### Abstract

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 language | English (US) |
---|---|

Journal | Physical Review Letters |

Volume | 89 |

Issue number | 18 |

DOIs | |

State | Published - Jan 1 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Theory of a Systematic Computational Error in Free Energy Differences.** / Zuckerman, Daniel; Woolf, Thomas B.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 89, no. 18. https://doi.org/10.1103/PhysRevLett.89.180602

}

TY - JOUR

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

AU - Zuckerman, Daniel

AU - Woolf, Thomas B.

PY - 2002/1/1

Y1 - 2002/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=18744379822&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18744379822&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.89.180602

DO - 10.1103/PhysRevLett.89.180602

M3 - Article

VL - 89

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 18

ER -