One- and two-dimensional 31P cross-polarization magic-angle-spinning nuclear magnetic resonance studies on two-spin systems with homonuclear dipolar coupling and J coupling

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Abstract
The effect of dipolar interactions on the solid state 31P cross‐polarization magic‐angle‐spinning (CP‐MAS) nuclear magnetic resonance (NMR) line shapes for the coupled two‐spin systems, sodium pyrophosphate decahydrate, Na4P2O7⋅10H2O, and tetraphenyl diphosphine‐1‐oxide, (C6H5)2PP(O)(C6H5)2, has been investigated. The one‐dimensional (1D)CP‐MAS spectra of Na4P2O7⋅10H2O shows spinning frequency dependent sideband splittings. A theory was developed to permit the calculation of the MAS NMR line shapes of the dipolar and J‐coupled two‐spin systems. An exact solution of the periodic Hamiltonian was obtained by the use of Floquet Hamiltonian theory. The experimental spectra of Na4P2O7⋅10H2O are well reproduced by the theoretical ones calculated from the present theory, in which the homonuclear dipolar interaction between the two 31P nuclei in the P2O74− group was taken into consideration. Our Hamiltonian also leads to calculated spectra which are in good agreement with the experimental observations even at low rotor spinning speeds. The two‐dimensional J‐resolved experiments, with rotationally synchronized acquisition in the t1 dimension, were performed for both Na4P2O7⋅10H2O and (C6H5)2PP(O)(C6H5)2. These experiments were found to be useful in distinguishing between the different mechanisms of the rotational sideband splitting of 1D spectra, as well as the dipolar interactions between spins with the same isotropic chemical shift, but different orientations of chemical shift tensors. These studies also allowed the identification of splittings caused by homonuclear J‐coupled interactions, because the resolution of the 2D J‐resolved spectra was greater than that of the 1D spectra.

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