Measurement of molecular motion in solids by nuclear magnetic resonance spectroscopy of half-integer quadrupole nuclei

Abstract

Articles you may be interested inSpin-locking of half-integer quadrupolar nuclei in nuclear magnetic resonance of solids: Second-order quadrupolar and resonance offset effects Measuring distances between half-integer quadrupolar nuclei and detecting relative orientations of quadrupolar and dipolar tensors by double-quantum homonuclear dipolar recoupling nuclear magnetic resonance experiments Double-quantum-filtered nuclear magnetic resonance spectroscopy applied to quadrupolar nuclei in solids An accurate and efficient formalism is presented for simulating the effects of molecular motion on satellite and central transition nuclear magnetic resonance ͑NMR͒ spectra of half-integer quadrupole nuclei. The approach is based on the principles of the density operator and the stochastic Liouvillevon Neumann equation and may be applied for both rotating and nonrotating samples. The symmetry properties of nuclear spin ensembles have been used to rewrite the stochastic Liouvillevon Neumann equation in the form of a linear homogeneous system of coupled first-order differential equations among the alignments and coherences. This system is highly stiff and can only be solved by methods that are sufficiently accurate and stable. The properties of Cartan-Weyl operators have been used to obtain the most efficient solution for secular interactions. The methodology has been incorporated into computer programs to simulate the effects of motion for any half-integer quadrupole nucleus. These programs include the first-and second-order quadrupole and first-order shielding interactions. The formalism has been used to calculate central transition 17 O NMR spectra of representative model systems. The calculations have revealed several interesting and important properties of central transition NMR spectra that have been discussed in terms of the functional form of the line shape. The validity of the methodology has been demonstrated experimentally by simulating variable temperature central transition 17 O NMR spectra of the silicate (SiO 2 ) mineral cristobalite for both rotating and nonrotating samples. The simulations have allowed the structural and dynamical details of the ␣-␤ phase transition in cristobalite to be separated. The line shapes can only be simulated if the effects of motion are included and are consistent with a model where the oxygen atoms reorient between six different orientations. It is found that the oxygen motion is present both before and after the ␣-␤ phase transition and does not change significantly at the transition temperature. The observed changes in the quadrupole and shielding parameters are shown not to be the results of motional averaging but derive from an abrupt structural change associated with the first-order character of the ␣-␤ phase transition. The structural changes may be interpreted in terms of a model where the Si-O-Si bond angle increases slightly.

29Si and 17O (Q)CPMG-MAS solid-state NMR experiments as an optimum approach for half-integer nuclei having long T1 relaxation times

“…By iterative fitting employing real-time pulses the quadrupole coupling constant (C Q ), the asymmetry parameter for the quadrupole tensor (g Q ), the isotropic chemical shift (d dynamics [11,12]. Taking dynamics into account at room temperature the parameters for a-cristobalite are given by C Q ¼ 5:35 MHz, g Q ¼ 0:21, d iso ¼ 37:5 ppm, d r ¼ 50 ppm, g r ¼ 0:9 having a relative orientation of the two tensors defined by the Euler angles X PC r ¼ ð270; 7; 90Þ° [12].…”

DFT calculations of quadrupolar solid‐state NMR properties: Some examples in solid‐state inorganic chemistry

“…Such an effect (a few kHz) is known to average out NMR second order quadrupole effects. 47,48 A partial dynamic averaging of the quadrupolar line shape leads to an ''apparent'' C Q value smaller than the computed one using DFT methods.…”

Water molecular reorientation in ice and tetrahydrofuran clathrate hydrate from lineshape analysis of 17O spin-echo NMR spectra

“…Besides the problem of water molecular reorientations, there is a wide interest in the fundamental spectroscopy, that is, to observe and understand the evolution of spectral patterns for half-integer nuclei from a static pattern to one where the quadrupolar coupling is completely averaged. [38][39][40][41][42][43] Because of the ubiquitous presence of water in its various phases, we expect considerable relevance of these results to water-containing systems.…”