Using Symmetry to Design Pulse Sequences in Solid-State NMR,

M. Carravetta, A. Brinkmann, X. Zhao, J. Schmedt auf der Günne, P. K. Madhu, and M. H. Levitt,
2nd Alpine Conference on Solid-State NMR, Chamonix-Mont Blanc, France (Sep. 2001), talk.

Full text (PDF) (via Malcolm H. Levitt's homepage)

Symmetry theorems simplify the task of designing rotor-synchronized pulse sequences in magic-angle spinning solid-state NMR. The theorems link the symmetry of the pulse sequence to selection rules for the average Hamiltonian. The pulse sequence is described by three symmetry numbers, denoted N, n and ν. The symmetry numbers n and ν correspond to winding numbers for the space and spin modulation. The symmetry number N indicates the number of steps in the rf phase modulation. By choosing N, n and ν, one can design pulse sequences with a wide range of useful properties. Two general classes have been developed: Sequences denoted CNnν, which are based on a cyclic sequence element, and sequences denoted RNnν, which are based on a 180° rotation element. The selection rules for these two classes are different, which creates additional flexibility.

We demonstrate the following symmetries and associated applications:

  • Double-quantum homonuclear recoupling: C721, C1445, R1426, R2249. 2D correlation spectroscopy; torsional angle measurements; C–C bond length measurements.
  • Zero-quantum homonuclear recoupling: R441 and R662. 2D correlation spectroscopy.
  • Heteronuclear recoupling, CSA recoupling, and heteronuclear polarization transfer: R1817, R1825. Bond length measurements: a new way of detecting and quantitating hydrogen bonds.
  • Selective heteronuclear recoupling: R2494,5, where different symmetry numbers are used on the I-spin and S-spin irradiation channels.
  • Selection of isotropic shifts: R1819. High resolution proton NMR in the presence of fast MAS.

Dr. Andreas Brinkmann
Measurement Science and Standards
National Research Council
1200 Montreal Road, M-40
Ottawa, Ontario K1A 0R6
Tel. +1-613-990-0319
Fax. +1-613-990-1555
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