where Ĥe is the electronic Hamiltonian made up of one-and two-body electronic operators, Ψ e is the antisymmetric many-body electronic wave function (parametrically dependent on the nuclear coordinates), and ⃗ x ≡ {r i , σ i } represents the collective spin and spatial coordinates of all the electrons in the system. In the present case we employ stationary nuclei, which is common for simulations of electronic processes on the femtosecond timescale.