The necessary ingredients for FSSH are (i) the adiabatic energy surfaces V J and the nuclear forces -∂V J /∂R α (as calculated at the instantaneous nuclear coordinate R α (t)), and (ii) the time-derivative matrix T (as constructed from the adiabatic eigenstates of the current and previous time step). While the on-the-fly calculation of the nuclear forces using electronic structure packages is usually the most computationally intensive step and propagating the electronic wavefunction is relatively fast and cheap, constructing the T matrix can also impose expensive overhead on top of the on-the-fly electronic structure calculation, especially for a large number of electronic states. Note that, within any semiclassical scheme, one would like to propagate the classical nuclear coordinates using Eq. ( ) using a larger time-step and integrate the electronic Schrodinger equation (Eq. ( )) with a smaller time step. Such a separation of time steps is essential for large-scale, multidimensional simulations, which makes it essential that the T-matrix be calculated as accurately as possible (and that one use the T-matrix as effectively as possible).