Can We Understand the Branching of Reaction Valleys for more than two Degrees of Freedom?

by
Wolfgang Quapp

submitted for J. Math. Chem. 2015


Mathematisches Institut, Universit"at Leipzig, Augustus-Platz, D-04109 Leipzig, Germany

keywords
Valley-ridge-inflection point, VRI manifold,  Potential energy surface, Newton trajectory

Abstract
The model of the chemical reaction path is fundamental in Chemistry.
We usually understand it as the pathway along a valley of the 
potential energy surface (PES). However, often a valley bifurcation occurs.
This is controlled by a valley-ridge-inflection point (VRI).
Up to now, 2-dimensional (2D) figures of a PES govern our understanding.  
But for more degrees of freedom, this might be misleading.
Here, we explain the matter over a 3D configuration space; the PES is then 
a 3D hypersurface in an R^4. In this case a visualization is possible.
We still can project curves on the PES down into the R^3 of the configuration space.
A method for the calculation of Newton trajectories (NT) is applied, 
because NTs bifurcate at VRI points.
The example used is a simple mathematical test function. 
It ends with a threefold combination manifold of three 1D VRI lines.