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Title: | Applications of analytic and geometry concepts of the theory of Calculus of Variations to the Intrinsic Reaction Coordinate model |
Authors: | Aguilar-Mogas, Antoni; Crehuet, Ramón CSIC ORCID CVN ; Giménez, Xavier; Bofill, Josep M. | Keywords: | Reaction path Intrinsic reaction coordinate Weierstrass E-function Hamilton-Jacobi equation Monge Cone Valley-Ridge inflection point |
Issue Date: | 21-Sep-2007 | Publisher: | Taylor & Francis | Citation: | Molecular Physics 105(19-22): 2475-2492 (2007) | Abstract: | A mathematical analysis of several algorithms, for the integration of the differential equation associated to the Intrinsic Reaction Coordinate path, is performed. This analysis first shows that the Intrinsic Reaction Coordinate path can be derived from a variational problem, so that it has the properties of an extremal curve. Then, one may borrow the mathematical methods for the integration of extremal curves, to formulate new algorithms for the integration of the Intrinsic Reaction Coordinate path. One may use also this theoretical framework, to recast recently formulated algorithms based on direct minimization of an arbitrary curve, such as the Nudged Elastic Band Method or String Method. In this view a new algorithm is proposed. Finally, the theory of broken extremals is used to analyse an Intrinsic Reaction Coordinate path possessing a valley ridge inflection point. | Description: | 17 pages, 6 figures.-- Dedicated in honor of Professor Peter Pulay on his 65th birthday. Printed version published Oct 2007. |
Publisher version (URL): | http://dx.doi.org/10.1080/00268970701519762 | URI: | http://hdl.handle.net/10261/9657 | DOI: | 10.1080/00268970701519762 | ISSN: | 1362-3028 |
Appears in Collections: | (IQAC) Artículos |
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