TY - JOUR

T1 - Pitfall in Free-Energy Simulations on Simplest Systems

AU - Wong, Kin-Yiu

AU - Xu, Yuqing

AU - Xu, Liang

N1 - Funding Information:
We thank Prof. Wei Yang for his strong encouragement to K.-Y. Wong, and for his enlightening discussion when we were writing an initial draft of this paper. We also thank Reviewers for their fruitful comments. 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).

PY - 2017/5

Y1 - 2017/5

N2 - 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?.

AB - 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?.

KW - Cartesian coordinate

KW - constraint

KW - contravariant space

KW - covariant space

KW - curvilinear coordinate

KW - Dirac delta function

KW - Fixman term

KW - free energy

KW - generalized coordinate

KW - Jacobian determinant

KW - Jacobian scale factor

KW - line element

KW - Liouville's theorem

KW - phase space

KW - potential of mean force

KW - reaction rate constant

KW - rectilinear coordinate

KW - transition-state theory

KW - volume element

UR - http://www.scopus.com/inward/record.url?scp=85041509740&partnerID=8YFLogxK

U2 - 10.1002/slct.201601160

DO - 10.1002/slct.201601160

M3 - Journal article

AN - SCOPUS:85041509740

SN - 2365-6549

VL - 2

SP - 4398

EP - 4418

JO - ChemistrySelect

JF - ChemistrySelect

IS - 16

ER -