A comparison of chain-of-states based methods for finding minimum energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local minima is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equivalent and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approximate inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based density functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111).
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7 April 2008
Research Article|
April 02 2008
Optimization methods for finding minimum energy paths
Daniel Sheppard;
Daniel Sheppard
Department of Chemistry and Biochemistry,
The University of Texas at Austin
, Austin, Texas 78712-0165, USA
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Rye Terrell;
Rye Terrell
Department of Chemistry and Biochemistry,
The University of Texas at Austin
, Austin, Texas 78712-0165, USA
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Graeme Henkelman
Graeme Henkelman
a)
Department of Chemistry and Biochemistry,
The University of Texas at Austin
, Austin, Texas 78712-0165, USA
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a)
Electronic mail: henkelman@mail.utexas.edu.
J. Chem. Phys. 128, 134106 (2008)
Article history
Received:
October 29 2007
Accepted:
January 18 2008
Citation
Daniel Sheppard, Rye Terrell, Graeme Henkelman; Optimization methods for finding minimum energy paths. J. Chem. Phys. 7 April 2008; 128 (13): 134106. https://doi.org/10.1063/1.2841941
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