Deuterium Cross-Polarization Magic-Angle Spinning

Abstract

In this publication a theoretical model is presented that describes cross-polarization magic-angle spinning (CPMAS) NMR experiments on a spin systemS(1)I_N, consisting of a set ofNabundant homonuclear spins withI= $\text{1}\text{2}$ coupled to a single rare spin withS= 1. The spin evolution during this magic-angle spinning experiment is described using Floquet theory. The model is an extension of the formalism that was recently introduced to describe CPMAS ofS($\text{1}\text{2}$)I_Nspin systems. First, experimental results of²H CPMAS experiments on partially deuterated dimethyl sulfone and malonic acid are shown. The rotational-echo intensities of the²H free-induction-decay signals were monitored and plotted as a function of the difference between the intensities of the RF fields applied on the deuterons and the protons during the mixing time. Then the Floquet description of a spin system withS= 1 is presented in order to enable the introduction of the Floquet model for CPMAS NMR. The Floquet Hamiltonian of the rotating quadrupolar spin is defined and the difference between spin locking in the rotating frame and in Floquet space is discussed. This is followed by a description of the spin evolution of theS(1)I_Nsystem during CPMAS experiments. The modified Hartmann–Hahn conditions for these experiments are derived and a methodology for calculating the cross-polarization S-spin signal intensities is demonstrated. The discussion is restricted to spin-1 nuclei with relatively small quadrupole interactions and is directed toward²H CPMAS. S-spin signal intensities as a function of mismatched Hartmann–Hahn conditions are evaluated for powder samples with quadrupolar frequencies of 40 and 120 kHz.