Abstract 

Symmetry Principles for the design of radiofrequency pulse sequences in the nuclear magnetic resonance of rotating solids,
Chem. Phys. Lett.
321,
205215,
(2000).
Some new symmetry theorems are presented which simplify the task of designing multiplepulse radiofrequency pulse sequences in magicanglespinning solidstate NMR. The symmetry theorems apply to sequences denoted RN_{n}^{ν}, where N, n and ν are integral symmetry numbers. A RN_{n}^{ν} sequence consists of N repetitions of a pulse sequence element R, alternating in phase between the values ±πν/N. Each R element ideally rotates the spins by an angle π about the rotating frame xaxis. The entire RN_{n}^{ν} sequence is timed to span n rotational periods. The symmetry theorems allow the construction of sequences suitable for a wide range of purposes in solidstate NMR. Specific applications are presented for homonuclear doublequantum recoupling, heteronuclear decoupling and heteronuclear recoupling. For the case of homonuclear doublequantum recoupling, we demonstrate a highperformance sequence with the symmetry R14_{2}^{6}. For the case of heteronuclear decoupling, we show that the existing theory provides a framework for understanding the operation of the twopulse phase modulation (TPPM) scheme (A. E. Bennett, C. M. Rienstra, M. Auger, K. V. Lakshmi and R. G. Griffin, J. Chem. Phys. 103, 6951 (1998)). We also demonstrate a heteronuclear dipolar recoupling sequence with the symmetry R18_{1}^{7}. 

Dr. Andreas Brinkmann Measurement Science and Standards National Research Council 1200 Montreal Road, M40 Ottawa, Ontario K1A 0R6 Canada Tel. +16139900319 Fax. +16139901555 Andreas.Brinkmann@nrccnrc.gc.ca 

Dr. Andreas Brinkmann, NRCMSS, 1200 Montreal Road, M40,
Ottawa, ON K1A 0R6, Canada Andreas.Brinkmann@nrccnrc.gc.ca 