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Optimization-Based String Method for Finding Minimum Energy Path

Published online by Cambridge University Press:  03 June 2015

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
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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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

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