Refinement of the crystal structure of fresnoite, Ba2TiSi2O8, from Löhley (Eifel district, Germany); Gladstone-Dale compatibility, electronic polarizability and vibrational spectroscopy of minerals and inorganic compounds with pentacoordinated TiIV and a titanyl bond.

Most known compounds with five-coordinated Ti⁴⁺ are natural and synthetic titanosilicates. The crystal structure of natural fresnoite, Ba₂TiSi₂O₈ [tetragonal, space group P4bm, a = 8.510 (1) Å, c = 5.197 (1) Å, V = 376.4 (1) ų, Z = 2], has been refined to R = 0.011 on the basis of 807 unique single-crystal reflections with I > 2σ(I). Titanium has fivefold coordination with one short (`titanyl') bond of 1.692 (5) Å. Bonds in the TiO<sub>5</sub> polyhedron are discussed in comparison to analogous coordination polyhedra in other minerals and compounds. A review of all known compounds with Ti<sup>4+</sup>O<sub>5</sub> polyhedra shows that most of them are titanosilicates in which titanium forms a short Ti-O bond (∼1.61 to ∼1.77 Å). Poor Gladstone-Dale compatibility between chemical composition, optical characteristics and density of these compounds is explained by the anomalous contribution of <sup>[5]</sup>Ti<sup>4+</sup> to the optical properties as shown by calculations based on the relationship between electronic polarizabilities and refractive indices. An improved Gladstone-Dale coefficient of 0.29 is suggested for TiO<sub>2</sub> with <sup>[5]</sup>Ti<sup>4+</sup>. A negative correlation between `titanyl' bond lengths and wavenumbers of the bands of Ti-O stretching vibrations (in the range of 890-830 cm^-1) in infrared and Raman spectra is observed.