where N S l (t) is the number of trajectories on state S l at time t (see Ref. for a detailed discussion on how to estimate electronic populations with CT-TSH). The cis and trans probabilities of Eqs. ( ) and ( ) as functions of time can be simply estimated by counting the number of trajectories with |ϕ α (t)| < π 2 (for cis) or |ϕ α (t)| > π 2 (for trans), irrespective of the values of q α (t) and of {x α j (t)}. Finally, since the observables of interest can be expressed as functions of classical phase space variables for each trajectory, i.e., O α (t) = O(P α ϕ (t), P α q (t), ϕ α (t), q α (t), {p α j (t)}, {x α j (t)}), the expression corresponding to Eq. ( ) in the quantum-classical case is a simple average over the trajectories