Investigation of the origin of the empirical relationship between refractive index and density on the basis of first principles calculations for the refractive indices of various TiO2 phases

On the basis of first principles electronic structure calculations, we determined the dielectric functions, the refractive indices, and the extinction coefficients of the seven different phases of TiO2 and then examined why the refractive index is related to the density by the empirical Glastone-Dale equation. The zero frequency limit of the refractive index, no, is found to be a good approximation for the refractive index n determined around 2 eV. Our study indicates that the major factor influencing n in a series of closely related systems is the structure compactness. This finding suggests a way of preparing new UV absorbers with low refractive index.