Variational Nature, Integration and Properties of Newton Reaction Path

Josep Maria Bofill,1   Wolfgang Quapp,2

1 Departament de Química Orgànica, Universitat de Barcelona, Martí i Franquès
  1, 08028 Barcelona, 
and Institut de Química Teòrica i Computacional de la Universitat de 
  Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
2 Mathematical Institute, University of Leipzig, Johannisgasse 26, Postfach
  10 09 20, D-04009 Leipzig, Germany

 November 2010

Abstract:  

The Distinguished Coordinate Path and the Reduced Gradient
Following Path or its equivalent formulation, the Newton Trajectory, are
analyzed and unified using the Theory of Calculus of Variations.  It is
shown that their minimum character is related with the fact that the curve 
is located in a valley floor. In this case we say that the Newton Trajectory 
is a reaction path with the category of minimum energy path. 
In addition to these findings a Runge-Kutta-Felhberg algorithm to integrate 
these curves is also proposed.