Within the non-adiabatic molecular dynamics terminology, 𝑀 𝑖,𝑗 is the leading term of the non-adiabatic coupling between states |𝑖⟩ and |𝑗⟩. In Eq. 7, we consider real coefficients of the electronic states without any loss of generality. Therefore, within the Fermi golden rule formalism, the incoherent hopping rate between vibronic states |𝑖⟩ and |𝑗⟩ is given by, 2