Here, Ψ 0 is the ground state electronic wave function and Ψ I is the excited current (active) state electronic wave function, ⃗ x collects spatial ⃗ r and spin σ variables of an electron, and N is the number of electrons. We note that the electronic wave functions depend parametrically on the nuclear coordinates R(t) (which, in turn, depend on time in quantum-classical trajectorybased methods), but we do not write explicitly this dependence for the sake of brevity. We also assume the wave functions to be real.