Let ρ(t) = |Ψ(t)⟩ ⟨Ψ(t)| be the density operator of the pure molecular state |Ψ(t)⟩ and introduce |R⟩ , {|φ n ; R⟩} n=1,...,N , i.e., the eigenstates of the nuclear position and of the electronic Hamiltonian, respectively. Even though we employ adiabatic states in the following, our discussion is independent of that choice. Furthermore, note that from the outset we restrict the number N of adiabatic states to be discrete and finite. This implies that we are employing the group Born-Oppenheimer approximation, which may be made rigorous by fixing the energy range available to the molecule and constructing an effective Hamiltonian that approximates well the exact Hamiltonian within this range. The electronic density operator at the nuclear position R, ρel (R, t) = ⟨R| ρ(t) |R⟩, can be written as ρel (R, t)