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Analysis of the Valley-Ridge inflection points through the partitioning technique of the Hessian eigenvalue equation

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Abstract

The Valley-Ridge inflection (VRI) points are related to the branching of a reaction valley or reaction channel. These points are a special class of points of the potential energy surface (PES). They are also special points of the Valley-Ridge borderline of the PES. The nature of the VRI points and their differences with respect to the other points of the Valley-Ridge borderline is analyzed using the Löwdin’s partitioning technique applied to the eigenvalue equation of the Hessian matrix. Eigenvalues and eigenvectors of the Hessian are better imaginable than the former used adjoint matrix.

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Acknowledgments

Financial support from the Spanish Ministerio de Economía y Competitividad, project CTQ2011-22505 and, in part from the Generalitat de Catalunya projects 2009SGR-1472 is fully acknowledged. We are indebted to a referee for a constructive comment.

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Authors and Affiliations

  1. Departament de Química Orgànica, Institut de Química Teòrica i Computacional, Universitat de Barcelona, (IQTCUB), Martí i Franquès, 1, 08028, Barcelona, Spain

    Josep Maria Bofill

  2. Mathematisches Institut, Universität Leipzig, PF 100920, 04009, Leipzig, Germany

    Wolfgang Quapp

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  1. Josep Maria Bofill
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  2. Wolfgang Quapp
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Correspondence to Josep Maria Bofill.

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Bofill, J.M., Quapp, W. Analysis of the Valley-Ridge inflection points through the partitioning technique of the Hessian eigenvalue equation. J Math Chem 51, 1099–1115 (2013). https://doi.org/10.1007/s10910-012-0134-3

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  • DOI: https://doi.org/10.1007/s10910-012-0134-3

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