Quadratic string method for determining the minimum-energy path based on multiobjective optimization

Based on a multiobjective optimization framework, we develop a new quadratic string method for finding the minimum-energy path. In the method, each point on the minimum-energy path is minimized by integration in the descent direction perpendicular to path. Each local integration is done on a quadrat...

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Bibliographic Details
Published in:The Journal of chemical physics 2006-02, Vol.124 (5), p.054109-054109-13
Main Authors: Burger, Steven K., Yang, Weitao
Format: Article
Language:English
Subjects:
Acetaldehyde - chemistry
Alcohols - chemistry
Algorithms
Chemistry, Physical - methods
Models, Chemical
Models, Statistical
Software
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Summary:Based on a multiobjective optimization framework, we develop a new quadratic string method for finding the minimum-energy path. In the method, each point on the minimum-energy path is minimized by integration in the descent direction perpendicular to path. Each local integration is done on a quadratic surface approximated by a damped Broyden-Fletcher-Goldfarb-Shanno updated Hessian, allowing the algorithm to take many steps between energy and gradient calls. The integration is performed with an adaptive step-size solver, which is restricted in length to the trust radius of the approximate Hessian. The full algorithm is shown to be capable of practical superlinear convergence, in contrast to the linear convergence of other methods. The method also eliminates the need for predetermining such parameters as step size and spring constants, and is applicable to reactions with multiple barriers. The effectiveness of this method is demonstrated for the Müller-Brown potential, a seven-atom Lennard-Jones cluster, and the enolation of acetaldehyde to vinyl alcohol.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.2163875