Theory of a Systematic Computational Error in Free Energy Differences

Daniel Zuckerman, Thomas B. Woolf

Research output: Contribution to journalArticle

123 Citations (Scopus)

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 languageEnglish (US)
JournalPhysical Review Letters
Volume89
Issue number18
DOIs
StatePublished - Jan 1 2002
Externally publishedYes

Fingerprint

free energy
estimates
availability
theorems
sampling

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.

In: Physical Review Letters, Vol. 89, No. 18, 01.01.2002.

Research output: Contribution to journalArticle

@article{780c66f8907f4b068d1d928e89ca7b7c,
title = "Theory of a Systematic Computational Error in Free Energy Differences",
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.",
author = "Daniel Zuckerman and Woolf, {Thomas B.}",
year = "2002",
month = "1",
day = "1",
doi = "10.1103/PhysRevLett.89.180602",
language = "English (US)",
volume = "89",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "18",

}

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

C2 - 12398588

AN - SCOPUS:18744379822

VL - 89

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 18

ER -