Time-dependent density functional theory (TDDFT) is a daily tool for exploring excited states in materials science for its compromise of accuracy and efficiency. It provides information of energies and transition patterns of excited states. TDDFT only provides adiabatic states that can evolve abruptly along nuclear distortion, since the building blocks of the method are the adiabatic Kohn-Sham orbitals. The hole-particle pairs involved in an excitation can be viewed as an image of the wave function of the excited state. With the transition density that is made of such pairs and contains information of hole-particle correlation, we developed a diabatization protocol to decompose the TDDFT excited states into diabatic states that maintain their electronic character regardless of nuclear distortion. This protocol helped characterize intralayer local excitons and interlayer charge-transfer excitons in our recent study of different stackings of silicane (SiH). This protocol also enables construction of diabatic electron-phonon coupling Hamiltonian. With a so-constructed Hamiltonian and using the augmented fewest switch surface hopping (AFSSH) non-adiabatic dynamics, we explored the transition time scale from direct band gap transition to indirect band gap transition of SiH, which is of critical importance in determining the utility of this class of 2D nanomaterials in optoelectronics, as good candidates in light emitting, photovoltaics, or photocatalysis.