Cross-term Splittings Due to the Orientational Inequivalence of Proton Magnetic Shielding Tensors: Do Water Molecules Trapped in Crystals Hop or Tunnel?

Abstract

Water molecules trapped in crystals of barium chlorate monohydrate have been investigated by magic-angle spinning (MAS) proton NMR spectroscopy in the temperature range 110-300 K. At high temperatures, a single spinning sideband pattern is observed. Below 150 K, however, two interleaved spinning sideband manifolds appear, with distinct centerbands that do not coincide with the average isotropic chemical shift seen at high temperatures. This hitherto unknown "cross-term splitting" results from the interplay of the homonuclear dipole-dipole coupling and two anisotropic proton shielding tensors that have identical principal components but nonequivalent orientations. The resulting cross terms cannot be averaged out by rotation about the magic angle. The analysis of the exchange-induced broadening, coalescence, and narrowing of the cross-term splitting in MAS spectra allows one to estimate the rate of exchange of the two protons between 140 and 190 K. The experimental data is compared with 2H and 1H NMR studies of the same sample reported in the literature. Density functional theory methods are utilized to estimate the thermal activation energy for a 2-fold hopping process of proton exchange about the H-O-H bisector. The Bell-Limbach model allows one to take into account contributions due to incoherent quantum tunneling in the low-temperature regime.