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 αBB deterministic branch and bound global optimization algorithm. This method is based on rigorous optimization methods and offers a theoretical guarantee of enclosing all solutions to the equation ∇V=0. We apply this method to Murrel–Sorbie analytic potential energy surfaces of HCN, HSiN, HBO, and CS2, and to the Empirical Conformational Energy Program for Peptides (ECEPP/3) potential energy surfaces of alanine, alanine dipeptide, and tetra-alanine. For alanine, alanine 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.