W.Quapp, M.Hirsch, D.Heidrich 


An Approach to Reaction Path Branching using
Valley-Ridge-Inflection Points of Potential Energy Surfaces


 Abstract

Valley-ridge-inflection points (VRI) of a potential energy surface
(PES) may have a strong relation to the occurence of bifurcations along
reaction pathways of molecular rearrangements.  
We discuss two different definitions of VRI points in the literature.
The calculation of symmetric VRI points has been alredy reported 
[W.Quapp et al., TCA 100 (1998) 285-299]. Here, we in addition calculate  
special asymmetric VRI points which are placed on gradient extremals (GE).
Following a GE opens the possibility to find the VRI point on it.
An application is presented to search for asymmetric VRI points
near the isomerization valley of the PES of the HCN molecule. 

A new method for GE following is based on a mathematical connection 
between the following of a reduced gradient (RGF) and the calculation of GEs. 
The tangent search method to follow a GE to the smallest eigenvalue
[W.Quapp et al., TCA 105 (2000) 145-155] is extended to
follow also GEs to higher eigenvalues in order to find a VRI point.
The new method needs gradient and second derivatives of the PES only.



2003  Preprint pp.41,  10 Figures