Empirical Electronic Polarizabilities for Use in Refractive Index Measurements III. Structures with Short [5]Ti–O and Vanadyl Bonds

The electronic polarizabilities of most cations, such as Na+, Ca2+, Fe2+, Fe3+, and Zr4+, show a monotonic decrease as the cation coordination increases. However, polarizabilities of the ions [5]Ti4+, [5]V5+, and [6]V5+ show strong deviations from a regular decrease. In this paper we characterize the [5]Ti and vanadyl compounds by infrared frequencies, by the short [5]Ti4+– O, [5]V4+–O, [6]V4+–O, [5]V5+–O, and [6]V5+–O bonds and the polarizabilities of [5]Ti4+, [5]V4+, [6]V4+, [5]V5+, and [6]V5+ determined from refractive index measurements. Analysis of the structures of 18 compounds containing short [5]Ti–O bonds supports the concept of the short Ti–O bond being associated with the bond valence sum (omitting Ti) around the oxygen atom O*. The short Ti–O* bond occurs to satisfy the bond valence requirement of (O2–) of ∼2.0 vu. Plotting the [5]Ti–O* distances of 18 minerals versus the bond valence sum (BVS) around O* shows an approximately linear relationship. Extrapolation to BVS = 0 yields a minimum distance of 1.65 Å. The mean value is 1.693 Å. The mean short distances in V4+ vanadyl minerals are 1.597 Å (CN = 5) and 1.590 Å (CN = 6), whereas the mean short distance in five V5+ minerals is 1.647 Å (CN = 5) and in 14 V5+ minerals is 1.644 Å (CN = 6). We compare the polarizabilities of [5]Ti and [5,6]V4+ and [5,6]V5+ ions with the polarizabilities of [4]-coordinated Ti4+ ([4]Ti4+ ) and [6]-coordinated Ti4+ ([6]Ti4+ ) and of [4]-, [5]-, and [6]-coordinated V4+ and V5+ ([n]V4+ and [n]V5+) and hypothesize that the reduced polarizability of [5]Ti4+, [5]V5+, and [6]V5+ ions is caused by the short Ti–O* and V=O bonds.