Abstract
A new approach is proposed for enclosing all stationary states, including saddle points of all orders, of a potential energy surface based on the \aBB\ deterministic branch and bound global optimization algorithm. This method is based on rigorous optimization methods and offers a theoretical guarentee of enclosing all solutions to the equation \grad V=0. This method is applied to the ECEPP/3 (Empirical Conformational Energy Program for Peptides) potential energy surfaces of unsolvated and solvated tetra-alanine. By analyzing the topography of the potential energy surfaces, we calculate reaction pathways, transition rate matrices, time-evolution of occupation probabilities, and rate disconnectivity graphs, and we identify appropriate criteria for the selection of a reaction coordinate.
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