TY - JOUR

T1 - Theory of a Systematic Computational Error in Free Energy Differences

AU - Zuckerman, Daniel M.

AU - Woolf, Thomas B.

N1 - Funding Information:
The authors have benefited greatly from discussions with Michael E. Fisher, Gerhard Hummer, Chris Jarzynski, Hirsh Nanda, Lawrence Pratt, Attila Szabo, Art Voter, and David Zuckerman. We gratefully acknowledge funding provided by the NIH (under Grants No. GM54782 and No. F32GM20394).

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevLett.89.180602

DO - 10.1103/PhysRevLett.89.180602

M3 - Article

C2 - 12398588

AN - SCOPUS:18744379822

SN - 0031-9007

VL - 89

JO - Physical Review Letters

JF - Physical Review Letters

IS - 18

ER -