Theoretical calculation for themultiplet structures of tetrahedrally coordinated Cr4+ insilicate crystals

Abstract

The multiplet structures of tetrahedrally coordinated Cr4+ inthe three silicate crystals Mg2SiO4 (forsterite),Ca2MgSi2O7 (åkermanite), and Y2SiO5 (yttriumorthosilicate (YSO)) were calculated by the many-electronelectronic structure calculation method developed by the authors.The method is a hybrid of the molecular orbital methodbased on the density functional theory and the configurationinteraction approach. For every crystal, the calculations wereconducted by using cluster models with the three sizes: (A)(CrO4)4- (without point charges) models, (B)(CrO4)4- (with point charges) models, and (C)(CrMg9Si2O37)44- (forsterite),(CrCa6Mg2SiO38)52- (åkermanite), and(CrY8O37)46- (YSO) models. The calculated multipletenergies of the triplet states agreed with the experimentallyobtained peak energies in the absorption spectra in the literature.The theoretical spectra showed polarization dependence of thepeak intensity. The best agreement was found in the resultsobtained from the largest models C. The difference in polarization dependence between Cr4+:forsterite andCr4+:åkermanite was related to the different mixing of themany-electron wave functions as regards the 3T2(et2) and3T1(et2) triplet terms. The covalency of the impurity-levelmolecular orbitals was also analysed. The results of models Cindicated that the wave functions of the atoms outside the CrO4tetrahedron should not be neglected. Both the degree of covalencyand the correlation-correction factor, which was introduced in themethod, were regarded as reduction factors of two-electronrepulsion. The two factors were multiplied together, and thereduction factor was a convenient indicator for simplyevaluating the magnitude of the reduction. The traditionalnephelauxetic parameter was obtained as 0.49. Someempirical values given recently in the literature were confirmed tohave appropriate magnitude.