Theoretical Studies on the Photophysical Properties of the Ag(I) Complex for Thermally Activated Delayed Fluorescence Based on TD-DFT and Path Integral Dynamic Approaches

Theoretical calculation not only is a powerful tool to deeply explore photophysical processes of the emitters but also provides a theoretical basis for material renewal and design strategy in the future. In this work, the interconversion and decay rates of the thermally activated delayed fluorescence (TADF) process of the rigid Ag(dbp)(P 2 - n CB) complex are quantitatively calculated by employing the optimally tuned range-separated hybrid functional (ω*B97X-D3) method combined with the path integral approach to dynamics considering the Herzberg-Teller and the Duschinsky rotation effects within a multimode harmonic oscillator model. The calculated results show that the small energy splitting Δ E (S 1 -T 1 ) = 742 cm -1 (experimental value of 650 cm -1 ) of the lowest singlet S 1 and triplet T 1 state and proper vibrational spin-orbit coupling interactions facilitate the reverse intersystem crossing (RISC) processes from the T 1 to S 1 states. The k RISC rate is estimated to be 1.72 × 10 8 s -1 that is far more than the intersystem crossing rate k ISC of 7.28 × 10 7 s -1 , which will greatly accelerate the RISC process. In addition, the multiple coupling routes of zero-field splitting (ZFS) interaction can provide energetically nearby lying states, to speed up the RISC pathway, and restrict the phosphorescence decay rate. A smaller ZFS D -tensor of 0.143 cm -1 , E / D ≈ 0.094 ≪ 1/3, and Δ g > 0 are obtained, indicating that the excited singlet states are hardly mixed into the T 1 state; thus, a lower phosphorescence decay rate ( k p = 9.29 × 10 1 s -1 ) is expected to occur, and the T 1 state has a long lifetime, which is helpful for the occurrence of the RISC process. These works are in excellent agreement with the experimental observation and are useful for improving and designing efficient TADF materials.