Navigating the Energy Landscape: Pathways and Rates

David Wales
University of Cambridge
Department of Chemistry

Stationary points of the potential energy surface provide a natural way to coarse-grain calculations of thermodynamics and kinetics, as well as a framework for basin-hopping global optimization. Thermodynamic properties can be obtained from samples of local minima, and kinetic information can be extracted if the samples are extended to include transition states. Using statistical rate theory a minimum-to-minimum rate constant can be associated with each transition state, and phenomenological rates between sets of local minima that define thermodynamic states of interest can be calculated using master equation or kinetic Monte Carlo methods. Since the number of stationary points grows exponentially with system size a sampling scheme is required to produce representative pathways. The discrete path sampling (DPS) approach provides a systematic way to achieve this objective once a single connected path between products and reactants has been located. In large systems such paths may involve dozens of stationary points of the potential energy surface. New algorithms have been developed for both geometry optimization and making connections between distant local minima, which have enabled rates to be calculated for a wide variety of systems, including biomolecules.

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