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

Josep Maria Bofill , Antoni Aguilar-Mogas (1) , Xavier Giménez (1) , Ramon Crehuet (2)

1 UB - Universitat de Barcelona
2 Institut de Investigacions Químiques i Ambientals de Barcelona

A mathematical analysis of several algorithms, for the integration of the differential equation associated to the Intrinsic Reaction Coordinate path, is performed. This analysis starts showing 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 as well 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 analyze an Intrinsic Reaction Coordinate path possessing a valley ridge inflection point.

Mots clés: Physical Sciences

Josep Maria Bofill, Antoni Aguilar-Mogas, Xavier Giménez, Ramon Crehuet. (SI) Applications of analytic and geometry concepts of the theory of Calculus of Variations to the Intrinsic Reaction Coordinate model. Molecular Physics, 2008, 105 (19-22), pp.2475-2492. ⟨10.1080/00268970701519762⟩. ⟨hal-00513124⟩