Locating All Transition States and Studying the Reaction Pathways of Potential Energy Surfaces

We propose a new method for calculating all stationary states, including saddle points of all orders, of a potential energy surface based on the BB deterministic branch and bound global optimization algorithm. This method is based on rigorous optimization methods and ooers a theoretical guarentee of enclosing all solutions to the equation rV = 0. We apply this method to Murrel-Sorbie analytic potential energy surfaces of HCN, HSiN, HBO, and CS 2 , and to the ECEPP/3 (Empirical Conformational Energy Program for Peptides) potential energy surfaces of alanine, alanine dipeptide, and tetra-alanine. For alanine, ala-nine dipeptide, and tetra-alanine, we proceed to analyze the topography of the potential energy surface by calculating reaction pathways, transition rate matrices, time-evolution of occupation probabilities, and rate disconnectivity graphs.