A simple coulombic model for ³¹P NMR spectra of cluster-encapsulated phosphorus atoms

While sophisticated computational methods can predict ³¹P NMR spectra of phosphorus atoms encapsulated within Keggin-derived heteropoly tungstate and molybdate cluster anions, calculated and experimental chemical shift values typically deviate considerably from one another. Motivated by the observation that experimentally determined ³¹P chemical shift values within a series of water-soluble plenary and metal-cation substituted lacunary Keggin anions, [PMⁿW₁₁O₃₉]⁽⁷−n)⁻ (Mⁿ = Ag⁺, Zn²⁺, Nb⁵⁺, W⁶⁺) and [(PW₁₁O₃₉)₂Mⁿ]⁽¹⁴−n)⁻ (Mⁿ = Y³⁺, Zr⁴⁺), varied as a linear function of the oxidation states, n, of the complexed Mⁿ cations, a linear correlation was sought between observed chemical shift values and the net Coulombic forces experienced by the encapsulated phosphorus atoms. The Coulombic model based on Shannon radii, published electronegativity values, and bond angles from X-ray crystallographic data remarkably accounted for the relative ³¹P chemical shift values of phosphorus atoms in over 50 metal-oxide cluster anions, including large structures comprised of up to four Keggin-derived fragments with an overall R² value of 0.974. With the model being applied here to three cluster anions whose ³¹P chemical shift values are reported here for the first time, predicted and experimental values differed by only ±0.4 ppm.