Department of Physics
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?
Cartesian coordinate, constraint, contravariant space, covariant space, curvilinear coordinate, Dirac delta function, Fixman term, free energy, generalized coordinate, Jacobian determinant, Jacobian scale factor, Liouville's theorem, line element;phase space, potential of mean force, reaction rate constant, rectilinear coordinate, transition-state theory, volume element
Source Publication Title
This is the peer reviewed version of the following article: K.-Y. Wong, Y. Xu, L. Xu, ChemistrySelect 2017, 2, 4398., which has been published in final form at http://dx.doi.org/10.1002/slct.201601160. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
This work has been supported in part to K.-Y. Wong by HK RGC (ECS-209813, GRF-12311416), NSF of China (NSFC-21303151, NSFC-21673199), HKBU FRG (FRG2/ 13-14/075, FRG2/15-16/037, FRG1/14-15/037, FRG1/15-16/015), and startup funds (38-40-088). Computing resources were partly provided by HKBU High Performance Cluster Computing Centre (for sciblade; supported by HK RGC) and Office of Information Technology (for jiraiya).
Link to Publisher's Edition
WONG, K., Xu, Y., & Xu, L. (2017). Pitfall in Free-Energy Simulations on Simplest Systems. ChemistrySelect, 2 (16), 4398-4418. https://doi.org/10.1002/slct.201601160
Additional FilesMathematical pitfall could force researchers to revisit chemical simulations.mp4 (6055 kB)