Color coordination of emerald on CIE color space based on first-principles calculations

Abstract

Be3Al2(SiO3)6 including Cr3+ known as emerald have been widely studied and utilized for solid-state laser materials. Numerous theoretical investigations on these systems have also been published in the literature since the electronic energy levels, optical properties, and structures of Cr3+ impurities in emerald systems have been thoroughly investigated using a variety of experimental approaches. In general, semi-empirical computations have been used to accomplish the majority of theoretical interpretations of experimental data. Although in the case of non-empirical calculations, the agreement between theoretical and experimental optical properties was improved by taking into account the energy corrections, quantitative evaluation of the color of emitted light was not feasible until recently. Here, the color coordinates of emerald under the standard illuminant has been calculated to perform a quantitative evaluation based on the optical spectra. The “theoretical” color was calculated and presented visually on the Commission Internationale d’Eclairage (CIE) color space based on the theoretical spectra obtained non-empirically using the so-called first-principles discrete variational multi-electron method, known as DVME. The absorption spectra of emerald were calculated using CrO69− model cluster with D3 symmetry. Several key effects in reproducing optical spectra were investigated in detail, such as lattice relaxation, energy correction, and orbital effects. The accuracy of this approach in predicting absorption spectra was analyzed thoroughly under various computational conditions. The results show that accounting for all of the above effects is important to producing the absorption spectra. Specifically, enlarging the considered orbital in the calculation improved the agreement between the computed and experimentally-observed colors. This study is crucial for validating the non-empirical calculations made using the DVME approach to assess the color of emitted light quantitatively.