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Optimization-Based String Method for Finding Minimum Energy Path

Published online by Cambridge University Press:  03 June 2015

Amit Samanta  and
Weinan E
Amit Samanta*
Affiliation:
Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA
Weinan E*
Affiliation:
Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA Beijing International Center for Mathematical Research, Peking University, Beijing, China
*
Corresponding author.Email:[email protected]
Email:[email protected]
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Abstract

We present an efficient algorithm for calculating the minimum energy path (MEP) and energy barriers between local minima on a multidimensional potential energy surface (PES). Such paths play a central role in the understanding of transition pathways between metastable states. Our method relies on the original formulation of the string method [Phys. Rev. B, 66,052301 (2002)], i.e. to evolve a smooth curve along a direction normal to the curve. The algorithm works by performing minimization steps on hyperplanes normal to the curve. Therefore the problem of finding MEP on the PES is remodeled as a set of constrained minimization problems. This provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method [J. Chem. Phys., 126(16), 164103 (2007)]. At the same time, it provides a more direct analog of the finite temperature string method. The applicability of the algorithm is demonstrated using various examples.

Keywords

37C10Rare eventsstring methodminimum energy pathdislocation nucleation
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 2 , August 2013 , pp. 265 - 275
Copyright
Copyright © Global Science Press Limited 2013

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