Reliable Predictions of Benzophenone Singlet-Triplet Transition Rates: A Second-Order Cumulant Approach

Fermi golden rule and second-order cumulant expansion of the time-dependent density matrix have been used to compute from first principles the rate of intersystem crossing in benzophenone, using minimum-energy geometries and normal modes of vibrations computed at the TDDFT/CAM-B3LYP level. Both approaches yield reliable values of the S₁ decay rate, the latter being almost in quantitative agreement with the results of time-dependent spectroscopic measurements (0.154 ps^-1 observed vs 0.25 ps^-1 predicted). The Fermi golden rule slightly overestimates the decay rate of S₁ state (k_d = 0.45 ps^-1) but provides better insights into the chemico-physical parameters, which govern the transition from a thermally equilibrated population of S₁, showing that the indirect mechanism is much faster than the direct one because of the vanishingly small Franck-Condon weighted density of states at ΔE of transition.