Phase modulated Lee-Goldburg magic angle spinning proton nuclear magnetic resonance experiments in the solid state: A bimodal Floquet theoretical treatment

Interference phenomena between sample spinning and radio frequency (RF) irradiation in solid state high resolution proton nuclear magnetic resonance (NMR) spectroscopy are examined. A bimodal Floquet treatment is exploited in order to overcome the limitations of the average Hamiltonian theory (AHT) approach. Frequency switched Lee Goldburg (FSLG) and its variant, phase modulated Lee Goldburg (PMLG-n), homonuclear dipolar decoupling experiments on protons that are rotating at the magic angle are examined. Average Hamiltonian theory (AHT) is used for the synchronous application of FSLG and PMLG-n RF sequences with the sample spinning. A bimodal Floquet approach is introduced to treat both synchronous and nonsynchronous cases. The Floquet approach, providing a general theoretical framework for describing rotating spin systems exposed to periodically applied RF field, reveals several features of the interference between the sample spinning and the RF irradiation. These features can be characterized by mapping out resonance conditions in terms of the Floquet energy level crossings. Line broadening effects occurring when the RF sequences are applied synchronously with the sample spinning are discussed. The appearances of RF-rotor frequency lines in the decoupled spectra are explained. In addition PMLG-n magic angle spinning (MAS) experiments with a reduced number of phases, n greater than or equal to3, per RF cycle are explored. All theoretical predictions are verified by simulations of proton spectra and by PMLG-n-MAS experiments on uniformly labeled C-13- tyrosine. (C) 2001 American Institute of Physics.