Double quantum cross polarization. Heteronuclear excitation and detection of NMR double quantum transitions in solids

Unravelling the mechanism of polarization transfer from spin-1/2 to spin-1 system in solids

An analytic theory based on the concept of "effective-fields" is proposed to explain the mechanism of polarization transfer from spin I = 1/2 to spin S = 1 in non-rotating (static) solids. Employing an isolated two-spin model system, the matching conditions responsible for polarization transfer in cross-polarization (CP) experiments are identified and described in terms of the single-transition operators. In contrast to other existing treatments, the polarization transfer among spins is quantified through analytic expressions highlighting the individual contributions emerging from all plausible CP matching conditions. The interplay between the CP matching conditions observed in experiments is outlined in both isotropic and anisotropic systems and verified through comparison between simulations based on analytic and exact numerical methods. The predictions emerging from the analytic theory are verified over a wide range of experimentally relevant parameters and could be beneficial in the optimization of the CP experiments.

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.

Sensitivity enhancement via multiple contacts in the {1H–29Si}–1H cross polarization experiment: a case study of modified silica nanoparticle surfaces

{¹H–²⁹Si}–¹H double cross polarization inverse detection (DCPi) solid-state NMR, has recently been shown to be a powerful tool for studying molecules adsorbed on the silica surface. In this contribution, we develop an improved version (MCPi) which incorporates a block of multiple contact pulses, and quantitatively compare the sensitivities of MCPi and DCPi over a typical range of experimental parameters. The MCPi pulse sequence aims at higher sensitivity and robustness for studying samples with various relaxation characteristics. In the case of dimethyl sulfoxide (DMSO) molecules adsorbed on the silica surface, MCPi performs equally well or up to 2.5 times better than DCPi over a wide range of parameters. The applicability to and performance of MCPi on composite materials was demonstrated using a sample of polymer–silica composite, where significantly higher sensitivity could be achieved at very long total mixing times. The results also showed that both techniques are surface specific in the sense that only the groups close to the surface can be detected.

In this paper we demonstrate {¹H–²⁹Si}–¹H multiple cross polarization inverse detection (MCPi) solid state NMR as a robust technique for studying modified silica nanoparticle surfaces.

Indirect detection of broad spectra in solid-state NMR using interleaved DANTE trains

We analyze the performances and the optimization of ¹H-{I} HMQC experiments using basic and interleaved DANTE schemes for the indirect detection of nuclei I = 1/2 or 1 exhibiting wide lines dominated by chemical shift anisotropy (CSA) or quadrupole interaction, respectively. These sequences are first described using average Hamiltonian theory. Then, we analyze using numerical simulations (i) the optimal lengths of the DANTE train and the individual pulses, (ii) the robustness of these experiments to offset, and (iii) the optimal choice of the defocusing and refocusing times for both ¹H-{I} J- and D-HMQC sequences for ¹⁹⁵Pt (I = 1/2) and ¹⁴N (I = 1) nuclei subject to large CSA and quadrupole interaction, respectively. These simulations are compared to ¹H-{¹⁴N} D-HMQC experiments on γ-glycine and L-histidine.HCl at B₀ = 18.8 T and MAS frequency of 62.5 kHz. The present study shows that (i) the optimal defocusing and refocusing times do not depend on the chosen DANTE scheme, (ii) the DANTE trains must be applied with the highest rf-field compatible with the probe specifications and the stability of the sample, (iii) the excitation bandwidth along the indirect dimension of HMQC sequence using DANTE trains is inversely proportional to their length, (iv) interleaved DANTE trains increase the excitation bandwidth of these sequences, and (v) dephasing under residual ¹H-¹H and ¹H-I dipolar couplings, as well as ¹⁴N second-order quadrupole interaction, during the length of the DANTE scheme attenuate the transfer efficiency.

Double cross polarization for the indirect detection of nitrogen-14 nuclei in magic angle spinning NMR spectroscopy

Nitrogen-14 NMR spectra at fast magic-angle spinning rates can be acquired indirectly by means of two-dimensional techniques based on double cross polarization transfer ¹H → ¹⁴N →¹H. Experimental evidence is given for polycrystalline samples of glycine, l-histidine, and the dipeptide Ala-Gly. Either one-bond or long-range correlations can be favored by choosing the length of the cross polarization contact pulses. Longer contact pulses allow the detection of unprotonated nitrogen sites. In contrast to earlier methods that exploited second-order quadrupolar/dipolar cross-terms, cross polarization operates in the manner of the method of Hartmann and Hahn, even for ¹⁴N quadrupolar couplings up to 4 MHz. Simulations explain why amorphous samples tend to give rise to featureless spectra because the ¹⁴N quadrupolar interactions may vary dramatically with the lattice environment. The experiments are straightforward to set up and are shown to be effective for different nitrogen environments and robust with respect to the rf-field strengths and to the ¹⁴N carrier frequency during cross polarization. The efficiency of indirect detection of ¹⁴N nuclei by double cross polarization is shown to be similar to that of isotopically enriched ¹³C nuclei.

Comparison of various NMR methods for the indirect detection of nitrogen-14 nuclei via protons in solids

We present an experimental comparison of several through-space Hetero-nuclear Multiple-Quantum Correlation experiments, which allow the indirect observation of homo-nuclear single- (SQ) or double-quantum (DQ) (14)N coherences via spy (1)H nuclei. These (1)H-{(14)N} D-HMQC sequences differ not only by the order of (14)N coherences evolving during the indirect evolution, t1, but also by the radio-frequency (rf) scheme used to excite and reconvert these coherences under Magic-Angle Spinning (MAS). Here, the SQ coherences are created by the application of center-band frequency-selective pulses, i.e. long and low-power rectangular pulses at the (14)N Larmor frequency, ν0((14)N), whereas the DQ coherences are excited and reconverted using rf irradiation either at ν0((14)N) or at the (14)N overtone frequency, 2ν0((14)N). The overtone excitation is achieved either by constant frequency rectangular pulses or by frequency-swept pulses, specifically Wide-band, Uniform-Rate, and Smooth-Truncation (WURST) pulse shapes. The present article compares the performances of four different (1)H-{(14)N} D-HMQC sequences, including those with (14)N rectangular pulses at ν0((14)N) for the indirect detection of homo-nuclear (i) (14)N SQ or (ii) DQ coherences, as well as their overtone variants using (iii) rectangular or (iv) WURST pulses. The compared properties include: (i) the sensitivity, (ii) the spectral resolution in the (14)N dimension, (iii) the rf requirements (power and pulse length), as well as the robustness to (iv) rf offset and (v) MAS frequency instabilities. Such experimental comparisons are carried out for γ-glycine and l-histidine.HCl monohydrate, which contain (14)N sites subject to moderate quadrupole interactions. We demonstrate that the optimum choice of the (1)H-{(14)N} D-HMQC method depends on the experimental goal. When the sensitivity and/or the robustness to offset are the major concerns, the D-HMQC sequence allowing the indirect detection of (14)N SQ coherences should be employed. Conversely, when the highest resolution and/or adjusted indirect spectral width are needed, overtone experiments are the method of choice. The overtone scheme using WURST pulses results in broader excitation bandwidths than that using rectangular pulses, at the expense of reduced sensitivity. Numerically exact simulations also show that the sensitivity of the overtone (1)H-{(14)N} D-HMQC experiment increases for larger quadrupole interactions.

Dynamic nuclear polarisation enhanced14N overtone MAS NMR spectroscopy

Dynamic nuclear polarisation has been used to obtain solid-state¹⁴N overtone NMR spectra with signal enhancement levels of over two orders of magnitude, including natural abundance C–N and H–N correlation spectra.

Probing amide bond nitrogens in solids using 14N NMR spectroscopy

A novel two-dimensional nuclear magnetic resonance (NMR) experiment is proposed for indirect observation of 14N nuclei in various types of nitrogen-containing solids. In a method somewhat similar to the heteronuclear single-quantum correlation (HSQC) experiment widely used for protein structure determination in solutions, this technique correlates spin S=1/2 nuclei, e.g., 1H, 13C, with the 14N spin I=1 nucleus in solids. The present experiment, however, transfers coherence from neighboring 1H or 13C nuclei to 14N via a combination of J-couplings and residual dipolar splittings (RDS). Projections of the two-dimensional NMR spectra onto the 14N dimension yield powder patterns that reflect the 14N quadrupolar interaction, which can be used to study molecular structure and dynamics. Indirect detection of amide nitrogen-14 via 1H and 13C is shown experimentally on a model compound of N-acetyl-glycine.

Indirect Detection of Nitrogen-14 in Solid-State NMR Spectroscopy

NMR spectra of (14)N (spin I=1) are obtained by indirect detection in powders spinning at the magic angle. The method relies on the transfer of coherence from a neighboring "spy" nucleus with S=1/2, such as (13)C or (1)H, to single- or double-quantum transitions of (14)N nuclei. The transfer of coherence can occur through a combination of scalar and residual dipolar splittings (RDS); the latter are also known as second-order quadrupole-dipole cross terms. The two-dimensional NMR spectra reveal powder patterns determined by second- and third-order quadrupolar couplings. These spectra depend on the quadrupolar coupling constant C(Q) (typically a few megahertz), on the asymmetry parameter eta(Q) of the (14)N nucleus, and on the orientation of the internuclear vector r(IS) between the I ((14)N) and S (spy) nuclei with respect to the quadrupolar tensor. These parameters, which can be subject to motional averaging, can reveal valuable information about the structure and dynamics of nitrogen-containing solids. Application of this technique to various amino acids, either enriched in (13)C or with natural carbon isotope abundance, with spectra recorded at various magnetic fields, illustrates the scope of the method.

Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei

Cross-polarization from (1)H to the multiple-quantum coherences of a quadrupolar nucleus is used in combination with the two-dimensional multiple-quantum magic angle spinning (MQMAS) NMR experiment in order to extract high-resolution CPMAS NMR spectra. The technique is demonstrated on (23)Na (S = 3/2), (17)O, (27)Al (both S = 5/2), and (45)Sc (S = 7/2) nuclei, showing the applicability of multiple-quantum cross-polarization to systems with differing spin quantum number, gyromagnetic ratio, and relative nuclide abundance. The utility of this two-dimensional MAS NMR experiment for spectral editing and site-specific measurement of cross-polarization intensities is demonstrated. The possibility of direct cross-polarization to higher order multiple-quantum coherences is also considered and three-, five-, and seven-quantum cross-polarized (45)Sc MAS NMR spectra are presented.

Corrections to the cross-polarization dynamics in solids. The effect of nonsecular terms of heteronuclear dipolar interaction on cross-relaxation

The dynamic theory of cross-polarization in solids is modified by considering the contribution of the nonsecular terms of the heteronuclear dipolar interaction Hamiltonian in the laboratory frame to cross-relaxation. This contribution is evaluated numerically and confirmed experimentally. It is shown that these nonsecular terms may play a considerable role in cross-relaxation in many systems, especially in those with fast internal molecular motion. The complication in the cross-polarization process is further revealed.