Applications of analytic and geometry concepts of the theory of Calculus of Variations to the Intrinsic Reaction Coordinate model
| Autor: | Xavier Giménez, Josep Maria Bofill, Ramon Crehuet, Antoni Aguilar-Mogas |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Differential equation
MathematicsofComputing_GENERAL Intrinsic reaction coordinate Biophysics Weierstrass E-function ComputingMilieux_LEGALASPECTSOFCOMPUTING Data_CODINGANDINFORMATIONTHEORY Reaction path String (physics) Hamilton–Jacobi equation GeneralLiterature_MISCELLANEOUS Monge cone Quantum mechanics Applied mathematics Physical and Theoretical Chemistry Molecular Biology Mathematics Hamilton-Jacobi equation Condensed Matter Physics ComputingMilieux_GENERAL Inflection point Path (graph theory) Valley-Ridge inflection point Calculus of variations Minification Monge Cone |
| Zdroj: | Digital.CSIC. Repositorio Institucional del CSIC instname |
| ISSN: | 1362-3028 0026-8976 |
| DOI: | 10.1080/00268970701519762 |
| Popis: | 17 pages, 6 figures.-- Dedicated in honor of Professor Peter Pulay on his 65th birthday. Printed version published Oct 2007. 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. Financial support from the Spanish Ministerio de Ciencia y Tecnología, DGI project CTQ2005-01117/ BQU and, in part from the Generalitat de Catalunya projects 2005SGR-00111 and 2005SGR-00175 is fully acknowledged. Ramon Crehuet gratefully acknowledges the Ramón y Cajal Program. Antoni Aguilar-Mogas gratefully thanks Ministerio de Ciencia y Tecnología for a predoctoral fellowship. |
| Databáze: | OpenAIRE |
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