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 2 -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 2 -nCB ligand, thus giving a small energy separation between the lowest singlet S 1 and triplet T 1 states of Δ E (S 1 - T 1 ) ≈ 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, ω 46 and ω 227 , effectively induce the strong SOC between S 1 and T 1 and speed up the reverse intersystem crossing (RISC) process dramatically. The computed k RISC value is 1.19 × 10 7 s -1 for the solid phase at 300 K, which are about 5 orders of magnitude larger than the mean phosphorescence rate, k P = 9.56 × 10 2 s -1 , and it is also far larger than ISC k 0 ISC = 7.84 × 10 2 s -1 rates from T 1 to S 0 . The S 1 state thus can be an efficient thermal repopulation from the T 1 state by the RISC pathway. Finally, we also note that the diabatic vibration coupling triplet pair T 1 /T 2 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.