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

Here, we demonstrate a method to estimate the uncertainty (confidence intervals and standard errors) of free energy differences calculated by molecular simulations. The widths of confidence intervals and standard errors can be calculated solely from temperature and the number of transitions between states. Uncertainty (95% confidence interval) lower than ±1 kcal/mol can be achieved by a simulation with four forward and four reverse transitions. For a two-state Markovian system, the confidence interval is exact, regardless the number of transitions.