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 -