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

J Chem Theory Comput. 2012 Dec 11;8(12):4856-62. doi: 10.1021/ct300654f. Epub 2012 Sep 4.

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.