Molecular dynamics of half-integer quadrupolar nuclei studied by QCPMG solid-state NMR experiments on static and rotating samples. Theory and simulations

Second-order quadrupolar line shapes under molecular dynamics: An additional transition in the extremely fast regime

NMR spectroscopy is a powerful tool for probing molecular dynamics. For the classic case of two-site exchange, NMR spectra go through the transition from exchange broadening through coalescence and then motional narrowing as the exchange rate increases passing through the difference between the resonance frequencies of the two sites. For central-transition spectra of half-integer quadrupolar nuclei in solids, line shape change due to molecular dynamics occurs in two stages. The first stage occurs when the exchange rate is comparable to the second-order quadrupolar interaction. The second spectral transition comes at a faster exchange rate which approaches the Larmor frequency and generally reduces the isotropic quadrupolar shift. Such a two-stage transition phenomenon is unique to half-integer quadrupolar nuclei. A quantum mechanical formalism in full Liouville space is presented to explain the physical origin of the two-stage phenomenon and for use in spectral simulations. Variable-temperature ¹⁷O NMR of solid NaNO₃ in which the NO₃^- ion undergoes 3-fold jumps confirms the two-stage transition process. The spectra of NaNO₃ acquired in the temperature range of 173-413K agree well with simulations using the quantum mechanical formalism. The rate constants for the 3-fold NO₃^- ion jumps span eight orders of magnitude (10²-10¹⁰s^-1) covering both transitions of the dynamic ¹⁷O line shape.

Second-order quadrupole interaction based detection of ultra-slow motions: Tensor operator framework for central-transition spectroscopy and the dynamics in hexagonal ice as an experimental example

The second-order quadrupolar broadening of the central transition of nuclear probes with half-integer spins I is demonstrated to be useful to detect ultraslow molecular motions. On the basis of density matrix calculations explicit expressions are derived for quadrupolarly modulated sin-sin and cos-cos signals of selectively excited nuclei with I=3/2, 5/2, 7/2, and 9/2. These correlation functions are suitable for implementation in two-dimensional exchange spectroscopy as well as for stimulated-echo experiments. As an application, ¹⁷O measurements of the reorientational correlation function of water molecules in hexagonal ice are presented.

On the practical aspects of recording wideline QCPMG NMR spectra

The practical aspects of applying CPMG for acquisition of wideline powder patterns are examined. It is shown that most distortions/modulations of spikelet spectra can be traced to the incoherent signal averaging from multiple coherence transfer pathways. A strategy for minimizing these distortions/modulations is described. Also, a few interesting observations regarding the implementation of the wideline WURST-QCPMG experiment are presented, namely the accumulation of second-order signal phase and the effects of varying the sweep rate and rf field of chirp pulses.

Effects of jump dynamics on solid state nuclear magnetic resonance line shapes and spin relaxation times

This paper describes EXPRESS (EXchange Program for RElaxing Spin Systems), a computer program that simulates the effects of Markovian jump dynamics for a wide variety of solid state nuclear magnetic resonance experiments. A graphical interface is described that facilitates the definition of rotational jumps around non-commuting axes that may occur at arbitrary, different rates. Solid state deuteron NMR is widely used to investigate such processes, and EXPRESS allows simulations of deuteron quadrupole echo and magic angle spinning line (MAS) shapes, as well as partially relaxed line shapes for measurements of anisotropic relaxation of Zeeman and quadrupolar order. Facilities are included for chemical shift tensors (at user-defined orientations relative to the quadrupole coupling tensors), so that EXPRESS is potentially useful for studies of paramagnetic systems where these interactions are of comparable magnitude. Many of the same techniques used for deuterons can be extended to half-integer quadrupolar nuclei. The same interface that specifies rotational "sites" for deuteron NMR studies is usable in EXPRESS to simulate static line shapes, MAS line shapes, and multiple pulse Carr-Purcell-Meiboom-Gill (CPMG) line shapes for the central transition of high spin quadrupoles with second order quadrupole coupling and chemical shift anisotropy. Representative simulations are displayed that show effects of slow libration on deuteron quadrupole echo line shapes and relaxation time anisotropies. EXPRESS is also used to investigate fundamental differences in the mechanism of echo formation in deuteron MAS and quadrupole CPMG experiments, and to illustrate significant differences between these techniques in the context of high spin quadrupolar nuclei. The program is modular and platform-independent, with facilities for users to add routines for experiments not yet envisioned.

Simulations of molecular dynamics in solid-state NMR spectra of spin-1 nuclei including effects of CSA- and EFG-terms up to second order

By numerical simulations MAS and QCPMG methods for acquiring spectra of spin-1 nuclei were compared in order to determine the most sensitive experiment for analysis of molecular dynamics. To comply with the large quadrupolar constants for 14N and the CSA reported for 6Li both of these interactions are included up to second order. For 2H and 6Li both QCPMG and single-pulse MAS experiments were suitable for dynamics studies whereas the single-pulse MAS experiment were the method of choice for investigation of 14N dynamics for C(Q)'s larger than 750kHz at 14.1T. This property prohibits excitation of the 14N lineshape using either single hard or softer composite rf-pulses. Focusing on 14N it was demonstrated that the centerband lineshape is sensitive toward both off-MAS and CSA effects. In addition, excitation by real-time pulses showed that proper lineshapes corresponding to a site with a C(Q) of 3MHz may be excited by a very short pulse.

Dynamic Effects in MAS and MQMAS NMR Spectra of Half-Integer Quadrupolar Nuclei: Calculations and an Application to the Double Perovskite Cryolite

Dynamic processes such as chemical exchange or rotations between inequivalent orientations can affect the magic-angle spinning (MAS) and the multiple-quantum (MQ) MAS NMR spectra of half-integer quadrupolar nuclei. The present paper discusses such dynamic multisite MAS and MQMAS effects and applies them to study the dynamic processes that occur in the double perovskite cryolite, Na3AlF6. Dynamic line shape simulations invoking a second-order broadening of the central transition and relying on the semiclassical Bloch-McConnell formalism for chemical exchange were performed for a variety of exchange models possessing different symmetries. Fitting experimental variable-temperature cryolite 23Na NMR data with this formalism revealed that the two inequivalent sodium sites in this mineral undergo an exchange characterized by a broad distribution of rates. To further assess this dynamic process a variety of 27Al and 19F MAS NMR studies were also undertaken; quantitative 27Al-19F dipolar coupling measurements then revealed a dynamic motion of the AlF6 octahedra that were qualitatively consistent with predictions stemming from molecular dynamic simulations on this double perovskite.