Bifurcation of reaction pathways: the set of valley ridge inflection points
of a simple three-dimensional potential energy surface

Wolfgang Quapp (1), Michael Hirsch (1), Dietmar Heidrich (2)

(1) Mathematisches Institut, Universität Leipzig, Augustus-Platz, D-04109
    Leipzig, Germany
(2) Institut für Physikalische und Theoretische Chemie, Universität Leipzig,
    Augustus-Platz, D-04109 Leipzig, Germany

Abstract.
This paper serves for the better understanding of the branching
phenomenon of reaction paths of potential energy hypersurfaces in more than
two dimensions. We apply the recently proposed reduced gradient following  
(RGF) method for the analysis of potential energy hypersurfaces having   
valley-ridge inflection (VRI) points. VRI points indicate the region of
possible reaction path bifurcation. The relation between RGF and the   
so-called global Newton search for stationary points (Branin method) is
shown. Using a 3D polynomial test surface, a whole 1D manifold of VRI points
is obtained. Its relation to RGF curves, steepest descent and gradient
extremals is discussed as well as the relation of the VRI manifold to 
bifurcation points of these curves.


Key words:
Three-dimensional potential energy surface ·
Reaction path bifurcation · Valley-ridge inflection ·
Reduced gradient following · Gradient extremal