where Ĥi and Ĥf represent the vibrational Hamiltonians of the initial and final vibronic states, respectively. If we account for the Boltzmann distribution of the initial-state vibronic manifold at the finite temperature and the molecular energy conservation for the nonradiative transition, i.e. ω = 0, Eq. ( ) becomes the following thermal rate constant form for the transition from the initial to the finial electronic states