Suppression of sidebands in magic-angle-spinning nuclear magnetic resonance: General principles and analytical solutions

Abstract

Several theoretical and experimental aspects of sideband suppression in the nuclear magnetic resonance (NMR) spectra of rotating solids are considered. The principles of sideband suppression are explored using general symmetry arguments and previous treatments are examined critically. Analytical solutions are given for sideband suppression pulse sequences employing four, five, six, and nine P pulses. The analytical solutions for four r pulses are complete. Experimental demonstrations are given.

Symmetry‐Based Pulse Sequences in Magic‐Angle Spinning Solid‐State NMR

“…Note that equation (22) represents the propagator over an arbitrary interval τ , while the average Hamiltonian terms in equation (24) involve integrals over the full period of the pulse sequence. This useful approximation allows results derived for entire periodic pulse sequences to be extended, with caution, to non-integral numbers of rf cycles.…”

Symmetry-Based Pulse Sequences in Magic-Angle Spinning Solid-State NMR

“…In the extraordinary sideband suppression and separation schemes of Dixon,21,22 carefully-timed sequences of strong π pulses were applied to the rotating sample in order to manipulate the spinning sideband patterns generated by the subsequent free-induction decay. Around the same time, Waugh and coworkers applied a repetitive pulse train synchronous with the sample rotation, and showed that the averaging effect of the magic-angle rotation on the chemical shift anisotropy could be suppressed.…”

Measurement of Orientation Distributions Using Chemical Shift Amplification

“…As with chemical shift amplification [12], careful calibration of the p-pulses is required to reduce sideband phase and amplitude distortions, and the quality of the sideband suppression in a five-pulse TOSS sequence was found empirically to be a suitable calibration criterion. Errors were further reduced by shifting the relative phases of successive p-pulses through the series 08; 3308; 608; 3308; 08; a procedure which has been used in a similar context by Antzutkin et al [13]. In order to reconstruct the required three-dimensional FID, two experiments are required in which the phase of the carbon-13 p=2 storage pulse j 3 is alternated p=2; p: These are combined in the receiver by simultaneous shifting of the reference phase by p=2: Further phase cycling of the carbon-13 pulses selects changes in coherence order Dp ¼ AE1 with j 1 and j 4 and Dp ¼ 0; AE2 across the whole of each five-pulse sequence with j 2 and j 5 : Because the t 1 and t 2 signals are periodic, are not modulated by the isotropic shift and do not decay due to T 2 relaxation, the lineshapes in o 1 and o 2 are delta functions.…”

“…The orientation of the CSA principal axis frame of a particular spin site relative to the MAS rotor is given by the Euler angles ða; b; gÞ: Following Antzutkin et al [13] we consider a ''carousel'' of spin sites which have a single value of a and b; but the full isotropic distribution of g angles. The NMR precession frequency of sites within …”