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

A. Brinkmann, M. Carravetta, M. Edén, T. Karlsson, M. H. Levitt, H. Luthman, and X. Zhao,
41st Experimental NMR Conference, Asilomar, California, USA (Apr. 2000), talk.

We have discovered some new symmetry theorems which greatly simplify the task of designing rotor-synchronized pulse sequences in 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 modulations. 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.

Previously, we demonstrated sequences with the symmetry C721 for efficient double-quantum excitation in MAS solids. We now demonstrate a sequence with the symmetry C1445 for work at high spinning frequency (examples will be given at 20 kHz spinning). In addition, we demonstrate the new symmetry R1426 which is more efficient than the C721-based sequences at moderate spinning frequency.

We also demonstrate heteronuclear recoupling at high spinning frequency using a sequence of the symmetry R1817, and show how the new theorems illuminate the operation of TPPM heteronuclear decoupling. Additional symmetries will be described for other tasks, such as single-quantum homonuclear dipolar recoupling, CSA recoupling, selection of J-couplings (TOBSY), homonuclear decoupling (CRAMPS), and simultaneous CSA and dipolar recoupling. We also show how the theorems may be extended to multiple-channel pulse sequences and demonstrate a sequence which implements heteronuclear recoupling between two dilute spin species, at the same as suppressing all homonuclear couplings and chemical shifts.

We also demonstrate a different method of double-quantum excitation in MAS NMR. We use rotational resonance to excite zero-quantum coherence mechanically, followed by phase-coherent transfer into double-quantum coherence. We have achieved 40% 2Q filtering efficiency, in the case of two 13C spins separated by 3 Angstroms.

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