On the time-dependent Hartree-Fock equations coupled with a classical nuclear dynamics

We prove a global-in-time existence and uniqueness result for the Cauchy problem in the setting of some model of Molecular Quantum Chemistry. The model we are concerned with consists of a coupling between the time-dependent Hartree-Fock equations (for the electrons) and the classical Newtonian dynamics (for the nuclei). The proof combines semigroup techniques and the Schauder fixed-point theorem. We also extend our result in order to treat the case of a molecule subjected to a time-dependent electric field.