Free Energy Differences from Molecular Simulations: Exact Confidence Intervals from Transition Counts

Here we demonstrate a method to estimate the errors of free energy differences calculated by molecular simulations. The widths of the confidence intervals can be calculated solely from temperature and the number of transitions between states. Accuracy better than ± 4.184 kJ/mol (1 kcal/mol) can be achieved by a simulation at 300 K with four forward and four reverse transitions. Markovianity of the process is a pre-requisite. For a two-state Markovian system, the confidence interval suggested below is exact (not only asymptotic or approximative), regardless the number of transitions. TOC Graphic