Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events

I derive a general method for accelerating the molecular-dynamics (MD) simulation of infrequent events in solids. A bias potential ( $\ensuremath{\Delta}{V}_{b}$) raises the energy in regions other than the transition states between potential basins. Transitions occur at an accelerated rate and the elapsed time becomes a statistical property of the system. $\ensuremath{\Delta}{V}_{b}$ can be constructed without knowing the location of the transition states and implementation requires only first derivatives. I examine the diffusion mechanisms of a 10-atom Ag cluster on the Ag(111) surface using a $220\ensuremath{\mu}\mathrm{s}$ hyper-MD simulation.