Intrinsic Analysis of Thermally Activated Delayed Fluorescence (TADF) for Ag(I) Complex Based on the Path Integral Approach: Origin of the Effective Spin-Flipping Channel and Vibrational Spin-Orbit Coupling Effect.

In order to design new Ag(I)-based materials for thermally activated delayed fluorescence (TADF), it is vital to develop a detailed understanding of the current best performing materials. The quantitative predictions of the photophysical processes of the Ag(dmp)(P-nCB) TADF complex are calculated using time-dependent density functional theory (TD-DFT) combined with the path integral approach for dynamics including the Herzberg-Teller effects. All calculated results are in good agreement with the experimentally available data, demonstrating the validity of our applied theoretical approach. Analysis of ETS-NOCV (extended transition state natural orbital for chemical valence) shows that there is a weak bond interaction dominated by electrostatic interactions and accompanied by some covalent components between Ag(I) and dmp ligands due to the introduction of the strongly electron-donating negatively charged P-nCB ligand, thus giving a small energy separation between the lowest singlet S and triplet T states of Δ(S - T) ≈ 532 cm. The SOC strongly depends on the geometrical alteration caused by the molecular "promotion" vibrations. Our study has revealed that a few "promotion" vibrational modes, that is, ω and ω, effectively induce the strong SOC between S and T and speed up the reverse intersystem crossing (RISC) process dramatically. The computed value is 1.19 × 10 s for the solid phase at 300 K, which are about 5 orders of magnitude larger than the mean phosphorescence rate, = 9.56 × 10 s, and it is also far larger than ISC = 7.84 × 10 s rates from T to S. The S state thus can be an efficient thermal repopulation from the T state by the RISC pathway. Finally, we also note that the diabatic vibration coupling triplet pair T/T will also be important for efficient and practical RISC. Our investigation will be of great utility toward designing and improving the Ag(I)-based TADF complexes.