The Reaction Pathway of a Potential Energy Surface
 as Curve with Induced Tangent

by
  MICHAEL HIRSCH &  WOLFGANG QUAPP 

 Mathematical Institute,  University of Leipzig,
 Augustus-Platz, D-04109 Leipzig,  Germany


abstract:
The reaction path is an important concept of theoretical chemistry. 
 We employ the definitions of the Newton trajectory (NT) and of the
 gradient extremal (GE).
 An NT follows a curve where the gradient is always a pointer to a fixed
 direction. A GE is a curve where the gradient of the potential energy 
 surfaces (PES) is  eigenvector of the Hessian.
 Examples are given with the M"uller-Brown potential  
 and further model PESs.
 An induced tangent opens the possibility to follow the curve by a
 predictor-corrector method.
 We show that the two kinds of curves can be treated as curves with
 induced tangent, however, the gradient descent, or intrinsic reaction
 coordinate (IRC) not.