Field dependent isotropic shifts in solid state nuclear magnetic resonance: A Floquet treatment

Progress in spin dynamics solid-state nuclear magnetic resonance with the application of Floquet-Magnus expansion to chemical shift anisotropy

The purpose of this article is to present an historical overview of theoretical approaches used for describing spin dynamics under static or rotating experiments in solid state nuclear magnetic resonance. The article gives a brief historical overview for major theories in nuclear magnetic resonance and the promising theories. We present the first application of Floquet-Magnus expansion to chemical shift anisotropy when irradiated by BABA pulse sequence.

Heteronuclear spin decoupling in solid-state NMR under magic-angle sample spinning

Achieving high spectral resolution is an important prerequisite for the application of solid-state NMR to biological molecules. Higher spectral resolution allows to resolve a larger number of resonances and leads to higher sensitivity. Among other things, heteronuclear spin decoupling is one of the important factors which determine the resolution of a spectrum. The process of heteronuclear spin decoupling under magic-angle sample spinning is analyzed in detail. Continuous-wave RF irradiation leads only in a zeroth-order approximation to a full decoupling of heteronuclear spin systems in solids under magic-angle spinning (MAS). In a higher-order approximation, a cross-term between the dipolar-coupling tensor and the chemical-shielding tensor is reintroduced, providing a scaled coupling term between the heteronuclear spins. In strongly coupled spin systems this second-order recoupling term is partially averaged out by the proton spin-diffusion process, which leads to exchange-type narrowing of the line by proton spin flips. This process can be described by a spin-diffusion type superoperator, allowing the efficient simulation of strongly coupled spin systems under heteronuclear spin decoupling. Low-power continuous-wave decoupling at fast MAS frequencies offers an alternative to high-power irradiation by reversing the order of the averaging processes. At fast MAS frequencies low-power continuous-wave decoupling leads to significantly narrower lines than high-power continuous-wave decoupling while at the same time reducing the power dissipated in the sample by several orders of magnitude. The best decoupling is achieved by multiple-pulse sequences at high RF fields and under fast MAS. Two such sequences, two-pulse phase-modulated decoupling (TPPM) and X-inverse-X decoupling (XiX), are discussed and their properties analyzed and compared.

Anomalous rotational resonance spectra in magic-angle spinning NMR

Magic-angle spinning NMR spectra of samples containing dilute spin-1/2 pairs display broadenings or splittings when a rotational resonance condition is satisfied, meaning that a small integer multiple of the spinning frequency matches the difference in the two isotropic shift frequencies. We show experimental rotational resonance NMR spectra of a 13C2-labeled retinal which are in qualitative disagreement with existing theory. We propose an explanation of these anomalous rotational spectra involving residual heteronuclear couplings between the 13C nuclei and the neighboring 1H nuclei. These couplings strongly influence the rotational resonance 13C spectrum, despite the presence of a strong radiofrequency decoupling field at the 1H Larmor frequency. We model the residual heteronuclear couplings by differential transverse relaxation of the 13C single-quantum coherences. We present a superoperator theory of the phenomenon and describe a numerical algorithm for rapid Liouville space simulations in periodic systems. Good agreement with experimental results is obtained by using a biexponential transverse relaxation model for each spin site.

A close look at 13C CPMAS linewidths in solids for rigid, strongly coupled carbons under CW proton decoupling

Ambient-temperature 13C linewidth (LW) and transverse relaxation (TC2) data are presented for the natural-abundance crystalline carbons of linear polyethylene (LPE) under CW proton decoupling conditions and magic angle spinning (MAS). This linewidth behavior typifies that seen for rigid methylene carbons whose attached protons are also strongly coupled to other protons. These data are presented for two LPE samples (unoriented, melt-crystallized and uniaxially oriented, extruded) as a function of several parameters including static field (1.4 T < B0 < 9.4 T), proton decoupling field strength (38 kHz < nuH1 < 90 kHz), MAS frequency (0.5 kHz < nur < 8 kHz) and RF frequency offsets from resonance (-4 kHz < Deltanuoff < 4 kHz). It is the ubiquitous nature of off-resonance proton irradiation (ORPI) (arising from fixed or rotationally dependent deviations from the true proton resonance condition) which provides the focus for this work. Corresponding contributions, LW(ORPI), to the total LW are treated within the general framework of the effective-field picture of CW decoupling. Then, considering the presence of spin fluctuations characteristic of the strongly-dipolar-coupled protons of LPE, LW(ORPI) can be traced to orbit-dependent TC2 contributions to LW. Important dependences demonstrated and discussed include: (1) For "off-resonance" decoupling, there is a quadratic dependence of LW(ORPI) on (Deltanuoff/nuH1) and there is a strong dependence of the corresponding parabolic coefficient on nur. From the latter dependence, characteristic times for spin fluctuations are also estimated. (2) For "on-resonance" decoupling, LW(ORPI) is proportional to (nuH1)-2 and shows very little sensitivity to nur. These LW(ORPI) contributions become more important at higher B0 since the principle reason for ORPI is the chemical shift anisotropy (CSA) of the 13C-bonded protons. The difference in sensitivities of LW(ORPI) to nur for the off-resonance and the on-resonance cases is traced back, respectively, to the scalar property of Deltanuoff for RF frequency offsets and to the tensorial character of the proton CSA. Contributions from LW(ORPI), possibly much larger than those seen in LPE, can be expected when protons near 13C nuclei sense any non-scalar, rotor-position-dependent magnetic fields, e.g., (a) local dipolar fields associated with third, magnetic nuclei or (b) perturbing magnetic-susceptibility fields arising from paramagnetic or ferromagnetic inclusions in a sample. By understanding the contributions to LW in LPE, one can forecast much more precisely what the potential benefits will be from new decoupling schemes like the recently reported "two-pulse phase modulation" (TPPM) since TPPM is designed to reduce LW(ORPI). Aside from LW(ORPI) contributions, the experimental LW data cover parameter space where another broadening mechanism, namely, MAS-assisted dipolar fluctuations (MADF), is seen. This mechanism, also recognized by others, creates a TC2-type linewidth contribution which increases rapidly as nuH1 decreases and which additionally has some orbit dependence. If the current trend in 13CCPMAS is toward higher B0 and nur, the nur-dependent MADF contributions can easily dominate LW relative to the B0-dependent LW(ORPI) contributions. One can avoid serious MADF broadening; however, the minimum acceptable values of nuH1 for good decoupling rise rapidly with B0. Finally, a few LW measurements are made on methyl-alpha-d-glucopyranoside tetraacetate (MGT), a rigid, polycrystalline material containing carbons with 0, 1, 2, and 3 attached protons. The behaviors of the methylene, methine, and methyl carbons at 9.4 T are compared with the behavior of LPE. Copyright 1998 Academic Press.