In practice, however, the computational cost of both IESH and FSSH-ER is very demanding and is determined by how efficiently one can (i) calculate the adiabatic potential energy surfaces and nuclear forces for each time step on the fly (Eq. ( )) and then (ii) propagate an electronic wavefunction spanning many, many excited states (Eq. ( )). While the bulk of the time is usually spent on the former (i.e. on the electronic structure calculations), the latter can also add a non-trivial increase to the cost of semiclassical simulations-especially because propagating the latter can dictate the maximum time step allowed in the former.