Reaction Pathways and Convexity of the Potential Energy
Surface:  Application of Newton Trajectories} 

by
 MICHAEL HIRSCH &  WOLFGANG QUAPP 

 Mathematical Institute,  University of Leipzig, 
 Augustus-Platz,  D-04109 Leipzig,  Germany
  
J Math Chem, Vol 36 No 4 (2004) 307-340 

abstract:
The reaction path is an important concept of theoretical chemistry. 
We employ the definitions of the intrinsic reaction 
coordinate (IRC), the gradient extremal (GE), and the Newton trajectory
(NT).
The usual imagination in chemistry is that a minimum energy path is
in a convex region of the potential energy surface. 
We describe different schemes of convexity to handle the situation. 
It comes out that NTs are the best ansatz for the problem:
NTs, which monotonically increase (or monotonically decrease), 
are automatically strictly pseudo-convex throughout, and 
they go throughout along a valley between minimum and saddle point.