Theoretical studies on thermally activated delayed fluorescence of "carbene-metal-amide" Cu and Au complexes: geometric structures, excitation characters, and mechanisms.

"Carbene-metal(I)-amide" (CMA) complexes have garnered significant attention due to their remarkable properties and potential TADF applications in organic electronics. However, the atomistic working mechanism is still elusive. Herein, we chose two CMA complexes, i.e. , cyclic (alkyl)(amino) carbene-copper[gold](I)-carbazole (CAAC-Cu[Au]-Cz), and employed both DFT and TD-DFT methods, in combination with radiative and nonradiative rate calculations, to investigate geometric and electronic structures of these two complexes in the ground and excited states, including orbital compositions, electronic transitions, absorption and emission spectra, and the luminescence mechanism. It is found that the coplanar or perpendicular conformations are coexistent in the ground state (S 0 ), the lowest excited singlet state (S 1 ), and the triplet state (T 1 ). Both the coplanar and perpendicular S 1 and T 1 states have similar ligand-to-ligand charge transfer (LLCT) character between CAAC and Cz, and some charge-transfer character between metal atoms and ligands, which is beneficial to minimize the singlet-triplet energy gaps (Δ E ST ) and increase the spin-orbit coupling (SOC). An interesting three-state (S 0 , S 1 , T 1 ) model involving two regions (coplanar and perpendicular) is proposed to rationalize the experimental TADF phenomena in the CMA complexes. In addition to the coplanar ones, the perpendicular S 1 and T 1 states also play a role in promoting the repopulation of the coplanar S 1 exciton, which is a primary source for the delayed fluorescence.