Here Ĥ0 is the nuclear Hamiltonian in the electronic ground state 0, ĤI is the Hamiltonian governing the initial excitation and nonadiabatic dynamic in the lower-lying excited states, ĤII is the Hamiltonian describing vibronic dynamics in higher-lying states, while Ĥ0I and its Hermite conjugated ĤI0 describe the NACs. The molecular electronic states fall into three manifolds 0, I and II according to their energies: I consists of the excited states interrogated via the pump pulse from the electronic ground state as well as of those states which are nonadiabatically coupled to them, while II includes the excited states accessible to the probe pulse from I.