14N overtone nuclear magnetic resonance of rotating solids.

By irradiating and observing at twice the 14N Larmor frequency, overtone (OT) nuclear magnetic resonance (NMR) is capable of obtaining 14NOT spectra without first-order quadrupolar broadening. Direct excitation and detection of the usually "forbidden" double-quantum transition is mediated by the perturbation from the large quadrupole interaction to the spin states quantized by the Zeeman interaction. A recent study [L. A. O'Dell and C. I. Ratcliffe, Chem. Phys. Lett. 514, 168 (2011)] has shown that 14NOT NMR under magic-angle spinning (MAS) can yield high-resolution spectra with typical second-order quadrupolar line shapes allowing the measurement of 14N chemical shift and quadrupolar coupling parameters. This article has also shown that under MAS the main 14NOT peak is shifted by twice the sample spinning frequency with respect to its static position. We present the theory of 14NOT NMR of static or rotating samples and the physical picture of the intriguing spinning-induced shift in the second case. We use perturbation theory for the case of static samples and Floquet theory for rotating samples. In both cases, the results can be described by a so-called OT parameter that scales down the 14NOT radio-frequency (rf) excitation and signal detection. This OT parameter shows that the components of the rf field, which are transverse and longitudinal with respect to the magnetic field, are both effective for 14NOTrf excitation and signal detection. In the case of MAS at angular frequency ωr , the superposition of the excitation and detection components in the OT parameter makes either the +2ωr or -2ωr term the dominant 14NOT signal, depending on the sense of sample spinning with respect to the magnetic field. This leads to an apparent 14NOT signal shifted at twice the spinning frequency. The features of 14NOT NMR spectra for both static and rotating samples are illustrated with simulations. The spinning induced shift and its dependence on the spinning direction are confirmed experimentally by reversing the spinning direction and the field of the 36 T series-connected hybrid magnet at the US National High Magnetic Field Laboratory.