Shizu & Kaji examined internal conversion in benzophenone across all vibrational normal modes, for both the singlet and triplet manifolds using the correlation-type formalism (Equation ). For the S 1 → S 0 transition, a rate constant of 3.3×10 6 s -1 was recorded, while on the triplet manifold, "uphill" rate constants from the T 1 state were no larger than 100 s -1 . For the near-degenerate T 2 → T 3 transition, the "uphill" transition was much faster, at ∼10 10 s -1 [170] Thermally allowed transitions across the triplet manifold otherwise were quite fast, of the order of 10 10 s -1 or larger. They then compared this with a cost-effective rate constant expression, in which a series of kinetic equations are derived for a given system, cast as :