A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

J Chem Theory Comput

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

Published: December 2012

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.

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http://dx.doi.org/10.1021/ct300654fDOI Listing

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