31P MAS Refocused INADEQUATE Spin−Echo (REINE) NMR Spectroscopy: Revealing J Coupling and Chemical Shift Two-Dimensional Correlations in Disordered Solids
Paul Guerry†, Mark E. Smith and Steven P. Brown*
Two-dimensional (2D) variations in 2JP1,P1, 2JP1,P2, and 2JP2,P2 are obtained—using the REINE (REfocused INADEQUATE spin−Echo) pulse sequence presented by Cadars et al. (Phys. Chem. Chem. Phys. 2007, 9, 92−103)—from pixel-by-pixel fittings of the spin−echo modulation for the 2D correlation peaks due to linked phosphate tetrahedra (P1−P1, P1−P2, P2−P1, and P2−P2) in a 31P refocused INADEQUATE solid-state MAS NMR spectrum of a cadmium phosphate glass, 0.575CdO−0.425P2O5. In particular, separate variations for each 2D 31P REINE peak are obtained which reveal correlations between the J couplings and the 31P chemical shifts of the coupled nuclei that are much clearer than those evident in previously presented 2D z-filtered 31P spin−echo spectra. Notably, such correlations between the J couplings and the 31P chemical shifts are observed even though the conditional probability distributions extracted using the protocol of Cadars et al. (J. Am. Chem. Soc. 2005, 127, 4466−4476) indicate that there is no marked correlation between the 31P chemical shifts of neighboring phosphate tetrahedra. For 2D peaks at the P2 31P chemical shift in the direct dimension, there can be contributions from chains of three units (P1−P2−P1), chains of four units (P1−P2−P2−P1), or longer chains or rings (−P2−P2−P2−): for the representative glass considered here, best fits are obtained assuming a glass comprised predominantly of chains of four units. The following variations are found: 2JP1,P1 = 13.4 ± 0.3 to 14.8 ± 0.5 Hz, 2JP1,P2 = 15.0 ± 0.3 to 18.2 ± 0.3 Hz, and 2JP2,P2 = 5.9 ± 0.6 to 9.1 ± 0.9 Hz from the fits to the P1−P1, P1−P2, and P2−P2 peaks, respectively. The correlation of a particular J coupling with the 31P chemical shifts of the considered nucleus and the coupled nucleus is quantified by the coefficients CF2 and CF1 that correspond to the average pixel-by-pixel change in the J coupling with respect to the chemical shift of the observed (F2) and neighboring (F1) 31P nuclei, respectively.