where ω is the average energy of the vibration-less level, ∆ 2 j is the dimensionless displacement of the j th normal mode, and η is a complex "correction" factor . This more generalised treatment, however, was limited to the weak coupling regime. The strong coupling limit was speculated to be treatable outside of the Condon approximation provided that the system is limited to a single oscillator model. For the non-Condon formalism, it was observed that for systems which could mimic the qualities of larger systems, decay would be underestimated by up to 3 orders of magnitude . Using Siebrand's reevaluation (Equation ), Kowaka and co-workers found very fast lifetimes, corresponding to ∼5×10 6 s -1 , for all transitions from the 1 B 3u state of pyrene, due to strong vibronic coupling with the higher 1 B 2u state. They also reported a 1 B 3u ← 1 B 2u rate of ∼2×10 9 s -1 .