We introduce a framework to investigate ab-initio the dynamics of rare
thermally activated reactions. 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
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. This approach
is very efficient and allows to study thermally activated reactions which
cannot be simulated using ab-initio molecular dynamics techniques. As a first
illustrative application, we characterize the dominant pathway in the
cyclobutene to butadiene reaction.Comment: 4 pages, 4 figure