In this paper, eight complexes M-1, M-2, M-3 and M-4 (M = Ir or Rh) in the general formula [M(C^N)2(N^N)] (C^N = cyclometalated ligands and N^N = ancillary ligands) are systematically investigated by density functional theory (DFT) and time-dependent DFT methods. With the aim to study the influence of metal centers for nonlinear optical (NLO) responses, the geometrical and electronic structures, first hyperpolarizabilities (βtot) and UV-Vis absorption spectra are investigated in detail. It is found that the βtot values increase 1.8–3.7 times as the metal atom changes from Rh to Ir. Among all the studied complexes, Ir-3 (C^N = 4-chloro-2-phenylquinoline with N^N = 2,9-dimethyl-1,10-phenanthroline) shows the highest βtot value with an amplitude of 2415.4 a.u. computed at the ωB97XD/6-31G+(d)/SDD level, which can be seen as a promising candidate for second-order NLO materials. In addition, the HOMO energy levels increase upon increasing the size of the metal atom, which contributes to a significant reduction in HOMO–LUMO gaps. The βtot values and HOMO–LUMO gaps are in an inverse relationship. Furthermore, tuning the center metals Ir/Rh can be seen as an effective method to modulate the charge transfer degree. We anticipate that this study may serve as a new strategy for the rational design and synthesis of second-order NLO materials.
