Ab Initio Calculation of Electronic Structure and 4f–5d Transition Energies of Ce³⁺ Doped in Y₃Al₅O₁₂ Nanocrystals

The elementary-state electronic structure and 4f–5d transitions of Y₃Al₅O₁₂:Ce³⁺ nanocrystals simulated by several clusters were computed by the ab initio self-consistent relativistic DV-Xα (discrete variational Xα) method. A 35-ion cluster was chosen to simulate the local surroundings of Ce³⁺ doped in Y₃Al₅O₁₂ bulk crystals while four additional smaller irregular clusters were also chosen to simulate the local surroundings of Ce³⁺ ions in nanocrystals. Besides obtaining the elementary-state 4f and 5d electronic structure, based on the transition-state calculations we also obtained the five 4f–5d transition energies for each of these clusters. We found that compared with the bulk crystals, for all the clusters simulating nanocrystals the first 4f–5d transition peak (the lowest energy peak) was blueshifted, and the second peak was redshifted a little, which are both in accordance with the observed experimental excitation spectra of 5d luminescence of Y₃Al₅O₁₂:Ce³⁺. We fitted the observed first two transition peaks in a published experimental excitation spectrum of nanocrystals by weighted summing of the excitation spectra of the selected clusters; therefore, the weight contribution of each cluster was obtained. Moreover, the other three unobserved peaks were all expected to be redshifted. According to these calculations and our understanding, in Y₃Al₅O₁₂:Ce³⁺ nanocrystals, the shift of the peaks can be mainly attributed to the reduction of the crystal field felt by Ce³⁺ ions—which results in the reduction of the splittings of 5d levels of Ce³—as well as to the increase of the difference between the 5d average level and the 4f average level of Ce³⁺.