A Stability Boundary Based Method for Finding Saddle Points on Potential Energy Surfaces

The task of finding saddle points on potential energy surfaces plays a crucial role in understanding the dynamics of a micromolecule as well as in studying the folding pathways of macromolecules like proteins. The problem of finding the saddle points on a high dimensional potential energy surface is transformed into the problem of finding decomposition points of its corresponding nonlinear dynamical system. This paper introduces a new method based on TRUST-TECH (TRansformation Under STability reTained Equilibria CHaracterization) to compute saddle points on potential energy surfaces using stability boundaries. Our method explores the dynamic and geometric characteristics of stability boundaries of a nonlinear dynamical system. A novel trajectory adjustment procedure is used to trace the stability boundary. Our method was successful in finding the saddle points on different potential energy surfaces of various dimensions. A simplified version of the algorithm has also been used to find the saddle points of symmetric systems with the help of some analytical knowledge. The main advantages and effectiveness of the method are clearly illustrated with some examples. Promising results of our method are shown on various problems with varied degrees of freedom.