A density matrix description of 14N overtone nuclear magnetic resonance in static and spinning solids

Overtone NMR is an experiment introduced by LeGros, Bloom, Tycko, and Opella, capable of providing 14N powder spectra devoid of first-order quadrupole broadenings by irradiation and observation of the nuclear spins at twice their Larmor frequency. This technique constitutes one of the most promising alternatives for the acquisition of high resolution solid 14N NMR spectra from random powders, particularly if it can be combined with strategies capable of removing the substantial second-order quadrupole broadenings remaining in the overtone line shapes. In order to facilitate the search for these averaging manipulations, we present here a theoretical description of the overtone experiment based on the time-domain propagation of density matrices. It is shown that by combining perturbation methods with appropriate rotating-frame transformations and diagonalizations, overtone spin-1 phenomena can be described using a single set of fictitious spin-1/2 operators. By contrast to conventional spin-1/2 irradiation ...