Theoretical calculation for the multiplet structures of tetrahedrally coordinated Cr4+ in silicate crystals

The multiplet structures of tetrahedrally coordinated Cr4+ in the three sil icate crystals Mg2SiO4 (forsterite), Ca2MgSi2O7 (akermanite), and Y2SiO5 (y ttrium orthosilicate (YSO)) were calculated by the many-electron electronic structure calculation method developed by the authors. The method is a hyb rid of the molecular orbital method based on the density functional theory and the configuration interaction approach. For every crystal, the calculat ions were conducted by using cluster models with the three sizes: (A) (CrO4 )(4-) (without point charges) models, (B) (CrO4)(4-) (with point charges) m odels, and (C) (CrMg9Si2O37)(44-) (forsterite), (CrCa6Mg2SiO38)(52-) (akerm anite), and (CrY8O37)(46-) (YSO) models. The calculated multiplet energies of the triplet states agreed with the experimentally obtained peak energies in the absorption spectra in the literature. The theoretical spectra showe d polarization dependence of the peak intensity. The best agreement was fou nd in the results obtained from the largest models C. The difference in pol arization dependence between Cr4+:forsterite and Cr4+:akermanite was relate d to the different mixing of the many-electron wave functions as regards th e T-3(2)(et(2)) and T-3(1)(et(2)) triplet terms. The covalency of the impur ity-level molecular orbitals was also analysed. The results of models C ind icated that the wave functions of the atoms outside the CrO4 tetrahedron sh ould not be neglected. Both the degree of covalency and the correlation-cor rection factor, which was introduced in the method, were regarded as reduct ion factors of two-electron repulsion. The two factors were multiplied toge ther, and the reduction factor was a convenient indicator for simply evalua ting the magnitude of the reduction. The traditional nephelauxetic paramete r was obtained as 0.49. Some empirical values given recently in the literat ure were confirmed to have appropriate magnitude.