In this publication a theoretical model is presented that deapproach and apply it to a system S(1)I N containing N abunscribes cross-polarization magic-angle spinning ( CPMAS ) dant I Γ
1 2 spins that are coupled to a single spin with S Γ
NMR experiments on a spin system S ( 1 ) I N , consisting of a set 1. We restrict ourselves to spin parameters that correspond of N abundant homonuclear spins with I Γ
1 2 coupled to a single to proton-deuterium spin systems. rare spin with S Γ
1. The spin evolution during this magic-Deuterium ( S Γ
1 ) MAS sideband spectra of deuterated angle spinning experiment is described using Floquet theory. compounds were already observed more than fifteen years The model is an extension of the formalism that was recently ago by Ackerman et al. ( 2 ) . Rotational-echo amplitudes introduced to describe CPMAS of S ( 1 2 ) I N spin systems. First, and sideband patterns were studied ( 3 -5 ) , and MAS exexperimental results of 2 H CPMAS experiments on partially periments were applied to enhance the sensitivity and resdeuterated dimethyl sulfone and malonic acid are shown. The olution of 2 H spectra ( 6 -8 ) and to achieve solid-state rotational-echo intensities of the 2 H free-induction-decay sigimages ( 9 ) . 2 H MAS spectroscopy has also been utilized nals were monitored and plotted as a function of the difference for chemical-exchange studies ( 10 -13 ) . Poupko et al. between the intensities of the RF fields applied on the deuterons and the protons during the mixing time. Then the Floquet de-( 14) demonstrated that 2 H MAS spectra can be obtained scription of a spin system with S Γ
1 is presented in order to from deuterons in natural abundance in organic materials enable the introduction of the Floquet model for CPMAS NMR. and they suggested applying this approach for measure-The Floquet Hamiltonian of the rotating quadrupolar spin is ments of ultraslow dynamic processes. Schmidt et al. ( 15 ) defined and the difference between spin locking in the rotating extended the MAS REDOR experiments to 2 H -13 C spin frame and in Floquet space is discussed. This is followed by a pairs and analyzed their deuterium signals in terms of description of the spin evolution of the S ( 1 )I N system during internuclear distances. CPMAS experiments. The modified Hartmann -Hahn condi-Mu Β¨ller ( 16 ) discussed proton -deuterium polarization tions for these experiments are derived and a methodology for transfer during magic-angle spinning. He showed that deucalculating the cross-polarization S-spin signal intensities is terons with large quadrupole frequencies can be spin demonstrated. The discussion is restricted to spin-1 nuclei with relatively small quadrupole interactions and is directed toward locked in the rotating frame. His theoretical model and 2 H CPMAS. S-spin signal intensities as a function of misexperimental results indicate that deuterium signals can matched Hartmann -Hahn conditions are evaluated for powder be enhanced by CPMAS and that off-resonance CP is samples with quadrupolar frequencies of 40 and 120 kHz. preferred in the case of large quadrupole interactions. Re-