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)(P2-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 P2-nCB ligand, thus giving a small energy separation between the lowest singlet S1 and triplet T1 states of ΔE(S1 - T1) ≈ 532 cm-1. 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, ω46 and ω227, effectively induce the strong SOC between S1 and T1 and speed up the reverse intersystem crossing (RISC) process dramatically. The computed kRISC value is 1.19 × 107 s-1 for the solid phase at 300 K, which are about 5 orders of magnitude larger than the mean phosphorescence rate, kP = 9.56 × 102 s-1, and it is also far larger than ISC k0ISC = 7.84 × 102 s-1 rates from T1 to S0. The S1 state thus can be an efficient thermal repopulation from the T1 state by the RISC pathway. Finally, we also note that the diabatic vibration coupling triplet pair T1/T2 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.