Efficient use of nonequilibrium measurement to estimate free energy differences for molecular systems

F. Marty Ytreberg, Daniel M. Zuckerman

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


A promising method for calculating free energy differences AF is to generate noiiequilibrium data via "fast-growth" simulations or by experiments - and then use Jarzynski's equality. However, a difficulty with using Jarzynski's equality is that AF estimates converge very slowly and unreliably due to the nonlinear nature of the calculation - thus requiring large, costly data sets. The purpose of the work presented here is to determine the best estimate for AF given a (finite) set of work values previously generated by simulation or experiment. Exploiting statistical properties of Jarzynski's equality, we present two fully automated analyses of nonequilibrium data from a toy model, and various simulated molecular systems. Both schemes remove at least several kBT of bias from ΔF estimates, compared to direct application of Jarzynski's equality, for modest sized data sets (100 work values), in all tested systems. Results from one of the new methods suggest that good estimates of AF can be obtained using 5-40-fold less data than was previously possible. Extending previous work, the new results exploit the systematic behavior of bias due to finite sample size. A key innovation is better use of the more statistically reliable information available from the raw data.

Original languageEnglish (US)
Pages (from-to)1749-1759
Number of pages11
JournalJournal of Computational Chemistry
Issue number14
StatePublished - Nov 15 2004
Externally publishedYes


  • Block averages
  • Extrapolation
  • Free energy
  • Jarzynski relation
  • Non-equilibrium

ASJC Scopus subject areas

  • Chemistry(all)
  • Computational Mathematics


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