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Title

Applications of analytic and geometry concepts of the theory of Calculus of Variations to the Intrinsic Reaction Coordinate model

AuthorsAguilar-Mogas, Antoni; Crehuet, Ramón CSIC ORCID CVN ; Giménez, Xavier; Bofill, Josep M.
KeywordsReaction path
Intrinsic reaction coordinate
Weierstrass E-function
Hamilton-Jacobi equation
Monge Cone
Valley-Ridge inflection point
Issue Date21-Sep-2007
PublisherTaylor & Francis
CitationMolecular Physics 105(19-22): 2475-2492 (2007)
AbstractA 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.
Description17 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
URIhttp://hdl.handle.net/10261/9657
DOI10.1080/00268970701519762
ISSN1362-3028
Appears in Collections:(IQAC) Artículos

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