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

Some general principles of radio-frequency pulse sequence design in magic-a ngle spinning nuclear magnetic resonance are discussed. Sequences with favo rable dipolar recoupling properties may be designed using synchronous helic al modulations of the space and spin parts of the spin Hamiltonian. The sel ection rules for the average Hamiltonian may be written in terms of three s ymmetry numbers, two defining the winding numbers of the space and spin hel ices, and one indicating the number of phase rotation steps in the radio-fr equency modulation. A diagrammatic technique is used to visualize the space -spin symmetry selection. A pulse sequence C14(4)(5) is designed which acco mplishes double-quantum recoupling using a low ratio of radio frequency fie ld to spinning frequency. The pulse sequence uses 14 radio frequency modula tion steps with space and spin winding numbers of 4 and 5, respectively. Th e pulse sequence is applied to the double-quantum spectroscopy of C-13(3)-l abeled 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 qu antum peaks in recoupled multiple-spin systems are discussed. A supercycle scheme which compensates homonuclear recoupling sequences for chemical shif ts is introduced. We show an experimental double-quantum C-13 spectrum of [ U-C-13]-L-tyrosine at a spinning frequency of 20.000 kHz. (C) 2000 American Institute of Physics. [S0021- 9606(00)01214-9].