THEORETICAL AND PRACTICAL ASPECTS OF THE CONVERGENCE PROPERTIES OF THE DYNAMICALLY DEFINED REACTION-PATH METHOD

In spite of much work on path-following methods, a solid mathematical foundation (especially convergence conditions and their practical meas ures) are lacking in most cases. In our previous articles the general theory of a new global searching procedure, the dynamically defined re action path (DDRP) method, its rigorous mathematical. formulation, the algorithm, a practical computation program, and some applications to abstract mathematical functions and simple chemical examples have been presented. In this article we give a short theoretical description an d some practical criteria and measures for the convergence of the meth od and illustrate the principles and uses by numerical mathematical an d chemical examples. (C) 1996 by John Wiley & Sons, Inc.