Ab initiomolecular dynamics on the electronic Boltzmann equilibrium distribution

We prove that for a combined system of classical and quantum particles, it is possible to describe a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem.In addition, these molecular dynamics (MD) do not need to assume that the electrons immediately follow the nuclear motion (in contrast to any adiabatic approach) and do not present problems in the presence of crossing points between different potential energy surfaces (conical intersections or spin-crossings).A practical application of this MD to the study of the effect of temperature on molecular systems presenting (nearly) degenerate states-such as the avoided crossing in the ring-closure process of ozone-is presented.