The variational Structure of Gradient Extremals

by

JOSEP MARIA BOFILL and WOLFGANG QUAPP and MARC CABALLERO


Abstract: 

The gradient extremals can be taken as a representation of reaction
paths. We prove that this type of curves possesses a variational nature. We
report the conditions such that these curves have the character of a minimal
curve. Finally we discuss the relations between the points of these curves
being turning points with respect to other special points of the potential
energy surface like the valley-ridged inflection points.

Keywords: Gradient Extremals, Reaction Path, Calculus of Variations,
Valley-Ridged Inflection Points, Euler-Lagrange Equation.


submitted to:  JCTC,  Nov 2011