Using Symmetry to Design Pulse Sequences in SolidState 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 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.
