A New Approach for Estimating the Free Energy Differences among Multiple Thermodynamic States in Statistical Simulations

In this letter, a new approach tocompute free energy differences(FEDs) between multiple thermodynamics states is introduced. The methoddirectly uses energy probability densities, which can be extractedwith high accuracy from equilibrium simulations to obtain FEDs. Methodsin current use, such as Bennett acceptance ratio (BAR), its multistategeneralization (MBAR), or the weighted histogram analysis method (WHAM),require iterative solution of nonlinear equations which are knownto be slowly convergent. The equations providing MBAR FEDs are identicalto those derived earlier by Souaille and Roux in a method that hasbecome known informally as binless WHAM. In contrast,we obtain FEDs by solution of linear equations. For the classic two-stateproblem, the statistical error of our method, solving linear equations,is shown analytically to match that of BAR under common conditions.

Automated summary

In this letter, a new method for calculating free energy differences (FEDs) between multiple thermodynamic states using energy probability densities is introduced. Existing methods such as BAR, MBAR, and WHAM require iterative solution of nonlinear equations, while our method solves linear equations to obtain FEDs. For the classic two-state problem, the statistical error of our method matches that of BAR under common conditions.