Computation of 31P NMR chemical shifts in Keggin-based lacunary polyoxotungstates

Density Functional Theory (DFT) calculations were employed to systematically study the accuracy of various exchange-correlation functionals in reproducing experimental P-31 NMR chemical shifts, delta(Exp)(P-31) for Keggin, [PW12O40](3-) and corresponding lacunary clusters: [PW11O39](7-), [A-PW9O34](9-), and [B-PW9O34](9-). Initially, computed chemical shifts, delta(Calc)(P-31) were obtained with without neutralising their charge in which associated error, delta(Error)(P-31), decreased as a function of Hartree-Fock (HF) exchange, attributed to constriction of the P-O tetrahedron. By comparison, delta(Calc)(P-31) performed with explicitly located counterions to render the system charge neutral, reduced discrepancies, delta(Error)(P-31) by 1-2 ppm. However, uncertainties in delta(Calc)(P-31) remain, particularly for [B-PW9O34](9-) anions attributed to direct electrostatic interactions between the counterions and the central tetrahedron. Optimal results were achieved using the PBE/TZP//PBE0/TZP method, achieving a mean absolute error (MAE) and a mean squared error (MSE) of 4.03 ppm. Our results emphasize that understanding the nature of the electrolyte and solvent environment is essential to obtaining reasonable agreement between theoretical and experimental results.