In this publication a theoretical model is presented that describes cr
oss-polarization magic-angle spinning (CPMAS) NMR experiments on a spi
n system S(1)I-N, consisting of a set of N abundant homonuclear spins
with I = 1/2 coupled to a single rare spin with S = 1. The spin evolut
ion during this magic-angle spinning experiment is described using Flo
quet theory. The model is an extension of the formalism that was recen
tly introduced to describe CPMAS of S(1/2)I-N spin systems. First, exp
erimental results of H-2 CPMAS experiments on partially deuterated dim
ethyl sulfone and malonic acid are shown. The rotational-echo intensit
ies of the H-2 free-induction-decay signals were monitored and plotted
as a function of the difference between the intensities of the RF fie
lds applied on the deuterons and the protons during the mixing rime. T
hen the Floquet description of a spin system with S = 1 is presented i
n order to enable the introduction of the Floquet model for CPMAS NMR.
The Floquet Hamiltonian of the rotating quadrupolar spin is defined a
nd the difference between spin locking in the rotating frame and in Fl
oquet space is discussed, This is followed by a description of the spi
n evolution of the S(1)I-N system during CPMAS experiments. The modifi
ed Hartmann-Hahn conditions for these experiments are derived and a me
thodology for calculating the cross-polarization S-spin signal intensi
ties is demonstrated, The discussion is restricted to spin-1 nuclei wi
th relatively small quadrupole interactions and is directed toward H-2
CPMAS. S-spin signal intensities as a function of mismatched Hartmann
-Hahn conditions are evaluated for powder samples with quadrupolar fre
quencies of 40 and 120 kHz. (C) 1996 Academic Press, Inc.