where C p is the pre-exponential factor. Using Equation 31, Andersson and co-workers[199] modelled the S 1 → S 0 internal conversion pathway for a series of carotenes. As a function of E mn , they reported negative exponential gradients of 1.315 cm -1 s -1 and 0.940 cm -1 s -1 solvated in nhexane toluene and 3-methylpentane, respectively. For larger carotenoids, Ehlers and co-workers found a gradient of 0.893×10 -3 cm -1 s -1 . Bachilo and co-workers instead studied internal conversion using the simplified energy gap law method using diphenylpolyenes, and reported rates between 0.003-2.040×10 8 s -1 with respect to the length of conjugation along the chromophore. Interestingly, the shortest species they studied was found to not fit into the exponential pattern typically expected, being several orders of magnitude faster compared to the next few in the series. Frank and co-workers highlighted this exponential relationship for a series of carotenoids decreasing from ∼9 × 10 11 s -1 with respect to the energy gap.