Cross-polarization phenomena in the NMR of fast spinning solids subject to adiabatic sweeps

Dipolar-order-based broadband adiabatic inversion as cross- polarization alternative in solid state Wideline NMR

Solid-state nuclear magnetic resonance (NMR) can shed light on atomic-level arrangements for most elements in the Periodic Table. This ability hinges on the possibility to overcome NMR's low sensitivity, particularly when dealing with unreceptive nuclei yielding ultra-wideline (>500 kHz) patterns from powdered samples. Herein, we present an experiment capable of enhancing the signals of such static samples, by transferring dipolar order from surrounding, highly polarized protons. The experiment, which we dub Dipolar-Order-based BRoadband Adiabatic INversion Cross-Polarization (DOBRAIN-CP), utilizes a Freeman-Kupče broadband inversion WURST pulse to perform CP over the wideline spectrum of the low receptivity species, while matching the low frequencies associated to 1H1H dipolar fields. We present analytical and numerical analyses of the spin-dynamics of DOBRAIN-CP for spin-½ nuclei, as well as for quadrupolar spins. Experimental results are also presented for spin-½, integer and half-integer quadrupolar spins; these show that although DOBRAIN-CP delivers broadband excitation and sensitivity enhancement compared to direct excitations, it does not exceed the sensitivity enhancement of the BRAIN-CP variant based on Hartmann-Hahn matching. The power requirements for DOBRAIN-CP are extremely low, yet long dipolar-order lifetimes T1D are needed to support the DOBRAIN-CP build-up times.

HORRENDOUS NMR: Establishing correlations in solution-state NMR by reinstating non-secular J-coupling terms

Homonuclear isotropic mixing modules allow J-coupled spins to exchange magnetization even when separated by chemical shift offsets that exceed their couplings. This is exploited in TOtal Correlation SpectroscopY (TOCSY) experiments and its variants, which facilitate these homonuclear polarization exchanges by applying broadband RF pulses. These then establish an effective Hamiltonian in which chemical shift offsets are erased, while J-coupling terms -including flip-flop components- remain active. The polarization that these non-secular terms will transfer among systems of chemically inequivalent sites over the course of a mixing period, are widely used modules in 1D and in multidimensional liquid-state NMR. Homonuclear correlation experiments are also common in solids NMR, particularly among X = ¹³C or ¹⁵N nuclei. Solids NMR experiments are often challenged by high-power RF demands which have led to a family of homonuclear solid-state correlation experiments that avoid pulsing on the nuclei of interest, and focus instead on the ¹Hs that are bonded to them. These solid experiments usually reintroduce/strengthen ¹H-X dipolar couplings; these, in conjunction with assistance from rotational resonance effects, bring back the truncated X-X dipolar interactions and facilitate the generation of cross peaks. The present study explores whether a similar goal can be achieved for solution-state counterparts, based on the reintroduction of truncated flip-flop terms in the J-coupling Hamiltonian via the pulsing on other, heteronuclear species. A proposal to achieve this is derived, and the resulting HOmonucleaR Recoupling by hEteroNuclear DecOUplingS (HORRENDOUS) approach to provide correlations between like nuclei without pulsing on them, is demonstrated.

Theory of radio-frequency pulses on periodically driven three-level systems: challenges and perspectives

Nuances of multiple-quantum transitions in periodically driven systems is discussed through analytical methods based on time propagators derived from Floquet theory.

Frequency-Swept Ultra-Wideline Magic-Angle Spinning NMR Spectroscopy

Recent years have witnessed the development of solid-state NMR techniques that allow the direct investigation of extremely wide inhomogeneously broadened resonance lines. To date, this typically involves the application of frequency sweeps as offered by wideband uniform rate smooth truncation (WURST) pulses. While the effects of such advanced irradiation schemes on static samples are well understood, the interference between the varying carrier frequency and the time-dependent evolution of the spin system under magic-angle spinning (MAS) conditions is more complex. Herein, we introduce the well-known WURST-Carr-Purcell-Meiboom-Gill (WCPMG) pulse sequence for spinning samples. Using numerical spin-density matrix analysis, an ideal design based on fast frequency sweeps and high truncation of the incorporated WURST pulses is presented that enables uniform excitation/refocusing under MAS conditions with low-to-moderate radio-frequency power requirements. This permits the acquisition of ultra-wideline MAS NMR lines exceeding 500 kHz with chemical shift resolution in a single transmitter step.

Broadband adiabatic inversion cross-polarization phenomena in the NMR of rotating solids

We explore the use of cross-polarization magic-angle spinning (CPMAS) methods incorporating an adiabatic frequency sweep in a standard Hartman-Hahn CPMAS pulse scheme, to achieve signal enhancements in solid-state NMR spectra of rare spins under fast MAS spinning rates, including spin-1/2, integer spin, and half-integer spin nuclides. These experiments, dubbed Broadband Adiabatic INversion Cross-Polarization Magic-Angle Spinning (BRAIN-CPMAS) experiments, involve an adiabatic inversion pulse on the S-channel of a rare spin nuclide while simultaneously applying a conventional spin-locking pulse on the I-channel (¹H). The signal enhancement imparted by this CP scheme on the S-spin is broadbanded, while employing low RF field strengths on both I- and S-channels. A feature demanded by these BRAIN-CPMAS methods is to impose a selective adiabatic frequency sweep over a single MAS spinning centerband or sideband, to avoid interference between the MAS modulation and sweeps over multiple sidebands. Upon implementing this swept-CP method, a number of MAS-driven processes happen, including broadband zero- and double-quantum CP transfers, and MAS-driven rotary-resonance phenomena. When this CP method is applied to integer and half-integer quadrupolar nuclei at very fast MAS spinning rates, a favorable double-quantum CP condition is found that can be easily achieved, and avoids the level-crossings among various m_s energy levels that complicate quadrupolar CPMAS NMR experiments along lines first shown by Alex Vega. An additional CP mechanism was found in the ¹H-²H case, involving static-like zero-quantum CP modes driven by a quadrupole-modulated RF-dipolar zero-order recoupling under MAS. All these phenomena were examined using average Hamiltonian theory, numerical simulations, and experiments on model compounds. Sensitivity-enhanced, distortion-free CP over wide bandwidths were predicted and observed for S = 1/2 and for S = 1 (²H) under fast MAS rates. BRAIN-CPMAS also delivered undistorted central transition NMR spectra of half-integer quadrupolar nuclei, while utilizing low RF field strengths that avoid complex level-crossing effects under high MAS rates.

Adiabatic sweep cross-polarization magic-angle-spinning NMR of half-integer quadrupolar spins

The use of frequency-swept radiofrequency (rf) pulses for enhancing signals in the magic-angle spinning (MAS) spectra of half-integer quadrupolar nuclides was explored. The broadband adiabatic inversion cross-polarization magic-angle spinning (BRAIN-CPMAS) method, involving an adiabatic inversion pulse on the S-channel and a simultaneous rectangular spin-lock pulse on the I-channel (¹H), was applied to I(1/2)→S(3/2) systems. Optimal BRAIN-CPMAS matching conditions were found to involve low rf pulse strengths for both the I- and S-spin channels. At these low and easily attainable rf field strengths, level-crossing events among the energy levels |3/2〉,|1/2〉,|-1/2〉,|-3/2〉 that are known to complicate the CPMAS of quadrupolar nuclei, are mostly avoided. Zero- and double-quantum polarization transfer modes, akin to those we have observed for I(1/2)→S(1/2) polarization transfers, were evidenced by these analyses even in the presence of the quadrupolar interaction. ¹H-²³Na and ¹H-¹¹B BRAIN-CPMAS conditions were experimentally explored on model compounds by optimizing the width of the adiabatic sweep, as well as the rf pulse powers of the ¹H and ²³Na/¹¹B channels, for different MAS rates. The experimental data obtained on model compounds containing spin-3/2 nuclides, matched well predictions from numerical simulations and from an average Hamiltonian theory model. Extensions to half-integer spin nuclides with higher spins and potential applications of this BRAIN-CPMAS approach are discussed.

Rapid acquisition of wideline MAS solid-state NMR spectra with fast MAS, proton detection, and dipolar HMQC pulse sequences

Fast MAS and proton detection are applied to rapidly acquire wideline solid-state NMR spectra of spin-1/2 and half-integer quadrupolar nuclei.

Solid-state NMR indirect detection of nuclei experiencing large anisotropic interactions using spinning sideband-selective pulses

Under Magic-Angle Spinning (MAS), a long radio-frequency (rf) pulse applied on resonance achieves the selective excitation of the center-band of a wide NMR spectrum. We show herein that these rf pulses can be applied on the indirect channel of Hetero-nuclear Multiple-Quantum Correlation (HMQC) sequences, which facilitate the indirect detection via spin-1/2 isotopes of nuclei exhibiting wide spectra. Numerical simulations show that this indirect excitation method is applicable to spin-1/2 nuclei experiencing a large chemical shift anisotropy, as well as to spin-1 isotopes subject to a large quadrupole interaction, such as (14)N. The performances of the long pulses are analyzed by the numerical simulations of scalar-mediated HMQC (J-HMQC) experiments indirectly detecting spin-1/2 or spin-1 nuclei, as well as by dipolar-mediated HMQC (D-HMQC) experiments achieving indirect detection of (14)N nuclei via (1)H in crystalline γ-glycine and N-acetyl-valine samples at a MAS frequency of 60kHz. We show on these solids that for the acquisition of D-HMQC spectra between (1)H and (14)N nuclei, the efficiency of selective moderate excitation with long-pulses at the (14)N Larmor frequency, ν0((14)N), is comparable to those with strong excitation pulses at ν0((14)N) or 2ν0((14)N) frequencies, given the rf field delivered by common solid-state NMR probes. Furthermore, the D-HMQC experiments also demonstrate that the use of long pulses does not produce significant spectral distortions along the (14)N dimension. In summary, the use of center-band selective weak pulses is advantageous for HMQC experiments achieving the indirect detection of wide spectra since it (i) requires a moderate rf field, (ii) can be easily optimized, (iii) displays a high robustness to CSAs, offsets, rf-field inhomogeneities, and fluctuations in MAS frequency, and (iv) is little dependent on the quadrupolar coupling constant.

Spin-locking and cross-polarization under magic-angle spinning of uniformly labeled solids

Spin-locking and cross-polarization under magic-angle spinning are investigated for uniformly (13)C and (15)N labeled solids. In particular, the interferences from chemical shift anisotropy, and (1)H heteronuclear and (13)C homonuclear dipolar couplings are identified. The physical origin of these interferences provides guidelines for selecting the best (13)C and (15)N polarization transfer rf fields. Optimal settings for both the zero- and double-quantum cross-polarization transfer mechanisms are recommended.