Investigation of multiaxis molecular motion by off-magic angle spinning deuteron NMR

The relatively new deuteron NMR method of off-axis-magic angle spinning (OMAS) has been extended and used to investigate multiaxis rotational jump motion. Floquet theory is developed for simulating deuteron OMAS spectra with multisite jumps at different rates about noncoincident axes, and efficient procedures are presented for computing the sideband line shapes. It is demonstrated experimentally that reproducible adjustment of the angle between the rotor axis and the static magnetic field is feasible with precision approaching ± 0.01 ° . This leads to the reintroduction of a scaled, first-order quadrupole coupling that defines a new kinetic window and makes deuteron OMAS much more sensitive than ordinary magic angle spinning to motion on the kilohertz time scale. Temperature-dependent deuteron OMAS line shapes of octanoic acid/urea- d 4 inclusion compound have been recorded and fitted, using least-squares procedures, to provide rates of rotation about both CN and CO bonds. The Arrhenius activation parameters for rotation about CN bonds, E a = 60.4 ± 2.4 kJ ∕ mol and ln ( A ) = 24.9 ± 0.3 , agree well with previous values determined by selective inversion experiments. However, OMAS yields E a = 26.3 ± 0.4 kJ ∕ mole and ln ( A ) = 24.9 ± 0.3 for whole-body rotation about the CO bond axis in contrast to previous analysis of static quadrupole echo (QE) line shapes which gave E a = 22.3 ± 0.3 kJ ∕ mole and ln ( A ) = 24.8 ± 0.6 for the same sample. The underlying homogeneous linewidths of OMAS spectra are much smaller than those of QE spectra, and this provides higher precision and less systematic error in the determination of rates.