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

Overtone NMR is an experiment introduced by LeGros, Bloom, Tycko, and Opell a, capable of providing N-14 powder spectra devoid of first-order quadrupol e broadenings by irradiation and observation of the nuclear spins at twice their Larmor frequency. This technique constitutes one of the most promisin g alternatives for the acquisition of high resolution solid N-14 NMR spectr a from random powders, particularly if it can be combined with strategies c apable of removing the substantial second-order quadrupole broadenings rema ining in the overtone line shapes. In order to facilitate the search for th ese averaging manipulations, we present here a theoretical description of t he overtone experiment based on the time-domain propagation of density matr ices. It is shown that by combining perturbation methods with appropriate r otating-frame transformations and diagonalizations, overtone spin-1 phenome na can be described using a single set of fictitious spin-1/2 operators. By contrast to conventional spin-1/2 irradiation and detection processes, how ever, overtone manipulations involve an unusual angular dependence on the a zimuthal angle defining rotations about the main Zeeman magnetic field. Thi s behavior introduces unexpected complications toward the narrowing of over tone resonances by conventional sample spinning techniques. Nevertheless, i t can still be shown that the removal of all spin-1 anisotropies by certain forms of dynamic-angle spinning overtone NMR remains feasible. (C) 1999 Am erican Institute of Physics. [S0021-9606(99)01806-1].