Vanadium-51 solid-state NMR electric field gradient tensors: a DFT-embedded ion and isolated cluster study of crystalline vanadium oxides.

Density functional theory (DFT) calculations (6-311+G(2d,p)/B3LYP level of theory) of (51)V electric field gradient (EFG) tensor elements are performed for embedded and isolated cluster models of orthovanadates. The structural models used to calculate the EFGs of (51)V are (I) an isolated H(4)VO(4)(+) cluster, (II) an isolated H(n)VO(4)(n-3) cluster (n=number of next-neighbor cations) (III) an isolated orthovanadate anion, VO(4)(-x), and (IV) a VO(4)(-x) ion embedded in a finite point-charge array whose electrostatic potential, at the embedded ion, is equivalent to that of the infinite lattice. For models III and IV, a charge x is assigned estimating the covalence of the system. Models III and IV provide results in good agreement with the experiment. Calculations, employing the embedded and isolated VO(4)(-x) models, are used to discuss site assignments for AlVO(4). Correlations between quadrupole coupling parameters and deviations of the orthovanadate structure from ideal tetrahedral symmetry are shown.