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Optimization methods for finding minimum energy paths.

Daniel Sheppard1, Rye Terrell, Graeme Henkelman

  • 1Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712-0165, USA.

The Journal of Chemical Physics
|April 10, 2008
PubMed
Summary
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The nudged elastic band (NEB) and string methods are the most efficient for finding minimum energy pathways (MEPs). Using a climbing-image and descending from the saddle point provides accurate MEPs with fewer images.

Area of Science:

  • Computational Chemistry
  • Materials Science
  • Surface Science

Background:

  • Accurate determination of minimum energy pathways (MEPs) is crucial for understanding chemical reactions and material processes.
  • Various chain-of-states methods exist to approximate MEPs, but their relative efficiency and optimal implementation are not fully established.

Purpose of the Study:

  • To compare the efficiency and accuracy of different chain-of-states methods for finding minimum energy pathways (MEPs).
  • To identify the most effective optimizers and strategies for calculating MEPs in surface science and materials modeling.

Main Methods:

  • Comparison of nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods.
  • Evaluation of various commonly used optimizers, including a globally updated limited-memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.

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  • Application to model systems: heptamer island rearrangements on Pt(111), Pd tetramer diffusion on MgO(100), and oxygen adsorption/diffusion on Au(111).

    • Main Results:

    • NEB and string methods are found to be equivalent and the most efficient for MEP calculation when paired with suitable optimizers.
    • A globally updated limited-memory BFGS optimizer demonstrated superior performance.
    • Employing a climbing-image strategy efficiently locates saddle points using minimal images.
    • For high accuracy, descending from the saddle point is more efficient than using numerous images in chain-of-states methods.

    Conclusions:

    • The NEB and string methods, combined with appropriate optimization techniques, represent the state-of-the-art for calculating minimum energy pathways.
    • Optimized strategies, including climbing-image and direct descent from saddle points, enhance the efficiency and accuracy of MEP calculations in computational materials science.