The classical time step t  can be divided into s m substeps, and eq (5) is integrated with a timestep / s tm   =  much smaller than the classical step of eq (1). Several algorithms are available in Newton-X for this integration, and we use the Butcher algorithm by default. Energies, nuclear velocities, and couplings are computed only at the classical steps. For the integration of eq (5), the values of these quantities in each substep are obtained by interpolating between classical steps. Instead of directly integrating eq (5), the coefficients c can also be obtained via local diabatization, as discussed in Section 3.4.