JCTC 2012 

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


by  Josep Maria Bofill,  Wolfgang Quapp,  and Marc Caballero

Keywords: 
Steepest ascent, Eikonal equation, Hamilton-Jacobi theory,
Partial differential equation of second order of hyperbolic type: wave equation


Abstract:

The potential energy surface (PES) of a molecule can be decomposed into
equipotential hypersurfaces. 
In this note we show 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.