Fig. 1. (Color online) A schematic energy diagram of the phonon degree of freedom at the initial electronic state and final electronic state .

Fig. 2. (Color online) The comparison of transition rates calculated using different formulas for the nonradiative transition of electron from the conduction band of bulk GaP to the Zn_Ga + O_P point defect. Marcus theory, quantum CT rate, 1D by Alkauskas's code, and 1D by our code, are all one dimensional models. They all give very similar results. Compared with experiment, the multiphonon static coupling formula gives the best results, while the adiabatic coupling results are almost two order of magnitudes smaller. In (a), the calculations are done using the as the perturbation starting point, while in (b), is used as the starting point. As one can see, the results of these two treatments are similar for the multiphonon formula of static coupling and adiabatic coupling. On the other hand, for all the 1D formula, the results are very different. The details of the calculations are described in Ref. [31]. The images are taken from Ref. [16] with permission.

Fig. 3. (Color online) The nonradiative electron transition rates for a hole from the valence band edge to a Zn_Ga+V_N complex defect state in GaN. The high temperature formula result is compared with direct t integration formula. When the temperature is smaller than 300 K, the high temperature formula under estimates the transition rate.