Abstract 

Using Symmetry to Design Pulse Sequences in SolidState NMR,
41st Experimental NMR Conference, Asilomar, California, USA
(Apr. 2000),
talk.
We have discovered some new symmetry theorems which greatly simplify the task of designing rotorsynchronized pulse sequences in solidstate 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 CN_{n}^{ν}, which are based on a cyclic sequence element, and sequences denoted RN_{n}^{ν}, 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 C7_{2}^{1} for efficient doublequantum excitation in MAS solids. We now demonstrate a sequence with the symmetry C14_{4}^{5} for work at high spinning frequency (examples will be given at 20 kHz spinning). In addition, we demonstrate the new symmetry R14_{2}^{6} which is more efficient than the C7_{2}^{1}based sequences at moderate spinning frequency. We also demonstrate heteronuclear recoupling at high spinning frequency using a sequence of the symmetry R18_{1}^{7}, and show how the new theorems illuminate the operation of TPPM heteronuclear decoupling. Additional symmetries will be described for other tasks, such as singlequantum homonuclear dipolar recoupling, CSA recoupling, selection of Jcouplings (TOBSY), homonuclear decoupling (CRAMPS), and simultaneous CSA and dipolar recoupling. We also show how the theorems may be extended to multiplechannel 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 doublequantum excitation in MAS NMR. We use rotational resonance to excite zeroquantum coherence mechanically, followed by phasecoherent transfer into doublequantum coherence. We have achieved 40% 2Q filtering efficiency, in the case of two ^{13}C spins separated by 3 Angstroms. 

Dr. Andreas Brinkmann Metrology National Research Council Canada W. G. Schneider Building M40 1200 Montreal Road Ottawa, Ontario K1A 0R6 Canada Tel. +16139900319 Fax. +16139901555 Andreas.Brinkmann@nrccnrc.gc.ca 

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