Theoretical study of radiative and nonradiative decay rates for Cu(i) complexes with double heteroleptic ligands

In this paper, we conducted DFT and TDDFT calculations on three double heteroleptic Cu(i) complexes to understand how different substituents on N<^>N ligands influence the phosphorescence quantum yield (PLQY). Both radiative and nonradiative decay processes were thoroughly investigated. Factors that determine the rate of radiative process (k(r)) were considered, including the lowest triplet excited state E(T-1), the transition dipole moment M-Sm,M-j of the S-m S-0 transition, the spin-coupled matrix element SOC, and the singlet-triplet splitting energies E(S-m-T-1). The results indicate that E(T-1), M-Sm,M-j and SOC increase and E(S-m-T-1) decreases upon introducing -Ph and -CH2- groups on the N<^>N ligands. The net results lead to a gradual increase of k(r) in the three Cu(i) complexes, from 1 (0.48 x 10(4) s(-1)) to 2 (0.64 x 10(4) s(-1)) and then to 3 (1.61 x 10(4) s(-1)). The rate of nonradiative decay process (k(nr)) was computed by a convolution method. We explored how k(nr) is determined by SOC between T-1 and S-0 states (T-1|SOC|S-0(2)), effective energy gap E and the Huang-Rhys factor (S). We found that T-1|SOC|S-0(2) and E contribute significantly to k(nr), but S does not determine the order of k(nr). k(nr) gradually decreases from complex 1 (2.51 x 10(6) s(-1)) to 2 (0.32 x 10(6) s(-1)) and then to 3 (0.14 x 10(6) s(-1)) after introducing -Ph and -CH2- groups on the N<^>N ligands. The computed PLQYs for the three complexes are 1: 0.0019, 2: 0.0198, and 3: 0.1011. These are quantitatively consistent with the experimental observation (1: 0.0028, 2: 0.0061, and 3: 0.1000).