where states, which is an ideal property for SH dynamics as revealed in our recent work of detailed complementary consistency. In addition, SC-CTSH scales linearly with the number of trajectories, thus also significantly increasing the simulation efficiency. Note that a timely and systematic benchmark of many mixed quantum-classical dynamics methods has been carried out recently. The present study offers novel perspectives for further developing theoretical methods based on XF and SH. Table . Summary of the investigated methods and their main features. The first column is the method. The second column shows the PES used to calculate the nuclear force, either the TDPES or the BO potential energy surface (BOPES) of the active state. The third column gives the equations to evolve the electronic coefficients (see Eqs. ( ), (10), (22), and ( )). The fourth column lists the method to calculate the populations.