Adaptive kinetic Monte Carlo for first-principles accelerated dynamics

The adaptive kinetic Monte Carlo method uses minimum-mode following saddle point searches and harmonic transition state theory to model rare-event, state-to-state dynamics in chemical and material systems. The dynamical events can be complex, involve many atoms, and are not constrained to a grid—relaxing many of the limitations of regular kinetic Monte Carlo. By focusing on low energy processes and asserting a minimum probability of finding any saddle, a confidence level is used to describe the completeness of the calculated event table for each state visited. This confidence level provides a dynamic criterion to decide when sufficient saddle point searches have been completed. The method has been made efficient enough to work with forces and energies from density functional theory calculations. Finding saddle points in parallel reduces the simulation time when many computers are available. Even more important is the recycling of calculated reaction mechanisms from previous states along the dynamics. For systems with localized reactions, the work required to update the event table from state to state does not increase with system size. When the reaction barriers are high with respect to the thermal energy, first-principles simulations over long time scales are possible.