Analysis of the Valley-Ridge Inflection Points through the
Partitioning Technique of the Hessian Eigenvalue Equation.

by
Josep Maria Bofill 1)  and   Wolfgang Quapp 2)

1 Departament de Qu´imica Org'anica, Universitat de Barcelona, 
and:
  Institut de Qu'imica Te'orica i Computacional, Universitat de
  Barcelona, (IQTCUB), Mart'i i Franques, 1, 08028 Barcelona, 
  Spain.

2 Mathematisches Institut, Universit"at Leipzig, PF 100920, 
  D-04009 Leipzig, Germany.

submitted  November 26, 2012

Abstract: 
The Valley-Ridge Inflection (VRI) points are related to the
branching of a reaction valley or reaction channel. These points are a 
special class of points of the Potential Energy Surface (PES). They 
are also special points of the Valley-Ridge borderline of the PES. 
The nature of the VRI points and their differences with respect to the
other points of the Valley-Ridge borderline is analyzed using the
L"owdin's partitioning technique applied to the eigenvalue equation of
the Hessian matrix.
Eigenvalues and eigenvectors of the Hessian are better imaginable than the
former used adjoint matrix.

Keywords: 
Valley-Ridge Inflection Point; Bifurcation of Reaction Path;
L"owdin Partitioning Technique; Potential Energy Surface.