The classical limit is shown to provide a description exactly equivalent to the quantum mechanical one in the approximation where each electron is assigned to an orbital. Strictly speaking it is therefore not a limit but an alternative way of solving the problem. There are some merits of this reformulation, most notably in that it brings the phase of the orbitals to the forefront, on equal footing as the occupancies. This allows one to discuss, e.g., electron localization, in a clearer manner. But computationally the classical description is not superior. There will be a definite advantage for more realistic electronic Hamiltonians, i.e., for implementing configuration interaction, and/or when the nuclear motion is coupled to the electronic dynamics. In this paper we limit attention to a derivation and discussion of the simple orbital approximation.