TY - JOUR
T1 - Theory of a Systematic Computational Error in Free Energy Differences
AU - Zuckerman, Daniel M.
AU - Woolf, Thomas B.
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
VL - 89
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 18
ER -