Synchronous helical pulse sequences in magic-angle spinning nuclear magnetic resonance: Double quantum recoupling of multiple-spin systems,

A. Brinkmann, M. Edén, and M. H. Levitt,
J. Chem. Phys. 112, 8539-8554, (2000).
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Some general principles of radio-frequency pulse sequence design in magic-angle spinning NMR are discussed. Sequences with favourable dipolar recoupling properties may be designed using synchronous helical modulations of the space and spin parts of the spin Hamiltonian. The selection rules for the average Hamiltonian may be written in terms of three symmetry numbers, two defining the winding numbers of the space and spin helices, and one indicating the number of phase rotation steps in the radio-frequency modulation. A diagrammatic technique is used to visualize the space-spin symmetry selection. A pulse sequence C1445 is designed which accomplishes double-quantum recoupling using a low ratio of radio frequency field to spinning frequency. The pulse sequence uses 14 radio frequency modulation steps with space and spin winding numbers of 4 and 5 respectively. The pulse sequence is applied to the double-quantum spectroscopy of 13C3-labelled L-alanine. Good agreement is obtained between the experimental peak intensities, analytical results, and numerically exact simulations based on the known molecular geometry. The general symmetry properties of double quantum peaks in recoupled multiple-spin systems are discussed. A supercycle scheme which compensates homonuclear recoupling sequences for chemical shifts is introduced. We show an experimental double-quantum 13C spectrum of [U-13C]-L-tyrosine at a spinning frequency of 20.000 kHz.