Optimization-based string method for finding minimum energy path

Amit Samanta, E. Weinan

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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 languageEnglish (US)
Pages (from-to)265-275
Number of pages11
JournalCommunications in Computational Physics
Issue number2
StatePublished - Aug 2013

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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


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