title: A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.
abstract: The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.
authors.affiliation: Departament de Química Orgànica, Universitat de Barcelona, Martí i Franquès, 1, 08028 Barcelona, Spain.|Institut de Química Teòrica i Computacional, Universitat de Barcelona (IQTCUB), Martí i Franquès, 1, 08028 Barcelona, Spain.
authors.forename: Josep Maria
authors.initials: JM
authors.lastname: Bofill
authors.affiliation: Mathematisches Institut, Universität Leipzig, PF 100920, D-04009 Leipzig, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Quapp
authors.affiliation: Institut de Química Teòrica i Computacional, Universitat de Barcelona (IQTCUB), Martí i Franquès, 1, 08028 Barcelona, Spain.|Departament de Química Física, Universitat de Barcelona, Martí i Franquès, 1, 08028 Barcelona, Spain.
authors.forename: Marc
authors.initials: M
authors.lastname: Caballero