where the acti v e state is selected stochastically at every time step of dynamics according to the fewest-switches procedure of standard TSH. If during the propagation the active state changes between two time-steps, then the trajectory hops to the new active state, experiencing a change in potential energy which is accompanied by a change in kinetic energy to ensure the classical energy is conserved along the trajectory. Despite the coupled-trajectory nature of CTTSH, energy conservation is imposed at the level of the single trajectory, as done in standard TSH. In the case of a possible hop towards an electronic state higher in (potential) energy, the kinetic energy is expected to decrease. However, if a trajectory does not have sufficient kinetic energy to offset the extra potential energy gained during the hop, the hop is frustrated and does not take place. Note that in TSH, the electronic evolution equation is identical as the one in Ehrenfest, thus it is given by the first two terms of Eq. ( ).