Mathematical Programming

, Volume 100, Issue 1, pp 151–182 | Cite as

Computing mountain passes and transition states

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Abstract.

The mountain-pass theorem guarantees the existence of a critical point on a path that connects two points separated by a sufficiently high barrier. We propose the elastic string algorithm for computing mountain passes in finite-dimensional problems and analyze the convergence properties and numerical performance of this algorithm for benchmark problems in chemistry and discretizations of infinite-dimensional variational problems. We show that any limit point of the elastic string algorithm is a path that crosses a critical point at which the Hessian matrix is not positive definite.

Keywords

Transition State Variational Problem Limit Point Convergence Property Hessian Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneIllinois
  2. 2.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneIllinois

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