Recent advances in solid-state nuclear magnetic resonance spectroscopy of exotic nuclei

Highlights

• Progress in SSNMR of exotic nuclei is reviewed.

• The period 2007–2017 is covered.

• Advances in hardware are described.

• A survey of literature data for exotic nuclides is provided.

Abstract

We present a review of recent advances in solid-state nuclear magnetic resonance (SSNMR) studies of exotic nuclei. Exotic nuclei may be spin-1/2 or quadrupolar, and typically have low gyromagnetic ratios, low natural abundances, large quadrupole moments (when I > 1/2), or some combination of these properties, generally resulting in low receptivities and/or prohibitively broad line widths. Some nuclides are little studied for other reasons, also rendering them somewhat exotic. We first discuss some of the recent progress in pulse sequences and hardware development which continues to enable researchers to study new kinds of materials as well as previously unfeasible nuclei. This is followed by a survey of applications to a wide range of exotic nuclei (including e.g., ⁹Be, ²⁵Mg, ³³S, ³⁹K, ⁴³Ca, ^47/49Ti, ⁵³Cr, ⁵⁹Co, ⁶¹Ni, ⁶⁷Zn, ⁷³Ge, ⁷⁵As, ⁸⁷Sr, ¹¹⁵In, ¹¹⁹Sn, ^121/123Sb, ^135/137Ba, ^185/187Re, ²⁰⁹Bi), most of them quadrupolar. The scope of the review is the past ten years, i.e., 2007–2017.

Introduction

During the last decade, experiments in the field of solid-state nuclear magnetic resonance (SSNMR) have undergone tremendous technical advances as a result of improvements in pulse sequences, techniques, and hardware. Various NMR methods have become increasingly accessible and widely implemented, enabling the detailed analysis of a multitude of materials including proteins, catalysts, biomaterials, pharmaceuticals, metal-organic materials, and so on. NMR spectroscopy is well known for its ability to probe molecules and materials at an atomic scale. However, considering the nature of various materials of interest, NMR spectroscopy has had to adapt. While Bragg diffraction techniques can determine the long-range periodic structure of powdered samples, SSNMR of a powdered sample offers local, isotope-specific structural information. This complementarity is of great interest for crystallography and chemistry in a broad sense. Facilitated by advances in computational chemistry, a new area of SSNMR spectroscopy has emerged under the term “NMR crystallography” [1]. Combining information gathered from NMR, diffraction, and computational approaches can afford a complete description of the overall chemical and crystallographic structure of a compound. Despite the inherent complications of interpreting some spectra, NMR results can help to understand short range interactions, and is seen as a local probing technique [2].

Although nearly every element in the periodic table has an NMR-active isotope (spin I ≠ 0), some of these isotopes are much less receptive and amenable to NMR, with limited reports available in the literature. Such isotopes are usually referred to as exotic nuclei (see Table 1). The Oxford Dictionary states that ‘exotic’ denotes ‘[…] of a kind not ordinarily encountered; [special]; out of the ordinary’. The dedicated expression ‘exotic nuclei’ seems appropriate in the context of SSNMR. In this contribution, we review the recent advances and major breakthroughs made in the field of SSNMR investigations of exotic nuclei, specifically in the last decade (2007–2017). While there have been many contributions in this field, this review aims to capture the major progress and most notable studies. To provide a working definition of the ‘exotic nuclei’ covered herein (see Section 1.3), various properties of nuclides are first discussed below.

The difficulties in studying exotic nuclei arise from several inherent isotopic properties: low gyromagnetic ratio (γ), low natural abundance (NA), high quadrupole moment (Q), and quantum spin number (I). That being said, most isotopes of interest here are quadrupolar (I > 1/2), which represent about 75% of the NMR active nuclei (see Fig. 1). However, this review also covers a number of spin I = 1/2 nuclei that fit into general criteria of being little-studied or difficult to analyse.

When the degeneracy of the Zeeman levels is lifted by the application of an external magnetic field (B₀), 2(I + 1/2) energy levels and 2I single quantum transitions result. Therefore, spin-1/2 nuclei only exhibit one transition whereas quadrupolar nuclei exhibit multiple single-quantum transitions. There are two types of single-quantum transitions for half-integer quadrupolar nuclei: the central transition (CT) and the satellite transitions (ST). To first order, only the STs are impacted by the quadrupolar interaction (QI), resulting in anisotropic spectral broadening which is typically much larger than that experienced by the CT. The QI must then be considered to second-order to explain the position and line shapes perturbations of the CT. Quadrupolar nuclei have a non-spherical charge distribution within the nucleus and a concomitant non-vanishing nuclear electrical quadrupole moment, Q (often expressed in millibarn (mb, equal to 10⁻³¹ m²)) [3]. The quadrupolar coupling of Q with the electric field gradient (EFG, described by a traceless, symmetric second-rank tensor with principal components: V₁₁, V₂₂, V₃₃) at the nucleus can reach up to several hundreds or thousands of MHz, much larger than all other internal interactions. As a result, the NMR spectra of quadrupolar nuclei are typically much broader than those of spin-1/2 nuclei. Despite this broadening, data extracted from such spectra are of great interest as they offer insight at the location of the nucleus itself, which is very useful for characterizing molecules and materials (vide infra). The magnitude of the nuclear electric QI can be described by the quadrupolar coupling constant (C_Q) and the EFG asymmetry parameter (η_Q):

$$C_Q=\frac{\mathit{eQ}{V}_{\text{33}}}{h}$$

$${\eta }_Q=\frac{V_{\text{11}}-V_{\text{22}}}{V_{\text{33}}}$$

Here, V₁₁, V₂₂, and V₃₃ (with V₁₁ + V₂₂ + V₃₃ = 0) are the principal components of the traceless electric field gradient (EFG) tensor, with |V₃₃| ≥ |V₂₂| ≥ |V₁₁|, e is the fundamental charge, h is Planck’s constant, and Q is the nuclear quadrupole moment.

The line width factor, $\ell$(in fm⁴) [4], is usually defined as follows in solution NMR:

$$\ell =\frac{Q^2(2I+3)}{I^2(2I-1)}$$

This parameter can offer a rapid and rough estimation of the extent of signal broadening. In order to get a more accurate and suitable value, Wu and Zhu proposed a modified line-width factor for the central transition signal, $\ell$_CT [5], that allows one to predict the CT line width for solid-state signals. $\ell$_CT is expressed in fm⁴ rad⁻¹ T s in the following equation:

$${\ell }_{\text{CT}}=\frac{1}{|\gamma |}{\left[\frac{3Q(1-{\gamma }_{\infty })}{2I(2I-1)}\right]}^2\left[I(I+1)-\frac{3}{4}\right]$$

where γ_∞ is the Sternheimer antishielding factor [6], [7]; it corresponds to a correction of the EFG at the nucleus caused by the polarization of inner-shell electrons.

In the solid state, the chemical shift anisotropy (CSA) is not averaged by molecular tumbling (Brownian motion) as in the isotropic liquid state, and thus directly impacts the line shape of a given spectral signal. Within the Herzfeld-Berger convention, the magnitude of this interaction can be described by three parameters: the isotropic chemical shift (δ_iso), the span (Ω), and skew (κ):

$${\delta }_{\text{iso}}=\frac{\left({\delta }_{11}+{\delta }_{22}+{\delta }_{33}\right)}{3}$$

$$\Omega \approx {\delta }_{11}-{\delta }_{33}(\Omega \ge \text{0})$$

$$\kappa =\frac{3({\delta }_{\text{22}}-{\delta }_{\text{iso}})}{\Omega };(-1⩽\kappa ⩽+1)$$

The principal components of the chemical shift (CS) tensor are ordered as δ₁₁ ≥ δ₂₂ ≥ δ₃₃. The chemical shift range depends on the studied isotope and can be as wide as, e.g., 6800 ppm for ^185/187Re or as narrow as 50 ppm for ⁹Be [8], [9].

The receptivity represents the ease with which a signal of a given isotope may be acquired relative to another one [4]:

$$\text{Receptivity}\propto {\gamma }^{\text{3}}\left(\text{NA}\right)\mathit{I}(\mathit{I}+1)$$

For example, the receptivity of ⁴³Ca with respect to ¹³C (at natural abundance of 1.11%) is only 0.05 [10], which makes it a rather difficult nucleus to study; for comparison, the receptivity of ⁹Be relative to ¹³C is 81.5 [4]. Lowly receptive nuclei are more arduous to study and receptivity values should be considered in any definition of ‘exotic nuclei’. Presented in Table 1 is a liberally defined list of nuclides which may be considered as exotic, for various reasons. For example, ⁹Be is included due to the dearth of studies in the literature, despite its good receptivity and small quadrupole moment. ¹⁷O is listed due its low receptivity; however, it is clear that this isotope is broadly studied in the literature (often with isotopic enrichment) and can hardly be considered as exotic nowadays (vide infra). Other nuclides with good receptivities may be included due to their prohibitively large nuclear electric quadrupole moments (e.g., ¹¹⁵In, ¹⁸⁷Re, or ²⁰⁹Bi). Thus, as stated in the table heading, the list summarizes the nuclei that we consider to be exotic; they are further discussed in the following sections of this review. The frequency ratios, Ξ, which corresponds to the ratio of frequency of the reference to that of the protons of TMS at high dilution (1%) in CDCl₃ are also given in Table 1 [4].

One major difficulty associated with studying some exotic nuclei is the ubiquitous Achilles’ heel of NMR spectroscopy: sensitivity. Indeed, although SSNMR offers insights at the molecular scale for any spin-active isotope, sensitivity is the most significant challenge that NMR spectroscopy faces when compared with many other analytical methods. In a more general context, materials chemistry deals with new compounds designed to present particular and desired properties. The structures of such materials are typically linked to their properties. X-ray diffraction may not be applicable to certain materials (e.g., amorphous compounds), while SSNMR can still provide nucleus-specific information. However, combined with some of the other properties inherent to particular nuclides (vide supra), sensitivity issues can become very problematic. Various strategies for increasing the sensitivity of the NMR experiment, with a focus on exotic nuclides, are discussed briefly below. An overview of more modern signal enhancement methods is given in Section 2.

The observed SSNMR signal is directly linked to various factors including the natural abundance of the isotope. Oxygen-17 has one of the lowest natural abundances in the periodic table at only 0.038%. Other important elements are also present at a very low natural abundance, e.g., ⁴³Ca and ¹⁵N with natural abundances of 0.135% and 0.37%, respectively. One brute force way to counter this problem is to consider isotopic enrichment of the sample. For example, ¹⁷O enrichment is strongly advised in order to observe any signal (although there are exceptions to this rule now as a result of advances in dynamic nuclear polarization methodologies, vide infra). This nucleus is of great interest in several areas, from pharmaceuticals [12], [13], [14] to geochemistry [15], inorganic compounds [16] or biomolecules (amino acids, proteins, etc.) [17], [18]. Enrichment is carried out by using an ¹⁷O-labelled precursor; however, synthetic yields can be a limiting factor, and the enrichment processes can be challenging. Enriched compounds can be expensive. Moreover, the number of enriched synthetic compounds which are practically accessible is reduced due to the limited number of available enriched precursors. Recently, Métro et al. proposed an appealing synthetic route for ¹⁷O enrichment via mechanochemical synthesis [19]. They used a ball mill for the ¹⁷O-enrichment of various compounds, from ibuprofen to Sr(OH)₂·8H₂O. This method requires at most a few hundreds of μL of isotopically-enriched precursor (e.g., H₂¹⁷O) per synthesis, as opposed to a few mL with classical wet chemistry enrichment processes. Enrichment methods are not always trivial and most of the time very costly; therefore, other signal enhancement approaches must absolutely be pursued and implemented.

To characterize chemical shift and quadrupolar coupling tensors, experiments carried out on stationary and magic-angle spinning powders are often useful and complementary. MAS has long been part of the toolkit for the spectroscopist. The advantages offered by this method have greatly helped SSNMR studies over the past decades [20], [21], [22]. As is well known to the readers of this journal, the method consists of spinning the sample at 54.74° (θ-value to cancel the second Legendre polynomial: P₂(cos θ) = (3cos²θ − 1)/2) with respect to B₀. Magnetic shielding can be described mathematically as a sum of isotropic and anisotropic (and antisymmetric) parts. The dependence of the anisotropic component on P₂ implies that it can be averaged by MAS. In favourable cases, the signal is reduced from a wide anisotropic powder pattern to a sharp isotropic peak. However, if the spinning speed is smaller than the magnitude of the CS interaction, spinning sidebands are observed in the spectrum. These sidebands are separated by the spinning frequency, the envelope of the overall spectrum mimicking the static line shape. The QI can also be described in a similar fashion. The first-order interaction is effectively averaged by MAS; nevertheless, spinning sidebands are observed for STs as the QI magnitude is usually much larger than the spinning speed. In both cases of CSA and first-order QI, the spectrum appears as a family of spinning sidebands if the interaction is not sufficiently averaged by MAS. With regards to the second-order QI, the mathematical description shows that it depends on two Legendre polynomials (P₂ and P₄) which cannot be cancelled simultaneously by sample spinning about a single axis (vide infra). Consequently, the signal will be narrowed but MAS does not completely remove the second-order quadrupolar broadening.

Larger volume MAS rotors allow a larger number of spins to be analysed; however, as can be seen in Fig. 2, the relative sensitivity per unit volume is greater for smaller rotors.

Typical rotor diameters of 7 mm, 4 mm, 3.2 mm, or 2.5 mm can safely spin up to ∼8, ∼15, ∼25 and ∼35 kHz, respectively. However, these speeds are not always fast enough to entirely average the CSA or the QIs, and so experimentalists might consider so-called ultrafast probes. Nowadays, ultrafast (>40–50 kHz) experiments are becoming more routine thanks to tremendous technical advances in NMR probe design, motivated in large part by the advantages of averaging of ¹H–¹H dipolar couplings. In order to be able to spin faster, the rotor diameter is reduced (e.g., 0.7 mm and 0.75 mm o.d. probes are offered by Bruker and JEOL which can spin in the 110–120 kHz range). Recent breakthroughs in the development of MAS NMR probes with spinning frequencies exceeding 100 kHz have opened a wide range of potential applications [24], [25], [26], [27]. During MAS experiments, it is well-known that in the absence of external temperature regulation, the sample heats up, especially if the spinning speed is high [26], [28]. This also applies to the inner pressure arising from the centrifugal forces. Therefore, attention should be paid to the thermal stability of the compound and to the temperature regulation, when the spinning speed reaches very high frequencies. As already mentioned, working at ultrafast spinning speed presents a major trade-off, e.g., a low spin number; such a method is thus often used for high resolution NMR (typically of protons) and benefits from dipolar coupling averaging.

The MAS NMR spectra of heavy spin-1/2 nuclides like platinum-195 can be rendered complex by very large CSA that results in numerous spinning sidebands. In 2017, Perras et al. published an article describing a pulse sequence (D-HMQC-MAT) that allows one to record MAS spectra corresponding to infinite speed of heavy spin-1/2 nuclides by indirect detection [29]. They applied it to Pt-containing metal-organic frameworks (MOFs) which display ultra-wide spectra (Fig. 3) and successfully resolved Pt coordination environments in complex mixtures.

The comparison between the three pulse sequences, CT-D-HMQC, D-HMQC-aMAT and D-HMQC-MAT, gives 1D ¹H signal intensity ratios of 1.00, 0.52 and 0.06, respectively (first slice) (Fig. 3). However, the MAT advantage resides in the two-dimensional experiment, as shown in Fig. 3: sensitivity is greatly improved by folding the spinning sidebands into the centerband. Moreover, the centerband intensity is now greatly increased. The authors also mention that this strategy could be competitive and complementary to Dynamic Nuclear Polarization (DNP).

Larmor frequencies are directly proportional to the applied external magnetic field, B₀ (${\nu }_L=|\gamma |B_0/2\pi$). This implies that ultrahigh magnetic fields (UHF) provide a tremendous advantage for low-γ nuclei. From the Boltzmann distribution, it is easily understood that the spin polarization is related to the Larmor frequency, thus implying that low-γ nuclei will display a poorer sensitivity. Working at UHF not only improves the S/N directly; the effects of the QI and CSA also depend on B₀. Second-order quadrupolar broadening is reduced (as inversely proportional to B₀), thus implying a resolution enhancement, but the CSA is proportional to the external magnetic field (in frequency units) and is therefore increased at UHF. The highest magnetic field currently available for NMR experiments is about 45 T and is used for experiments where high homogeneity is not needed [30]; however, a new series-connected resistive/superconducting hybrid magnet operating with good homogeneity up to 35.2 T (corresponding to 1.5 GHz for ν_L(¹H)) in the National High Magnetic Field Laboratory, Tallahassee, has recently provided very promising results and potential for future applications [31]. Multifield experiments can also be of great help, and are often essential, to refine the quadrupolar and CS parameters extracted from spectra if the sensitivity is good enough [32]. NQR experiments are quite often a good alternative to measure the quadrupolar coupling constant of exotic nuclei, especially when the quadrupole moment is large [33].

This very brief presentation summarizes the basic strategies commonly accessible for SSNMR experiments on difficult nuclei. To briefly recapitulate, when considering SSNMR experiments, one should first of all carefully think about the pulse sequence, the rotor size and probe used, the magnetic field available and the experiments (MAS, static) that are required before analysing the sample. These practical considerations are particularly important for exotic nuclei. Further description of more advanced pulse sequences and techniques constitutes a separate section of this review wherein we will elaborate on the advantages and possibilities offered by some specific sequences.

Nuclides with integer spin quantum number (I = n with n ∈ $\mathbb{Z}$⁺) represent a small fraction of quadrupolar isotopes in the periodic table. Their particularity lies in the fact that no central transition can be observed as the Zeeman interaction leads to an odd number of energy levels (2I + 1, see Fig. 4). Therefore, their NMR spectra will be highly affected by the first-order quadrupolar coupling. The most commonly studied integer spin nuclides are hydrogen-2 (deuterium), nitrogen-14, and lithium-6; however, others exist including boron-10, potassium-40, vanadium-50, lanthanum-138, and lutetium-176 (with I = 3, 4, 6, 5, and 7, respectively). Only the first three will be briefly reviewed here as the other ones are extremely rare if not absent from the literature during the last ten years.

As an illustration, consider ¹⁴N, a spin I = 1 nucleus. It displays two different kinds of transitions between the three energy levels: two single-quantum (SQ, +1 ↔ 0 and 0 ↔ −1) and one double quantum (DQ, +1 ↔ −1) transitions.

Fig. 4 shows that SQ transitions are highly affected by first-order QI whereas DQ transitions will only be affected by second and higher order QIs. The SQ transitions thus generally lead to broad signals whereas the DQ transitions present narrower spectra. Direct generation of DQ coherence is called overtone transition (OT) NMR spectroscopy (with rf irradiation at 2ν_L(¹⁴N)). A review by Dib et al. has nicely recapitulated recent works focused on nitrogen-14 [35]. As stated in the beginning of their review, spectroscopists usually prefer to study ¹⁵N despite its very low natural abundance (0.37% vs. 99.63% for ¹⁴N). This is due partially to the relative ease of labelling with this isotope, but also because ¹⁵N is a spin-1/2 nuclide which circumvents the difficulties arising from the quadrupolar ¹⁴N isotope. Readers are therefore directed to this review article if they are interested in more details on this isotope.

The second interesting integer spin nuclide is hydrogen-2 (²H or ²D) which is also a spin-1 nuclide. This isotope has also a very low NA (0.011%), which when combined with a medium γ (4.11 × 10⁷ rad s⁻¹ T⁻¹) and a small Q (2.8 mb) results in a receptivity of 1.1 × 10⁻⁶ relative to ¹H. In the last 10 years, various articles have used ²H SSNMR in order to study dynamics [36], [37], [38], adsorption [39], or dehydration [40], [41]. Finally, lithium-6 (I = 1) is cited here but will not be further discussed as we will not include it in our definition of exotic nuclei; indeed extensive literature is easily found, along with work on the isotope ⁷Li (I = 3/2).

For the purposes of this article, we propose a practical definition for exotic nuclei which includes those which suffer from (i) typically moderate to large nuclear quadrupolar coupling constants, (ii) low natural abundance, (iii) low gyromagnetic ratio, or combinations thereof. We also discuss some nuclides which for other reasons have been rarely studied, thereby qualifying them as ‘exotic’ as well.

In the first part of the remainder of this article, some techniques to counter the sensitivity problems of exotic nuclei are discussed. These range from manipulating the satellite transitions with the help of frequency sweeps to hyperpolarization of the sample via dynamic nuclear polarization (DNP). In the second part, we will survey the literature of the past decade for so-called exotic nuclides. The review covers roughly the past ten years, but is not meant to be exhaustive. Readers are referred to excellent review articles relating to specific nuclei where appropriate.