Unorthodox uses of Bennett's acceptance ratio method

We illustrate the application of Bennett's acceptance ratio method (BAR) to problems in which standard methods to compute free energy differences (thermodynamic integration, exponential formula) are not practical. Our starting point is the observation that BAR can often compute the free energy difference between two states without the need for intermediate states usually employed (and necessary) in alchemical free energy simulations. This is demonstrated first for the free energy difference between ethane and methanol in aqueous solution. We then show how BAR can be used to compute directly rather unusual free energy differences, such as the free energy difference resulting from changing the treatment of electrostatic interactions, from switching the force field, or from using an implicit solvent model. Calculations of this kind should prove useful for force field development and the validation of implicit solvent methods.