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There are currently no methods for the acquisition of ultra-wideline (UW) solid-state NMR spectra under static conditions that enable reliable separation and resolution of overlapping powder patterns arising from magnetically distinct nuclei. This stands in contrast to the variety of techniques available for spin-1/2 or half-integer quadrupolar nuclei with narrow central transition patterns under magic-angle spinning (MAS). Resolution of overlapping signals is routinely achieved in MRI and solution-state NMR by exploiting relaxation differences between nonequivalent sites. Preliminary studies of relaxation assisted separation (RAS) for separating overlapping UWNMR patterns using pseudo-inverse Laplace Transforms have reported two-dimensional spectra featuring relaxation rates correlated to NMR interaction frequencies. However, RAS methods are inherently sensitive to experimental noise, and require that relaxation rates associated with overlapped patterns be significantly different from one another. Herein, principal component analysis (PCA) denoising is implemented to increase the signal-to-noise ratios of the relaxation datasets and RAS routines are stabilized with truncated singular value decomposition (TSVD) and elastic net (EN) regularization to resolve overlapped patterns with a larger tolerance for differences in relaxation rates. We extend these methods for improved pattern resolution by utilizing 3D frequency- R 1 – R 2 correlation spectra. Synthetic and experimental datasets, including 35 Cl ( I = 3/2), 2 H ( I = 1), and 14 N ( I = 1) NMR of organic and biological compounds, are explored with both regularized 2D RAS and 3D RAS; comparison of these data reveal improved resolution in the latter case. These methods have great potential for separating overlapping powder patterns under both static and MAS conditions. 

Solid‐state NMR (SSNMR) spectroscopy of integer‐spin quadrupolar nuclei is important for the molecular‐level characterization of a variety of materials and biological solids; of the integer spins,²H (S = 1) is by far the most widely studied, due to its usefulness in probing dynamical motions. SSNMR spectra of integer‐spin nuclei often feature very broad powder patterns that arise largely from the effects of the first‐order quadrupolar interaction; as such, the acquisition of high‐quality spectra continues to remain a challenge. The broadband adiabatic inversion cross‐polarization (BRAIN‐CP) pulse sequence, which is capable of cross‐polarization (CP) enhancement over large bandwidths, has found success for the acquisition of SSNMR spectra of integer‐spin nuclei, including¹⁴N (S = 1), especially when coupled with Carr–Purcell/Meiboom–Gill pulse sequences featuring frequency‐swept WURST pulses (WURST‐CPMG) forT₂‐based signal enhancement. However, to date, there has not been a systematic investigation of the spin dynamics underlying BRAIN‐CP, nor any concrete theoretical models to aid in its parameterization for applications to integer‐spin nuclei. In addition, the BRAIN‐CP/WURST‐CPMG scheme has not been demonstrated for generalized application to wideline or ultra‐wideline (UW)²H SSNMR. Herein, we provide a theoretical description of the BRAIN‐CP pulse sequence for spin‐1/2 → spin‐1 CP under static conditions, featuring a set of analytical equations describing Hartmann–Hahn matching conditions and numerical simulations that elucidate a CP mechanism involving polarization transfer, coherence exchange, and adiabatic inversion. Several experimental examples are presented for comparison with theoretical models and previously developed integer‐spin CP methods, demonstrating rapid acquisition of²H NMR spectra from efficient broadband CP.

 

Field‐stepped NMR spectroscopy at up to 36 T using the series‐connected hybrid (SCH) magnet at the U.S. National High Magnetic Field Laboratory is demonstrated for acquiring ultra‐wideline powder spectra of nuclei with very large quadrupolar interactions. Historically, NMR evolved from the continuous‐wave (cw) field‐swept method in the early days to the pulsed Fourier‐transform method in the modern era. Spectra acquired using field sweeping are generally considered to be equivalent to those acquired using the pulsed method. Here, it is shown that field‐stepped wideline spectra of half‐integer spin quadrupolar nuclei acquired using WURST/CPMG methods can be significantly different from those acquired with the frequency‐stepped method commonly used with superconducting magnets. The inequivalence arises from magnetic field‐dependent NMR interactions such as the anisotropic chemical shift and second‐order quadrupolar interactions; the latter is often the main interaction leading to ultra‐wideline powder patterns of half‐integer spin quadrupolar nuclei. This inequivalence needs be taken into account to accurately and correctly determine the quadrupolar coupling and chemical shift parameters. A simulation protocol is developed for spectral fitting to facilitate analysis of field‐stepped ultra‐wideline NMR spectra acquired using powered magnets. A MATLAB program which implements this protocol is available on request.