Volume 14, Issue 2
Optimization-Based String Method for Finding Minimum Energy Path

Amit Samanta & Weinan E

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

Published online: 2014-08

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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.

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@Article{CiCP-14-265, author = {}, title = {Optimization-Based String Method for Finding Minimum Energy Path}, journal = {Communications in Computational Physics}, year = {2014}, volume = {14}, number = {2}, pages = {265--275}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.220212.030812a}, url = {http://global-sci.org/intro/article_detail/cicp/7159.html} }
TY - JOUR T1 - Optimization-Based String Method for Finding Minimum Energy Path JO - Communications in Computational Physics VL - 2 SP - 265 EP - 275 PY - 2014 DA - 2014/08 SN - 14 DO - http://dor.org/10.4208/cicp.220212.030812a UR - https://global-sci.org/intro/article_detail/cicp/7159.html KW - AB -

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.

Amit Samanta & Weinan E. (2020). Optimization-Based String Method for Finding Minimum Energy Path. Communications in Computational Physics. 14 (2). 265-275. doi:10.4208/cicp.220212.030812a
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