Overcoming finite-sampling errors in fast-switching free-energy estimates: extrapolative analysis of a molecular system

We perform a block-averaging and extrapolation analysis of fast-switching free-energy difference (ΔF) estimates for a computer-modeled, fully solvated ethane↔methanol transformation. The results suggest that the analysis can greatly reduce the `finite-sampling errorʹ in ΔF estimated from a small number of very fast switches. This error, which can be many times kBT, is the difference between an estimate based on a finite amount of data and that from an infinite data set; it is inherent in the ΔF calculations. Our blocking/extrapolation procedure appears to be particularly useful for broad, non-Gaussian distributions of data which typically produce large finite-sampling errors.