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

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