In this section, we briefly discuss the mapping-based quantum dynamics approaches used in this work. Details of the standard Ehrenfest dynamics and surface hopping approaches are provided in the Supplemental Information. The common starting point of these mapping dynamics is the Meyer-Miller-Stock-Thoss (MMST) formalism, which maps the discrete quantum DOF (described as discrete states) onto continuous phase space variables. A Hamiltonian in the diabatic representation {|a⟩} is expressed as