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On the analytical representation of free energy profiles with a Morse/long-range model: Application to the water dimer

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10.1063/1.4810006

### Abstract

We investigate the analytical representation of potentials of mean force (pmf) using the Morse/long-range (MLR) potential approach. The MLR method had previously been used to represent potential energy surfaces, and we assess its validity for representing free-energies. The advantage of the approach is that the potential of mean force data only needs to be calculated in the short to medium range region of the reaction coordinate while the long range can be handled analytically. This can result in significant savings in terms of computational effort since one does not need to cover the whole range of the reaction coordinate during simulations. The water dimer with rigid monomers whose interactions are described by the commonly used TIP4P model [W. Jorgensen and J. Madura, Mol. Phys.56, 1381 (Year: 1985)]10.1080/00268978500103111 is used as a test case. We first calculate an “exact” pmf using direct Monte Carlo (MC) integration and term such a calculation as our gold standard (GS). Second, we compare this GS with several MLR fits to the GS to test the validity of the fitting procedure. We then obtain the water dimer pmf using metadynamics simulations in a limited range of the reaction coordinate and show how the MLR treatment allows the accurate generation of the full pmf. We finally calculate the transition state theory rate constant for the water dimer dissociation process using the GS, the GS MLR fits, and the metadynamics MLR fits. Our approach can yield a compact, smooth, and accurate analytical representation of pmf data with reduced computational cost.

© 2013 AIP Publishing LLC

Received 01 November 2012
Accepted 28 May 2013
Published online 18 June 2013

Acknowledgments: We thank Dr. Alexander Brown and Fred McCourt for useful discussions. Y.T.M. thanks Lisa Verge, Mary McPherson, Ph.D. (candidate) Andrea Prier, and Erica McKellar for all their helpful suggestions while preparing this manuscript. This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Foundation for Innovation (CFI). T.Z. thanks NSERC (PDF-403739-2011) and the Ministry of Research and Innovation of Ontario for postdoctoral fellowships.

Article outline:

I. INTRODUCTION

II. THEORY AND METHODS

A. Generating potential of mean force data

B. Analytical representation of the potential of mean force: The Morse/long-range form

1. The coefficient of the leading long-range term in the *u* _{LR} function: *C* _{6}

C. Variational transition state theory and the reaction rate

III. RESULTS AND DISCUSSION

A. Fitting the direct integration pmf to the MLR form

B. Fitting the pmf from metadynamics to the MLR form

C. Obtaining the variational rate constant k_{VTST}

IV. CONCLUDING REMARKS

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2013-06-18

2014-04-18

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