Density-functional calculation of the ¹⁸³W and ¹⁷O NMR chemical shifts for large polyoxotungstates

A phosphane sulfate relativistic DFT method (ZORA) has been used to calculate the ¹⁸³W and ¹⁷O NMR chemical shifts for large polyoxotungstates, including W₆O₁₉^2-, CH ₃OTiW₅O₁₈^3-, W₅O ₁₈W^IINO^3-, W₁₀O₃₂ ^4-, α-δ-γ-XW₁₂O₄₀ ^n-, β-PW₉O₂₈Br₆^3-, P₂W₁₈O₆₂^6-, PW₂O ₁₄^3-, and W₇O₂₄^6-, based on their optimized molecular structures. Despite sizeable deviations between the calculated and experimental values, the calculations correctly reproduce the trends in the change of the chemical shift for both nuclei. As expected, the diamagnetic term is almost constant throughout the whole series. The change in the chemical shifts is shown to be determined by the paramagnetic term, which depends on the electronic structure of the whole anion under study and, in particular, on the local geometry around a given tungsten atom. On the other hand, there is no correlation between the chemical shift and HOMO-LUMO gap, showing that deeper occupied levels and several unoccupied orbitals play an important role in the paramagnetic term. However, analysis of the components of the paramagnetic shielding has shown that the most significant transitions determining the change of both ¹⁸³W and ¹⁷O NMR chemical shifts for anions consisting of tungsten and oxygen atoms are the occupied-occupied and not the occupied-virtual ones.