Spin–Vibronic Model for Quantitative Prediction of Reverse Intersystem Crossing Rate in Thermally Activated Delayed Fluorescence Systems

Computationally predicting reverse intersystem crossing (RISC) rates is important for designing new thermally activated delayed fluorescence (TADF) materials. We report a method that can quantitatively predict RISC rates by explicitly considering the spin–vibronic coupling mechanism. The coupling element of the spin–vibronic Hamiltonian is obtained by expanding the spin–orbit and the non-Born–Oppenheimer terms to second order and is then brought into the Golden Rule rate under the Condon approximation. The rate equation is solved directly in the time domain using a correlation function approach. The contributions of the first-order direct spin–orbit coupling and the second-order spin–vibronic coupling to an RISC rate can be quantitatively analyzed in a separate manner. We demonstrate the utility of the method by applying it to a representative TADF system, where we observe that the spin–vibronic portion is substantial but not dominant especially with a relatively small triplet–singlet energy gap. Likewise, our method may elucidate the physical background of efficient nonradiative transitions from the lowest triplet to a higher lying singlet in other purely organic TADF systems, and it will be of great utility toward designing new such molecules.