Theory of a systematic computational error in free energy differences.
Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, N. Free energy differences (Delta)F between two states or systems are critically important examples of such averages. Previous work has demonstrated, empirically, that the "finite-sampling error" can be very large--many times k(B)T--in (Delta)F estimates for simple molecular systems. Here we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of 1/N for large N, the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.
Zuckerman
Daniel M
DM
Department of Physiology, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205, USA. dzuckerman@ceoh.pitt.edu
Woolf
Thomas B
TB
D004735:Energy Transfer; D008954:Models, Biological; D008956:Models, Chemical; D008962:Models, Theoretical; D013223:Statistics as Topic / Q000379:methods