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 S-1 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 S-1 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 S-1, showing that the indirect mechanism is much faster than the direct one because of the vanishingly small Franck-Condon weighted density of states at Delta E of transition.

Automated summary

The Fermi golden rule and second-order cumulant expansion of the time-dependent density matrix were used to calculate the rate of intersystem crossing in benzophenone. The latter approach was in quantitative agreement with experimental results, while the Fermi golden rule provided insights into the chemico-physical parameters governing the faster indirect mechanism compared to the direct one.