perturbation') and Bennett's acceptance ratio method (BAR). Although our examples should be transferable to other kinds of free energy simulations, we focus on applications of multi-scale free energy simulations. Such calculations are especially complex, since they connect two different levels of theory with very different requirements in terms of speed, accuracy, sampling and parallelisability. We try to reconcile all those different factors by developing some simple criteria to guide the early stages of the development of a free energy protocol. This is accomplished by quantifying how many intermediate steps and how many potential energy evaluations are necessary in order to reach a certain level of convergence.