Molecular dynamics simulation of rare events: Calculation of rate constants

We present a computationally efficient molecular dynamics method based on holonomic constraints devised to estimate the rate constants of rare activated events of short duration.We assume that the process is described by a reaction coordinate $ \xi(r)$, a well-defined function in configuration space, and we constrain the system at the ``bottleneck" region by prescribing the value of $ \xi(r)$. MD trajectories sample now phase space according to a biased configurational distribution and averages can be taken from such a new, {\it Blue Moon }, ensemble with suitable reweighting to study rare events. Applications are not restricted to classical processes and ways to extend the method to quantum activated processes in condensed phases are also outlined.