Up-Conversion Intersystem Crossing Rates in Organic Emitters for Thermally Activated Delayed Fluorescence: Impact of the Nature of Singlet vs Triplet Excited States

The rates for up-conversion intersystem crossing (UISC) from the T1 state to the S1 state are calculated for a series of organic emitters with an emphasis on thermally activated delayed fluorescence (TADF) materials. Both the spin-orbit coupling and the energy difference between the S1 and T1 states (ΔEST) are evaluated, at the density functional theory (DFT) and time-dependent DFT levels. The calculated UISC rates and ΔEST values are found to be in good agreement with available experimental data. Our results underline that small ΔEST values and sizable spin-orbit coupling matrix elements have to be simultaneously realized in order to facilitate UISC and ultimately TADF. Importantly, the spatial separation of the highest occupied and lowest unoccupied molecular orbitals of the emitter, a widely accepted strategy for the design of TADF molecules, does not necessarily lead to a sufficient reduction in ΔEST; in fact, either a significant charge-transfer (CT) contribution to the T1 state or a minimal energy difference between the local-excitation and charge-transfer triplet states is required to achieve a small ΔEST. Also, having S1 and T1 states of a different nature is found to strongly enhance spin-orbit coupling, which is consistent with the El-Sayed rule for ISC rates. Overall, our results indicate that having either similar energies for the local-excitation and charge-transfer triplet states or the right balance between a substantial CT contribution to T1 and somewhat different natures of the S1 and T1 states, paves the way toward UISC enhancement and thus TADF efficiency improvement.