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 51V 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 51V are (I) an isolated H4VO4+ cluster, (II) an isolated HnVO4n−3 cluster (n=number of next-neighbor cations) (III) an isolated orthovanadate anion, VO4−x, and (IV) a VO4−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 VO4−x models, are used to discuss site assignments for AlVO4. Correlations between quadrupole coupling parameters and deviations of the orthovanadate structure from ideal tetrahedral symmetry are shown.