Title:  REDUCED GRADIENT METHODS AND THEIR RELATION TO REACTION PATHS

DOI No: 10.1142/S0219633603000604
Source: Journal of Theoretical and Computational Chemistry, 
        Vol. 2, No. 3  (2003) 385-417
Copyright: World Scientific Publishing Company

Author:    WOLFGANG QUAPP
Telephone: [49] {0}341-97 32153 
fax:       [49] {0}341-97 32199
http://www.mathematik.uni-leipzig.de/MI/quapp/

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

History: Received 27 December 2002
Accepted 14 April 2003

Abstract: The reaction path is an important concept in theoretical
chemistry. We discuss different definitions, their merits as well as their
drawbacks: IRC (steepest descent from saddle), reduced gradient following
(RGF), gradient extremals, and some others. Many properties and problems are
explained by two-dimensional figures. This paper is both a review and a
pointer to future research. The branching points of RGF curves are
valley-ridge inflection (VRI) points of the potential energy surface. These
points may serve as indicators for bifurcations of the reaction path. The
VRI points are calculated with the help of Branin's method. All the
important features of the potential energy surface are independent of the
coordinate system. Besides the theoretical definitions, we also discuss the
numerical use of the methods.

Keywords: Potential energy surface; reaction path following; minimum and
saddle point; projected gradient; gradient extremal; valley-ridge inflection
point; reaction path bifurcation; Branin method; turning point

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