Symmetry-based recoupling in double-rotation NMR spectroscopy

In this contribution, we extend the theory of symmetry-based pulse sequences of types CNn nu and RNn nu in magic-angle-spinning nuclear resonance spectroscopy [M. H. Levitt, in Encyclopedia of Nuclear Magnetic Resonance, edited by D. M. Grant and R. K. Harris (Wiley, Chichester, 2002), Vol. 9]. to the case of rotating the sample simultaneously around two different angles with respect to the external magnetic field (double-rotation). We consider the case of spin-1/2 nuclei in general and the case of half-integer quadrupolar nuclei that are subjected to weak radio frequency pulses operating selectively on the central-transition polarizations. The transformation properties of the homonuclear dipolar interactions and J-couplings under central-transition-selective spin rotations are presented. We show that the pulse sequence R2(2)(1)R2(2)(-1) originally developed for homonuclear dipolar recoupling of half-integer quadrupolar nuclei under magic-angle-spinning conditions [M. Eden, D. Zhou, and J. Yu, Chem. Phys. Lett. 431, 397 (2006)] may be used for the same purpose in the case of double rotation, if the radio frequency pulses are synchronized with the outer rotation of the sample. We apply this sequence, sandwiched by central-transition selective 90 degrees pulses, to excite double-quantum coherences in homonuclear spin systems consisting of Na-23 and Al-27 nuclei.