Theoretical studies of the spin dynamics of quadrupolar nuclei at rotational resonance conditions

A theory of the spin dynamics of $\text{I=3/2}$ quadrupolar nuclei in the sudden-passage limit is discussed in relation to the recently observed rotational resonance (RR) effects on the excitation and conversion of triple-quantum coherence in the FASTER multiple-quantum magic-angle spinning (MQMAS) experiments [T. Vosegaard, P. Florian, D. Massiot, and P. J. Grandinetti, J. Chem. Phys. 114, 4618 (2001)]. A novel interaction frame, which combines the quadrupolar interaction with the central transition radio frequency irradiation, is shown to be useful in understanding the complex spin dynamics at and away from RR conditions. Analytical expressions for the Hamiltonian obtained from bimodal Floquet theory are included in order to provide insight into the spin dynamics observed in the FASTER MQMAS experiments. Numerical simulations have been performed and were found to support the theoretical formalism.