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
NRC Metrology
National Research Council Canada
W. G. Schneider Building (M40)
1200 Montreal Road
Ottawa, Ontario K1A 0R6
Tel. +1-613-990-0319
Fax. +1-613-990-1555