Commun. Comput. Phys., 14 (2013), pp. 265-275.


Optimization-Based String Method for Finding Minimum Energy Path

Amit Samanta 1*, Weinan E 2

1 Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA.
2 Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA; and Beijing International Center for Mathematical Research, Peking University, Beijing, China.

Received 22 February 2012; Accepted (in revised version) 3 August 2012
Available online 27 November 2012
doi:10.4208/cicp.220212.030812a

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.

AMS subject classifications: 37C10

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Key words: Rare events, string method, minimum energy path, dislocation nucleation.

*Corresponding author.
Email: asamanta@math.princeton.edu (A. Samanta), weinan@math.princeton.edu (W. E)
 

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