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

Abstract

Cross-term splittings due to the orientational inequivalence of proton magnetic shielding tensors: Do water molecules trapped in crystals hop or tunnel?2 AbstractWater molecules trapped in crystals of barium chlorate monohydrate have been investigated by magic angle spinning 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 dipoledipole coupling and two anisotropic proton shielding tensors that have identical principal components but non-equivalent 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 2 H and 1 H NMR studies of the same sample reported in the literature. DFT methods are utilized to estimate the thermal activation energy for a two-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.

Orientation-Dependent Proton Relaxation of Water Molecules Trapped in Solids: Crystallites with Long-Lived Magnetization

“…Since the fluctuations of the CSA interactions provide the driving force of relaxation, we have repeated our relaxation measurements at B0 = 18.8 T (800 MHz for 1 H) and, surprisingly, found substantially identical results, with a bi-exponential behavior of the integral over the entire width of the Pake pattern described by T1 (1) = 9.9  0.6 s and T1 (2) Indeed, simulations show that for kex = 4.5  10 8 s -1 (i.e., 10 times slower than the value estimated at T = 298 K by extrapolation in our earlier study), 23 the relaxation rates are predicted to increase by no more than 10% between 400 and 800 MHz. This mismatch is reasonable if one considers that we did not observe changes in spectral features for temperatures above 200 K.…”

“…15 ppm or 6 kHz at 9.4 T) that affect the Pake pattern can be investigated by means of NMR spectroscopy as they result in a clear asymmetry of the 'shoulders' of the powder pattern at high fields. [19][20][21][22] Furthermore, peculiar cross-term splittings which stem from the orientational inequivalence of the two proton CSA tensors have been recently observed by 1 H MAS NMR spectroscopy at temperatures below 150 K. 23 In this study, the orientation dependence of T1 across the static lineshape is determined experimentally and rationalized theoretically. In some parts of the Pake pattern, the relaxation behavior is bi-exponential, in other parts it is mono-exponential.…”

Spin Thermometry: A Straightforward Measure of Millikelvin Deuterium Spin Temperatures Achieved by Dynamic Nuclear Polarization

“…On the other hand, well-resolved dipolar Pake patterns can be observed in 1 H NMR of water molecules that are isolated in suitable matrices such as crystals of barium chlorate monohydrate. [25][26][27][28] As we shall discuss in a separate paper, the spin temperature of the protons in such isolated water molecules can be lowered by DNP after suspending the crystallites in a solution of radicals prior to freezing.…”

Natural abundance oxygen-17 solid-state NMR of metal organic frameworks enhanced by dynamic nuclear polarization

“…These sideband patterns are due to second-order cross terms between quadrupolar and shift interactions that cannot be averaged out by magic-angle spinning. [38,39] For the 3-OH sites, on the other hand, the central transitions can be clearly identified in the simulated spectra. An unprotonated 3-O site is predicted to have an almost negligible quadrupolar broadening, resulting in nearly isotropic lines (orange spectrum in Fig.…”