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

Abstract

Density Functional Theory (DFT) calculations were employed to systematically study the accuracy of various exchange-correlation functionals in reproducing experimental ³¹P NMR chemical shifts, δ_Exp(³¹P) for Keggin, [PW₁₂O₄₀]³⁻ and corresponding lacunary clusters: [PW₁₁O₃₉]⁷⁻, [A-PW₉O₃₄]⁹⁻, and [B-PW₉O₃₄]⁹⁻. Initially, computed chemical shifts, δ_Calc(³¹P) were obtained with without neutralising their charge in which associated error, δ_Error(³¹P), decreased as a function of Hartree–Fock (HF) exchange, attributed to constriction of the P–O tetrahedron. By comparison, δ_Calc(³¹P) performed with explicitly located counterions to render the system charge neutral, reduced discrepancies, δ_Error(³¹P) by 1–2 ppm. However, uncertainties in δ_Calc(³¹P) 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.