Theory of a Systematic Computational Error in Free Energy Differences

Daniel M. Zuckerman, Thomas B. Woolf

Research output: Contribution to journalArticlepeer-review

141 Scopus citations


Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, [Formula presented]. Free energy differences [Formula presented] 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 [Formula presented]—in [Formula presented] 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 [Formula presented] for large [Formula presented], the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.

Original languageEnglish (US)
JournalPhysical Review Letters
Issue number18
StatePublished - 2002
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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