Parametrizations and Modifications for the String Method

Abstract

The transition pathways between two metastable states of a physical system and the energy barrier associated with these transitions is of great interest in the natural sciences. Mathematically, these metastable states are local minima of some potential energy surface, and the most probable transition paths between these states are minimum energy paths (MEPs). Finding the saddle points of the potential energy surface allows the calculation of the reaction rates.

The String Method was developed to fi nd MEPs between two given local minima. The Climbing String Method was used to find a saddle point directly connected to a local minimum. In this thesis, the diff erent parametrizations for these methods will be analyzed and compared. Moreover, an alternative method - the Climbing MEP is proposed for the second problem. By forcing the string to climb along an MEP, it will de nitely converge to a saddle point.