Communications: Ab initio dynamics of rare thermally activated reactions.

We introduce a framework to investigate ab initio the dynamics of rare thermally activated reactions, which cannot be studied using the existing techniques. The electronic degrees of freedom are described at the quantum-mechanical level in the Born-Oppenheimer approximation, while the nuclear degrees of freedom are coupled to a thermal bath, through a classical Langevin equation. This method is based on the path integral representation for the stochastic dynamics and yields the time evolution of both nuclear and electronic degrees of freedom, along the most probable reaction pathways, without spending computational time to explore metastable states. As a first illustrative application, we characterize the dominant pathway in the cyclobutene-->butadiene reaction, using the semiempirical Parametrized Model 3 (PM3) approach.