As an illustrative study of the combination of the TDQT approach with exact factorization for nonadiabatic dynamics using the TDPES (7), we simulate the well-known Tully models. These are one-dimensional models in nuclear space (as are those discussed in Section 3.1), and include two coupled electronic states: Tully model 1 presents a singled avoided crossing between the potential energy curves; Tully model 2 is a dual avoided crossing model; Tully model 3 shows an extended coupling region and manifests possible reflections of the incoming wavepacket. In this work we use the original models, whose electronic Hamiltonian Ĥel is given in the diabatic basis representation.