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) irr adiation 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 mod ulated Lee Goldburg (PMLG-n), homonuclear dipolar decoupling experiments on protons that are rotating at the magic angle are examined. Average Hamilto nian theory (AHT) is used for the synchronous application of FSLG and PMLG- n RF sequences with the sample spinning. A bimodal Floquet approach is intr oduced to treat both synchronous and nonsynchronous cases. The Floquet appr oach, providing a general theoretical framework for describing rotating spi n systems exposed to periodically applied RF field, reveals several feature s of the interference between the sample spinning and the RF irradiation. T hese features can be characterized by mapping out resonance conditions in t erms of the Floquet energy level crossings. Line broadening effects occurri ng when the RF sequences are applied synchronously with the sample spinning are discussed. The appearances of RF-rotor frequency lines in the decouple d spectra are explained. In addition PMLG-n magic angle spinning (MAS) expe riments with a reduced number of phases, n greater than or equal to3, per R F cycle are explored. All theoretical predictions are verified by simulatio ns of proton spectra and by PMLG-n-MAS experiments on uniformly labeled C-1 3- tyrosine. (C) 2001 American Institute of Physics.