Pitfall in Free-Energy Simulations on Simplest Systems

Kin-Yiu Wong*, Yuqing Xu, Liang Xu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

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Free-energy simulation (FES) is widely used in science and engineering. Unconstrained FES (UFES, e. g., umbrella sampling with histogram binning) and constrained FES (CFES, e. g., blue-moon sampling with mean-force/thermodynamic integration) are two different types of FES. People prefer UFES to CFES, e. g., people correct constrained free-energy profile (CFEP) to unconstrained FEP (UFEP), not the other way around. But remarkably, herein we show for a 1D free body subject to zero force, from an UFEP we find an infinitely-high energy barrier. By contrast, we find no energy barrier from any CFEP. Besides, by providing in-depth comparisons between UFEP and CFEP from the perspective of Jacobian scale factor, this work may also partially address recent issues on FES: (1) UFEP is preferred, but why do three recent papers conclude we should use CFEP for the transition-state theory and why are these three papers not fully consistent with one another? (2) For relating UFEP to CFEP, why are there two different versions of Fixman term associated with velocity and momentum constraints, respectively? (3) How to normalize CFEP, for which the equation seems to be even unavailable?.

Original languageEnglish
Pages (from-to)4398-4418
Number of pages21
Issue number16
Publication statusPublished - May 2017

Scopus Subject Areas

  • Chemistry(all)

User-Defined Keywords

  • Cartesian coordinate
  • constraint
  • contravariant space
  • covariant space
  • curvilinear coordinate
  • Dirac delta function
  • Fixman term
  • free energy
  • generalized coordinate
  • Jacobian determinant
  • Jacobian scale factor
  • line element
  • Liouville's theorem
  • phase space
  • potential of mean force
  • reaction rate constant
  • rectilinear coordinate
  • transition-state theory
  • volume element


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