The first-principles calculation is based on the phonon-assisted charge transfer model. The ionic vibration brings the two electronic states closer whereby the charge carriers hop from one state to another with a transition rate. The charge transport mechanism is phonon-assisted charge transfer between localized electronic states. shown schematically, a carrier (in this case a hole) originally reside at red state; thermal fluctuations of geometry lead to the transition between the overlapping states.
We used this method to predict the hole mobility in disordered small molecules DPP which is donor material in OPV. The predicted logarithm hole mobility as a function of trapping energy and trap density (the trap-free mobility is shown as horizontal line).
Phonon-assisted charge transfer model: Thermal fluctuations of geometry lead to overlap of localized electronic states inducing electronic hopping between the overlapping states.