We prove a global-in-time existence and uniqueness result for the Cauchy pr
oblem in the setting of some model of Molecular Quantum Chemistry. The mode
l we are concerned with consists of a coupling between the time-dependent H
artree-Fock equations (for the electrons) and the classical Newtonian dynam
ics (for the nuclei). The proof combines semigroup techniques and the Schau
der fixed-point theorem. We also extend our result in order to treat the ca
se of a molecule subjected to a time-dependent electric field.