### 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.

Original language | English (US) |
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Pages (from-to) | 265-275 |

Number of pages | 11 |

Journal | Communications in Computational Physics |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - Aug 2013 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Keywords

- Dislocation nucleation
- Minimum energy path
- Rare events
- String method

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## Cite this

*Communications in Computational Physics*,

*14*(2), 265-275. https://doi.org/10.4208/cicp.220212.030812a