³³S NMR: Recent Advances and Applications

Abstract

The purpose of this review is to present advances and applications of ³³S NMR, which is an underutilized NMR spectroscopy. Experimental NMR aspects in solution, chemical shift tendencies, and quadrupolar relaxation parameters will be briefly summarized. Emphasis will be given to advances and applications in the emerging fields of solid-state and DFT computations of ³³S NMR parameters. The majority of the examples were taken from the last twenty years and were selected on the basis of their importance to provide structural, electronic, and dynamic information that is difficult to obtain by other techniques.

1. Introduction

Sulfur is a widely distributed element in organic, inorganic, polymeric, industrial, and biological systems. It is the 16th most abundant element in the crust of the earth by mass and, thus, an essential component of minerals. Sulfur is transported, with a variety of oxidation states from −2 to +6, by fluids and melts during a wide range of geological processes. Among the four sulfur stable isotopes (³²S, 94.8%; ³⁴S, 4.37%; ³³S, 0.76%; and ³⁶S, 0.02%), only ³³S possesses a nuclear spin and, thus, is NMR active. Compared to ¹H, ¹³C, ¹⁵N, ³¹P, and ¹⁹F NMR, however, ³³S has received little attention since it suffers from low natural abundance (0.76%,

Table 1. Magnetic properties and nuclear magnetic resonance parameters of the sulfur-33 nucleus [1,2,3,4,5].

Property		Units	Ref.
Spin number	3/2
Nuclear magnetic moment	0.6432555 (10)	Nuclear magneton	[6]
	0.6432474 (107)		[7]
	0.643251 (16)		[8]
Magnetogyric ratio	2.055685	×10−7 Radians s−1 Tesla−1
Resonance frequency
(at 9.398 Tesla)	30.714	MHz
Chemical shift range	ca. 1000	ppm
Quadrupole moment	−0.0678	Electron m2
Nuclear quadrupole coupling
constant range	−10 to +42	MHz
Relaxation times	<0.2	s
Natural abundance	0.76	%
Relative sensitivity per
nucleus (1H = 1) a	2.27 × 10−3
Absolute relative sensitivity at natural abundance (1H = 1) b	1.72 × 10−5
Relative Receptivity to 13C	0.101

^a Relative to proton, at constant field, for equal number of nuclei. ^b Product of relative sensitivity and natural abundance.

), a low gyromagnetic ratio (2.055685 × 10⁻⁷ rad T⁻¹ s⁻¹), and extremely low absolute sensitivity relative to that of protons (1.72 × 10⁻⁵) [1,2,3,4,5]. Furthermore, ³³S is quadrupolar in nature, with a spin quantum number of I = 3/2 and a relatively large nuclear quadrupole moment of −0.0678 × 10⁻²⁸ m². As a result, the interaction between the nuclear quadrupole moment and the electric field gradient at the nucleus provides very effective relaxation mechanisms and, thus, broad linewidths in solution and significant anisotropic broadening of powder line shapes in the solid state.

Recent developments in instrumentation, new pulse sequences and methodologies, especially in the solid state, the large chemical shift range, and the availability of elemental ³³S (99.8 atom%) as the starting material for ³³S enrichment have alleviated some of the experimental difficulties. In addition, due to the widespread application of DFT calculations of NMR parameters, an increased use of ³³S NMR can be foreseen. General features and available experimental data for ³³S NMR spectroscopy are discussed in a number of earlier comprehensive reviews and compilations. As an example, Barbarella [2] summarized a wide range of applications up to 1992, while Musio [3] published a very comprehensive review that covers all aspects of ³³S NMR, including experimental conditions, the theoretical background of various NMR parameters, and a wide range of applications up to 2008.

In the present review, we have attempted to treat both experimental aspects and the theoretical background of ³³S parameters and a wide range of applications, with particular emphasis on the solid state and computational DFT methods. Most examples are selected from publications in the last 20 years, yet some older but classic ³³S NMR papers will also be discussed. An attempt will also be made to define areas where ³³S NMR could provide atomic structural information that is difficult to obtain using other techniques.

2. Revision of Nuclear Properties

Makulski [6] reinvestigated several nuclear dipole moments and magnetic shielding constants, including those of ³³S, using ³He atoms in mixtures with gas molecules of nuclei under investigation. The SF₆ gas, in the pressure range of 5–25 atm, resulted in very narrow ³³S signals (Δν_1/2 ~ 1 Hz), due to the zero electric field gradient on the sulfur nuclei, with a well-defined ¹J(³³S, ¹⁹F) = 250.91 Hz (Figure 1). The ³He and ³³S NMR frequencies showed linear density dependencies (Figure 2), which, upon extrapolation to the zero-pressure limit, resulted in a ³³S nuclear magnetic moment in terms of μ(³He). Since the experimental μ(³He) is known to have high accuracy, the resulting μ(³³S) = 0.6432555(10)μ_Ν is more accurate by an order of magnitude than those previously reported [7,8] (Table 1).

3. ³³S Enrichment

The stringent requirements in ³³S NMR studies, at natural abundance, are the extensive signal averaging and the high concentrations needed for a successful spectrum. In most cases, especially for biologically relevant low concentrations, the use of [³³S]-labeled compounds is necessary. The synthesis of labeled compounds usually involves typical inorganic and organic reactions using, in most cases, elemental ³³S (99.8 atom%) as the starting material. A typical example is the synthesis of [³³S]-taurine, which was achieved according to Scheme 1: disulfide ions, ³³${\mathrm{S}}_2^{2-}$, which were prepared by the reaction of elemental ³³S (99.8 atom%) with NaOH in the presence of hydrazine, reacted with 2-(Boc-amino) ethyl bromide to produce [³³S₂]-dissulfide. Treatment with performing acid produced [³³S]-taurine [9]. [³³S₂]-L-cystine was also prepared with a similar synthetic root [10]. Literature procedures were also used for the synthesis of [³³S]-diphenyl disulfide and its precursor, thiophenol [11].

The ³³S NMR spectrum of 0.1 mM [³³S]-taurine in D₂O (δ = −6.7 ppm, Δν_1/2 = 11.5 Hz), at 14.1 T (see Figure 3), shows a reasonable signal with S/N = 9, using 4 × 10⁴ scans and a total experimental time of ~10.4 h. Taking into consideration that T₁ ≈ 51 ms, the pulse repetition time, Τ_p, could be as short as Τ_p = 4T₁ ≈ 250 ms; thus, the total experimental time can be reduced by a factor of ~3.7. In humans, the concentrations of taurine are in the range of 10 to 100 μM in plasma and 10 to 70 μM in skeletal muscles and the heart; ³³S-labeled taurine, therefore, can be detected in metabolic and pharmacokinetic studies.

4. Experimental NMR Aspects of Liquid Samples

4.1. Ultra-High Magnetic Fields and High Sensitivity Detection Schemes

The use of ultra-high magnetic fields has significantly increased the sensitivity of ³³S NMR, in addition to increasing signal dispersion in the case of more complicated systems. The use of ultra-high field instrumentation is also most advantageous in the case of: (a) large molecular weight systems in solution, outside the extreme narrowing condition, since the m = ½ → m = −1/2 component will dominate the spectrum and it is significantly narrower than the other component (see below on quadrupolar relaxation); and (b) in the solid state since the second-order quadrupolar linewidth of the m = ½ → m = −1/2 decreases linearly with the magnetic field B_o (see Section on Solid State).

A 10 mm ³³S cryogenic probe with an inner RF coil in the temperature range of 9–12 K was described as having a 3.5-fold increase in sensitivity relative to that of a conventional 5 mm broadband probe [12]. A further improvement in sensitivity was achieved with a preamplifier and switch that were cooled to 60 K by a cold helium gas [13]. The quality factor Q of the rf coil was increased to 271 compared to 54 at room temperature. Figure 4 shows a comparison of the ³³S NMR sensitivity using: (a) the conventional 5 mm broadband probe; (b) the 10 mm cryoprobe at room temperature; and (c) the 10 mm cryoprobe with a cold switch and preamplifier. The achievable sensitivity enhancement of ~9.8 in (c) provides a technique to investigate biologically important samples at low mM concentrations for ³³S nuclei in highly symmetric environments.

4.2. Optimization of Experimental Parameters—Effects of Low-Viscosity Solvents and Temperature

In the case of a non-symmetric electronic environment around the ³³S nucleus, the extremely short quadrupolar relaxation times result in extensive line broadening and, thus, a reduction in the S/N ratio. Sensitivity, however, should be evaluated relative to the achievable S/N ratio in a given period of time. For the broad ³³S resonance, T₁ = T₂, thus significantly short pulse repetition times of ~4T₂ can be used. This results in an S/N ratio per unit time that is practically independent of T₂ and, thus, resonance linewidth (see below on the effect of acoustic ringing on the achievable S/N ratio).

Increasing the temperature and/or dilution of high-viscosity liquids with low viscosity solvents can reduce the linewidth of ³³S. For moderate dilution, an optimum balance in resolution vs. S/N ratio can be achieved [14]. Further reductions in linewidths can be achieved with the use of supercritical solvents, which combine fluid densities with gas-like viscosities. Unfortunately, despite some original optimism, the resolution advantages were significantly inferior to those expected on the basis of the viscosities of supercritical solvents [2]. Thus, no further applications have so far been reported.

4.3. Acoustic Ringing

Observation of broad resonances of low natural abundance, low frequency, and sensitivity in quadrupolar nuclei is very problematic due to rolling baseline artifacts. They were attributed to ultrasonic waves from the effect of the rf. pulses and are often referred to as acoustic ringing [14,15]. The most commonly used method to alleviate the problem is the use of a preacquisition delay, Δt, which inevitably results in a significant reduction in the S/N ratio by a factor of exp(−Δt/T₂). Thus, resonances with linewidths greater than 4–5 kHz are virtually lost. The most efficient methods for recording very broad resonances are the use of multipulse sequences such as the RIDE and extended spin-echo sequences, which can be routinely applied without any hardware or probe modification [14,15]. More recently, an interactive baseline correction algorithm for solid-state NMR spectra was reported [16]. The method, which can also be applied to liquid states, does not make any hypothesis regarding the NMR line shapes and does not modify the recorded FID data points.

4.4. Magnetization Transfer Experiments—2D Inverse Detection

Inverse detection schemes in which polarization is transferred from ¹H to the X nucleus through ⁿJ(¹H,X) couplings and then back to ¹H for detection have proved extremely useful for the I = 1/2 nuclei. In the case of ³³S, inverse detection was possible only in high-symmetric systems with a zero electric field gradient. Jackowski et al. [17] investigated intermolecular interactions on ³³S chemical shifts of gaseous SF₆ and its binary complexes with Xe, CO_2, and NH₃ at 298 K with the use of a refocused ¹⁹F-³³S heteronuclear multiple-quantum coherence NMR. This polarization transfer experiment from ¹⁹F to ³³S permitted the indirect detection of ³³S even in low-density samples (Figure 5). This allowed investigation of the density dependence of δ(³³S) and ¹J(¹⁹F-³³S). Similarly, ¹⁹F-³³S HMBC experiments were used to investigate SF₆ dissolved in thermotropic liquid crystals [18].

4.5. Referencing Techniques

For ³³S NMR, as is common with several heteronuclei, a variety of reference compounds and referencing procedures, both internal and external, have been suggested. There are two adopted scales of ³³S NMR chemical shifts, namely the one based on neat carbon disulfide, CS₂, and the other one—on saturated (NH₄)₂SO₄ in D₂O. The ³³S NMR signals of both standards are relatively sharp, with the former being noticeably broader because of increased electronic asymmetry around the nucleus, which is illustrated in Figure 6. Despite the IUPAC recommendation of the use of saturated (NH₄)₂SO₄ in D₂O as a reference compound [5], Cs₂SO₄, Na₂SO₄, and other sulfates have also been utilized. The ${\mathrm{S}\mathrm{O}}_4^{2^{-}}$ chemical shift was shown to be dependent on concentration, nature of counterion, pH, and temperature. As discussed in detail in [3], the reported chemical shift variations are not significant compared to the accuracy of recording very broad ³³S resonances. Several authors also still use CS₂ as a reference. The conversion of the ${\mathrm{S}\mathrm{O}}_4^{2^{-}}$ and the CS₂ scales was reported to be [3]:

$$\mathsf{\delta }\left({\mathrm{S}\mathrm{O}}_4^{2^{-}}\right)=\mathsf{\delta }\left({\mathrm{C}\mathrm{S}}_2\right)-333$$

(1)

For diamagnetic solutions, the double tube method was used with the reference compound in the inner tube or capillary, without any susceptibility correction, since it is expected to be much smaller than the accuracy of the measurement of the chemical shift. It should be emphasized, however, that due to the high B₀ stability of modern NMR instrumentation, the spectrum of the reference compound can be recorded in a separate experiment (when unlocked) with the chemical shift calculated at 0 ppm. For the study of paramagnetic solutions, the use of a cylindrical and a spherical tube has been proposed [14,19]. The ³³S resonance of the reference compound is recorded in both cells; the bulk magnetic susceptibility correction is the chemical shift difference of the two measurements.

Recently, Jackowski and Wilczek [20] recommended the use of helium-3 gas as a primary universal reference standard. Gas phase ³He NMR measurements provided the resonance frequency of an isolated helium-3 atom, which is independent of temperature, and no rovibration correction is needed. In addition, very accurate shielding constant calculations of σ_ref(³He) are known [21]. The shielding from ³H to, e.g., ³³S can be obtained with the double resonance method using the ²D NMR signal of the lock solvent; thus, no reference standard is needed.

5. Chemical Shifts

Experimental Chemical Shift Ranges

The ³³S NMR scale has a wide chemical shift range of over 1000 ppm, as illustrated in Figure 7, which partly compensates for experimental difficulties in observing the NMR signals. The order of increasing deshielding follows the trend (with several exceptions): (i) singly bonded sulfur; (ii) multiply bonded sulfur; (iii) sulfur belonging to delocalized functional groups; and (iv) sulfur bonded to several oxygen atoms. Inorganic sulphides $\left({\mathrm{S}}^{2-}\right)$ cover an extremely wide range of −680 ppm (Li₂S) to −42 ppm (BaS), linear and cyclic organic sulphides (-S-) a region of −573 to −302 ppm, thiols (RSH) −458 to −332 ppm, thiophenes −200 to −113 ppm, sulfoxides (R₂SO) −213 to 27 ppm, sulfones (RSO₂R′) −18 to 25 ppm, cyclic sulphones −88 to 42 ppm, sulphonates (R- ${\mathrm{S}\mathrm{O}}_3^{-}$) a very narrow range of −19 to 4 ppm, aromatic sulphonates −19 to 0 ppm, inorganic sulfates (${\mathrm{S}\mathrm{O}}_4^{2-})$ −13 to 67 ppm and sulfur-nitrogen compounds (sulphimides, sulphoximides and sulphonamides) −39 to 2 ppm. There are several miscellaneous organic and inorganic compounds that exhibit highly shielded or deshiled ³³S resonances, such as OCS (−594 ppm), PhNCS (−570 ppm), (CH₃)₃PS (−536 ppm), SO₂ (374.9 ppm), (NH₄)₂ [MoS_nO_4−n]: n = 4 (344 ppm), n = 3 (240 ppm), n = 2 (123 ppm), n = 1 (−25 ppm), and (nPr₄N)₂[xCuS₂MoS₂], x: CN (445 ppm), x = PhS (436 ppm).

As noted above, the ³³S NMR linewidth is dependent on the magnitude of the electric field gradient at the sulfur nucleus, which in turn depends on the degree of symmetry around sulfur. Thus, while narrow lines are observed for compounds with high molecular symmetry, compounds with lower molecular symmetry, such as sulfoxides and sulfides, give much broader lines.

Table 2. Experimental ³³S NMR chemical shifts and line widths of the representative sulfides, sulfoxides, and sulfones ^a.

Cmpd.	Formula	Sulfides (X = S)		Sulfoxides (X = SO)		Sulfones (X = SO2)
		Chemical Shift, ppm	Line Width, Hz	Chemical Shift, ppm	Line Width, Hz	Chemical Shift, ppm	Line Width, Hz
1	CH3–X–CH3	−428 (−9.5)	2500	−8 (325)	5500	−13 (320)	20
2		−573 (−240)	3220	−213 (120)	4950	−88 (245)	300
3		−302 (302)	4000	32 (365)	4950	−2 (331)	230
4		−336 (−3)	5500	27 (360)	2990	35 (368)	69
5		−363 (−30)	5500			−12 (321)	92

^a Chemical shifts are given in the SO₄^2– and CS₂ scales (the latter are given in parenthesis).

and

Table 3. Experimental ³³S NMR chemical shifts and line widths of several representative sulfones.

Cmpd.	Formula	Solvent	33S NMR Chemical Shift, ppm		Line Width, Hz
			SO42− Scale	CS2 Scale
	CH3–SO2–R, R =
6	CH2Cl	CDCl3	−7.2	325.8	90
7	CHCl2	CDCl3	−0.2	332.8	280
8	CCl3	CDCl3	4.5	337.5	300
9	F	CHCl3	1	334
10	Cl	CHCl3	2	335	1500
11	Br	CHCl3	−19	317
12	I	CHCl3	−76	257
	C6H5–SO2–R, R =
13	Me	neat	−17	316	210
14	Et	neat	−9	324	460
15	i-Pr	neat	0	333	1100
16	t-Bu	neat	−3	330	1500
17	Me2SO2	DMSO-d6/CDCl3	−7	326	90
18	Et2SO2	DMSO-d6/CDCl3	10	343	200
19	n-Pr2SO2	DMSO-d6/CDCl3	7	340	130
20	n-Bu2SO2	DMSO-d6/CDCl3	7	340	320
21	n-Hex2SO2	DMSO-d6/CDCl3	9	342	400
22	(CH2=CH)2SO2	DMSO-d6/CDCl3	−26	307	60
23	(CH2=CH-CH2)2SO2	DMSO-d6/CDCl3	3	336	80
24	PhSO2Me	DMSO-d6/CDCl3	−20	313	120
25	PhSO2CH=CH2	DMSO-d6/CDCl3	−18	315	90
26	Ph2SO2	DMSO-d6/CDCl3	−23	310	130
27	(PhCH2)2 SO2	DMSO-d6/CDCl3	1	334	90
28		DMSO-d6/CDCl3	42	375	50
29		CS2	−12	321	92
30		CHCl3	−18	315	100
31		CS2	−8	325	190
32		CHCl3	−10	323	200
33		CHCl3	−20	313	200
34		acetone-d6	39	372	8
35		DMSO-d6/CDCl3	32	365	50
36		DMSO-d6/CDCl3	26	359	50
37		DMSO-d6/CDCl3	17	350	430
38		DMSO-d6/CDCl3	4	337	330

contain experimental ³³S NMR chemical shifts and line widths of several representative sulfides, sulfoxides, and sulfones compiled from the reviews by Musio [3] (compounds 1–12, 28–33), Aliyev [22] (compounds 13–16), and the original paper by Ngassoum et al. [23] (compounds 17–27, 34–38). Most of the original experimental data (which were largely not included in those tables) were published in the early papers by different authors; see most representative reviews [1,2,3] and key original references given therein.

It appears that δ(³³S) is sensitive to the electronic effects of substituents, molecular conformation, ring strain, ionization state, temperature, solvent, and, in a few cases, concentration. Characteristic structural trends dealing with the ring strain of cyclic sulfides, sulfoxides, and sulfones were explicitly formulated by Musio [3]. By comparing dimethyl derivatives and the corresponding thiiranes, significant shielding is observed upon cyclization due to the influence of ring strain tension (−145 ppm for thiirane, −205 ppm for thiirane 1-oxide, and −75 ppm for thiirane 1,1-dioxide). Three-membered ring compounds are markedly more shielded than larger rings. On going from three- to four-membered rings, a significant deshielding is observed; from four- to five-membered rings, a further deshielding is observed only in the case of sulphonyl compounds. ³³S is more shielded in six-membered rings than in five-membered rings by approximately 40–50 ppm, and, thus, it occurs in the same range as the open-chain compounds. This can be attributed to the geometric stability of six-membered rings and the absence of ring-strain interactions.

Several empirical correlations have been reported, which have been analyzed in detail in the comprehensive review of Musio [3]. Thus, only a brief account will be given below. A linear correlation between δ(³³S) of sulphonates, R${\mathrm{S}\mathrm{O}}_3^{-}$, and δ(³³C) of carboxylates, RCOO⁻, was obtained in the form

δ(³³S) = −390.37 + 2.129 δ(¹³C)

(2)

which shows that δ(³³S) is two times more sensitive to substituent effects than that of δ(¹³C). Good linear correlations between δ(³³S) and Taft polar substituent constant σ* were obtained for symmetric dialkyl sulphones of the form

δ(³³S) = −155 σ* − 133

(3)

and monosubstituted dimethyl sulfones of the form

δ(³³S) = 8.78 σ* − 18

(4)

In the last fifteen years, there has been no significant research activity on empirical correlations, presumably due to the fact that theoretical calculations of ³³S chemical shifts can provide accurate results and, thus, important information on electron distribution and bonding properties (see Section on Computations).

6. Relaxation Properties

6.1. Relaxation in the Extreme Narrowing Condition

In the absence of chemical exchange, the linewidth of quadrupolar nuclei in isotropic systems is given by

$${\mathsf{\Delta }\mathsf{\nu }}_{1/2}=\frac{1}{\mathsf{\pi }{\mathsf{{\rm T}}}_1}=\frac{1}{\mathsf{\pi }{\mathsf{{\rm T}}}_2}=\frac{3\mathsf{\pi }}{10}\frac{2\mathsf{{\rm I}}+3}{{\mathsf{{\rm I}}}^2(2\mathsf{{\rm I}}-1)}{C}_Q^2\left(1+\frac{{\eta }_Q^2}{3}\right){\mathsf{\tau }}_{\mathrm{c}}$$

(5)

where T₁ and T₂ are the longitudinal and transverse relaxation times, respectively, $C_Q$ is the nuclear quadrupolar coupling constant (NQCC) defined as

C_Q = e²q_zz Q/h

(6)

where Q is the nuclear electric quadrupole moment, q_zz is the largest component of the electric field gradient tensor at the ³³S nucleus, e is the charge of the electron, $n_Q$ is the asymmetric parameter given by

$$n_Q=\frac{q_{xx}-q_{yy}}{q_{zz}}, \left|q_{zz}\right|\ge \left|q_{yy}\right|\ge \left|q_{xx}\right|$$

(7)

and ${\mathsf{\tau }}_{\mathrm{c}}$ is the correlation time, which for spherical molecules is given by the Stokes-Debye formula.

$${\mathsf{\tau }}_{\mathrm{c}}=\frac{4\mathsf{\pi }{\mathrm{r}}^3{n}_{\mathrm{v}}}{3{\mathrm{K}}_{\mathrm{B}}\mathrm{T}}$$

(8)

where r is the radius of the molecule, n_v is the viscosity of the solution, K_B—the Boltzmann factor, and T—the absolute temperature.

Narrow resonances can be expected for small molecular weight molecules and $C_Q$ values at elevated temperatures and low viscosity values. ³³S NMR signals of a few Hz can only be observed in highly symmetric electronic environments around the sulfur nucleus, such as ${\mathrm{S}\mathrm{O}}_4^{2^{-}}$ anions. The product $C_Q^2$(1 + ${\eta }_Q^2$/3) can be obtained from ³³S relaxation times when the correlation time can be estimated through Equation (8). More precise values of τ_c can be obtained from relaxation time measurements of other nuclei, such as ¹³C and ²D, denoted as the dual spin probe method. Thus, the ³³S NQCCs of the C₆H₄${\mathrm{S}\mathrm{O}}_3^{-}$ (0.5 MHz) and 3-${\mathrm{N}\mathrm{H}}_3^{+}$C₆H₄${\mathrm{S}\mathrm{O}}_3^{-}$ (1.0 MHz) anions were determined with the combined use of ³³S linewidths, ¹³C T₁ relaxation times, and NOE measurements [24]. The ³³S NQCCs of (CH₃)₂SO₂ (1.8 MHz) and CS₂ (13.8 MHz) were measured in liquid crystalline solvents [25]. The order parameters were obtained from ¹H NMR spectra for (CH₃)₂SO₂ and ¹³C chemical shifts for CS₂. Information on the NQCC of (CH₃)₂SO₂ in chloroform solution was also obtained (1.63 MHz for $n_Q$= 0 and 1.41 MHz for $n_Q=$ 1) with the combined use of ³³S and ²D T₁ relaxation time measurements. The values in chloroform solution are lower than those reported for liquid crystalline solvents, presumably due to solvent effects and experimental errors [25]. In the last twenty years, however, the great majority of ³³S NQCCs were obtained with solid-state and zero-field NMR techniques (see Section 8 on Solid State and Section 9 on Computations).

6.2. Relaxation Outside the Extreme Narrowing Condition

The decay of the longitudinal and transverse magnetization components outside the extreme narrowing condition, ω₀${\mathsf{\tau }}_{\mathrm{c}}$ >> 1, is no longer exponential but a weighted sum of I + 1/2 = 2 exponentials. The NMR signal of the m = 1/2 → m = −1/2 component will dominate the spectrum because it is significantly narrower than the other component [26,27]. This phenomenon has been successfully used in ¹⁷O NMR to investigate ligand binding to proteins [14] or small MW molecules dissolved in highly viscous solvents [28]. Unfortunately, no application of ³³S NMR has so far been reported in solution, contrary to the case in the solid state (see Section 8 on Solid State).

7. Selected Applications in Solution

7.1. Biological Applications

³³S was used to investigate the effect of the enzyme chondroitinase (ACII), a bacterial lyase that specifically digests chondroitin sulfate A (ChS-A), which is a sulfated glycosaminoglycan of over 100 residue disaccharides, each of which can be sulfated in variable positions and quantities [13]. ChS-A, in the absence of ACII, shows no observable ³³S NMR signal due to extensive linewidth broadening. With an increase in the incubation time and, thus, enzymatic catalysis, a sharp peak at −0.5 ppm appeared (Figure 8). This was attributed to ${\mathrm{S}\mathrm{O}}_4^{2^{-}}$ species produced due to the enzymatic cleavage of the N-acetylhexosaminide linkage in ChS-A. ³³S NMR was also utilized to investigate the tissue of the mantle edge, midgut, and adductor muscles of a scallop. ${\mathrm{S}\mathrm{O}}_4^{2^{-}}$ species were clearly identified relative to the taurine resonance (Figure 9).

7.2. ⁷⁷Se as a Substitution for Sulfur—¹H Detected ⁷⁷Se NMR in Proteins

⁷⁷Se enrichment of proteins has been used as a tool to expand the biological applications of NMR [29] based on the great sensitivity of ⁷⁷Se to electronic environments and dynamics [4]. Recently, sulfur sites with double-labeled ¹³C and ⁷⁷Se proteins were explored with the use of triple resonance ¹H-detected ⁷⁷Se NMR [30]. For the case of double-labeled methionine, the coupling constants ¹J(¹H, ¹³C) = 125–140 Hz and ¹J(¹³C, ⁷⁷Se) = 60–70 Hz were used for coherence transfers as follows:

¹³CH₃ → ¹³CH₃ → ⁷⁷Se → ¹³CH₃ → ¹³CH₃

The great resolution and sensitivity advantages of the method are illustrated in Figure 10 using a concentration of 300 μM of the protein CUE (MW = 6 kDa), in which methionine residues were substituted to ~95% with double-labeled ¹³CH₃-⁷⁷Se-methionine. Although ¹H and ¹³C chemical shift differences are very small, the ⁷⁷Se chemical shifts of the methionine residues M467 and M450 show a significant difference of 4.2 ppm. The technique requires specific hardware and decoupling schemes that are not, at present, commercially available. It remains to be seen what the advantages of the method are for proteins with molecular weights larger than 20 kDa since, at ultra-high magnetic fields, the line broadening might be significant due to the very large chemical shift anisotropy of ⁷⁷Se [4].

8. ³³S NMR in the Solid State

8.1. Basic Considerations

³³S NMR can provide important information about molecular structure and dynamics in the solid state; however, the extremely broad powder patterns ranging from hundreds of kHz to tens of MHz due to large quadrupolar anisotropic interaction and the very long longitudinal relaxation hinder the routine application of this nucleus [1,31]. Figure 11 shows the energy levels resulting from the Zeeman first- and second-order quadrupolar interactions for a nucleus with I = 3/2 [32]. The first-order quadrupolar interaction does not affect the central transition. The satellite transitions are shifted by ±2ω_Q, the exact amount of which is orientation-dependent. The second-order quadrupolar interaction moves the energy levels by equal and opposite amounts and strongly affects the satellite transitions 1/2 ↔ 3/2 and −3/2 ↔ −1/2, thus resulting in extremely broad resonances.

There are several methodologies that have been developed for the acquisition of ³³S NMR spectra in the solid state:

(i)

Static spectra: ultra-wideline Carr Purcell Meiboom Gill (CPMG) technique.

(ii)

Magic-angle spinning observation of the central transition: effects of B_o and population transfer.

(iii)

Dynamic nuclear polarization (DNP) in NMR.

(iv)

Indirectly detected satellite transition via saturation of the proton reservoir.

(v)

Zero-field and frequency/field-swept solid-state NMR.

A synopsis of (i) to (v) will be given below.

8.2. Static Spectra-Ultra-Wideline Carr Purcell Meiboom Gill (CPMG) Technique

Experimental ³³S static NMR spectra at 18.8 T of polycrystalline [³³S]-enriched taurine were recorded, and the line shapes, which cover a range of ~15 kHz, were used to calculate the following parameters: δ_iso = −2(3) ppm, δ₁₁ = 108(8) ppm, δ₂₂ = −35(8) ppm, δ₃₃ = −78(8) ppm, C_Q = 1.39(6) MHz, and $n_Q$ = 0.65(4) (Figure 12) [9]. The small C_Q value of the ${\mathrm{S}\mathrm{O}}_3^{-}$ group may be attributed to the high degree of symmetry even in the polycrystalline state.

For resonances broader than about 150 kHz, due to large C_Q values, it is difficult to accurately record lineshapes with a single pulse technique. To overcome the problem, several approaches have been proposed to carry out spin-echo experiments of broad band excitation and refocusing at several frequencies to map out the lineshape [33]. These approaches are time-consuming; nevertheless, Halat et al. [34] performed successful ultra-wideline quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) ³³S NMR experiments at natural abundance to investigate ${\mathrm{S}}^{2^{-}}$ sulfide and ${\mathrm{S}}_2^{2^{-}}$ disulfide units of the Li-ion battery conversion of the NbS₃ electrode. Seventeen variable offset cumulative spectra were acquired at 20 T with a step size of 1970 ppm (128.5 KHz) in order to cover a spectral width of ~2.6 MHz. Spectral features corresponding to both ${\mathrm{S}}^{2^{-}}$ and ${\mathrm{S}}_2^{2^{-}}$ with significantly different C_Q values were identified and supported with DFT calculations (see Section 9 on Computations).

8.3. Magic Angle Spinning Observation of the Central Transition: Effects of B_o and Population Transfer

The 1/2 ↔ −1/2 central transition of non-integer spins, such as ³³S, is not affected by first-order broadening. Consequently, the central transition appears as a relatively sharp peak at the center of the satellite transitions, which are often too broad to be detected. In several cases, however, the second-order effect of ³³S quadrupolar interactions contributes significantly to the line broadening of the central transition. MAS improves resolution but does not sufficiently remove anisotropic broadening. Thus, each distinct asymmetric ³³S electronic environment will give rise to a second-order quadrupolar power pattern under MAS, which can be several KHz wide, thus resulting in significant signal overlapping. The two main developments that have made ³³S solid-state NMR feasible are the availability of ultra-high magnetic field instruments and methods to enhance sensitivity via population transfer [35].

Second-order quadrupolar broadening, A, is inversely proportional to the strength of the static B_o field:

$$\mathrm{A}=\frac{3}{64}\frac{C_Q^2}{\frac{\mathsf{\gamma }}{2\mathsf{\pi }}{\mathsf{{\rm B}}}_{\mathsf{o}}}$$

(9)

The ³³S linewidth, therefore, is expected to be significantly reduced with a concomitant enhancement in sensitivity. Figure 13 shows the significant advantages of recording the spectrum of KAl (SO₄)₂·12H₂O at 17.6 T relative to that of 4.7 T [36].

Hansen et al. [37] reported significant sensitivity enhancements of 1.7 to 2.3 with the use of pairs of inversion pulses to induce selective polarization transfer between the four ³³S energy levels. The method was applied to surface ions and tetrathio metalates with quadrupolar nuclear parameter $C_Q$ values in the range of 0.3 to 1.2 MHz (Figure 14). The use of the WURST (wideband uniform rate smooth transaction) technique does not require a priori knowledge of the $C_Q$ and $n_Q$ values.

8.4. Dynamic Nuclear Polarization (DNP) NMR

DNP has been extensively utilized to increase the sensitivity of NMR by several orders of magnitude and involves the transfer of polarization from highly polarized electron spins to nearby nuclear spins in the sample [38]. Microwaves at a specific frequency cause transitions between coupled electron-nuclear spin states, resulting in nuclear spin polarization. Bellan et al. [39] performed the first ³³S DNP-NMR of ZnS nanoplatelets in order to characterize sulfur vacancies at the atomic scale. Figure 15A shows ³³S direct detection NMR spectra at 18.8 and 35.2 T with a total experimental time of 6 days 8 h and 6 h 20 min, respectively. Simulation of a single central transition resulted in δ_iso = −621 ppm, $C_Q$ = 5.2 MHz, and $n_Q$ = 0.40. On the contrary, the ⁶⁷Zn NMR showed the presence of three distinct central transitions due to the larger chemical shift range and, thus, sensitivity to the electronic environment. Application of the DNP method using a dipolar-mediated refocused INEPT technique (D-R INEPT) [40,41], in conjunction with QCPMG detection, resulted in a significant sensitivity enhancement by orders of magnitude of ³³S NMR, with a total experimental time of 6 h for the four subspectra (Figure 15B). The DNP-NMR spectrum was acquired at 105 K using the compound TEKPol as a polarizing agent at 9.4 T.

8.5. Indirectly Detected Satellite Transition via Saturation of the Proton Reservoir

Satellite transitions result, in most cases, in extremely broad resonances that are typically invisible for the low-natural abundance nuclei, like ³³S. Recently, Frydman and collaborators introduced a novel method for enhancing satellite transitions that is based on the progressive saturation of the proton reservoir (PROSPR) in static solids [42]. The PROSPR method includes a looped cross-polarization/spin diffusion process that progressively depletes the abundant ¹H polarization in solid samples. This ¹H depletion indirectly maps the NMR spectra of the heteronuclei as an attenuation of the abundant ¹H NMR signals. The achievable sensitivity enhancement with conventional NMR instruments and modest hardware modifications at room temperature is orders of magnitude greater in comparison to directly observed experiments [42].

Figure 16 illustrates the excellent sensitivity advantages of the PROSPR ³³S NMR spectrum of the ammonium sulfate (NH₄)₂SO₄) in natural abundance. The PROSPR NMR patterns appear with increased line width, which can be attributed to the limited spectral selectivity of the cross-polarizing ³³S r.f. pulse. The use of an adiabatic demagnetization in the rotating frame (ADRF) cross-polarization scheme results in more effective multiple repeats and improved heteronuclei (³³S) spectral selectivity (Figure 16).

8.6. Zero-Field and Frequency-Swept NMR in the Solid State

In the case of organosulfur molecules or covalent bonds, as in the case of sulfur elements, the $C_Q$ values are reported to be more than 40 MHz. Thus, even with the highest currently available magnetic fields up to 28.8 T, the ³³S NMR spectra would only be detected with frequency-swept or field-swept solid-state methods [43]. An alternative method, zero-field solid-state NMR or nuclear quadrupole resonance (NQR) spectroscopy, has been proposed, which utilizes the electric field gradient at the ³³S nucleus instead of an external magnetic field [43,44]. Figure 17 shows an excellent zero-field ³³S NMR spectrum of ³³S-enriched dibenzyl disulfide, with $C_Q$ = 46.8 MHz and $n_Q$ = 0.48 [7], which was recorded with a total experimental time of only 1 min [45]. The method does not provide chemical shifts; however, the $C_Q$ and $n_Q$ parameters strongly depend on the local electric field gradient tensor on the sulfur nucleus and, thus, are very important structural parameters at the atomic level.

8.7. Selected Applications in Transition Metal Complexes, Ferroelectric, and Ferromagnetic Materials

Jakobsen et al. [46] utilized the WURST inversion pulses of the two ±3/2 ±1/2 satellite transitions of the +1/2 −1/2 central transition, which resulted in an increase in the S/N ratio by a factor ≥ 2 [37] to investigate disordered tetrathio transition metal anions. The use of two MAS frequencies (5.0 and 10.0 KHz) at 14.1 T in combination with static QCPMG at 19.6 T allowed the analysis of complex spectra of disordered Re${\mathrm{S}}_4^{-}$ anions at natural abundance. The nuclear quadrupolar parameters, $C_Q$ and $n_Q$, the chemical shift anisotropy parameters, δ_ani and η_ani, and δ_iso of two different S sites of the four sulfur atoms in the Re${\mathrm{S}}_4^{-}$ anion were determined (

Table 4. ³³S Quadrupole coupling ($C_Q$ and $n_Q$), chemical shift anisotropy parameters (δ_ani and η_ani) and δ_iso for [(C₂H₅)₄N][ReS₄] determined from natural abundance WURST polarization transfer-enhanced ³³S MAS and ³³S static QCPMG NMR spectra. ^a Adopted with permission from [46]. Copyright 2010, Elsevier, Inc.

Entry Experiment	Sites	CQ (MHz)	${\mathit{n}}_{\mathit{Q}}$	δani (ppm)	ηani (ppm)	δiso (ppm) b
I
14.1 T, MAS	S1	2.21	0.00	68	0.00	475 (808.0)
II
14.1 T, MAS	S1	2.27	0.00	91	0.00	474.5 (807.5)
νr = 10.0 kHz	S2	2.48	0.18	67	0.37	433.4 (766.4)
III
14.1 T, MAS	S1	2.21	0.00	83	0.00	476.8 (809.8)
νr = 5.0 kHz	S2	2.51	0.17	122	0.51	444.3 (777.3)
IV
19.6 T, static	S1	2.21	0.00	91	0.00	474.1 (807.1)
spin–echo	S2	2.51	0.17	67	0.37	433.5 (766.5)

^a The optimum parameter set is shown in entry II. In the simulations for the S1 and S2 sites, the intensity ratio used was S1:S2 = 1:3, in accordance with the crystal structure for [(C₂H₅)₄N][ReS₄]. Due to the three-fold symmetry axis for S1, no error limits are given for $n_Q$. The error limits for the $C_Q$ values for both the S1 and S2 sites are within ±0.05 MHz. These error limits apply for all $C_Q$ and $n_Q$ values in Table 1, entries I–IV. ^b In parenthesis are the original chemical shifts reported relative to CS₂ (0 ppm).

). It was concluded that the use of high MAS speed resulted in narrow second-order line shapes for the central transition and, thus, improved precision of the CSA parameters.

³³S MAS NMR (at 18.8 T), XANES, and Raman spectroscopy were applied to investigate sulfur speciation in iron-free and iron-poor glasses and, more specifically, to quantify the relative concentrations of S²⁻, S⁶⁺, and any intermediate oxidation states present in silicate glasses quenched from melts [47]. ³³S NMR can be used to detect S²⁻ and S⁶⁺ in isotopically enriched samples with concentrations down to ~300 μg/g and long acquisition times of 1–2 days. However, both species have not been recorded simultaneously, although XANES and Raman showed the coexistence of S²⁻ and S⁶⁺ in the glass samples. It was concluded that ³³S NMR can be applied to very specific synthetic S-rich systems but not to Fe-bearing natural compositions.

Frydman and collaborators [48] used the ³³S PROSPR method to investigate ammonium sulfate, which undergoes a phase transition from its paraelectric (PE) to ferroelectric (FE) phase at T_c = 223.5 K. In the temperature range of 296–224 K, there is a monotonic increase in the C_Q values from 0.58 MHz to 0.67 MHz. At T_c = 223.5 K, the spectrum showed the coexistence of both the PE and FE phases (Figure 18). The satellite transitions (STs) are much more sensitive to temperature changes of $C_Q$ than central transitions (CTs) and, thus, are of great importance in investigating dynamic processes over a wide range of time scales.

³³S NMR measurements using ³³S-entiched ferromagnetic EuS were performed in the range of 1.3 to 4.2 K [49]. The extrapolated NMR signal at T = 0 has a value of 12.73 MHz (≈39 kG). EuS displays T^1.71 behavior above 4.2 K and T² dependence below 4.2 K.

9. Computations of ³³S NMR Parameters

9.1. Computational ³³S NMR in the Gas and Liquid Phase

Theoretical calculations of ³³S NMR parameters, including the computation of ³³S isotropic nuclear shieldings, spin-spin coupling constants involving the ³³S isotope, and ³³S nuclear quadrupole coupling constants, received reasonable attention; see review by Musio [3]. This was mainly for two reasons: calculations could help in identifying and elucidating the structural properties of the sulfur-containing molecules and, on the other hand, provide important information on the electron distribution and bonding situation around the sulfur atom. However, quite a few papers deal with computational ³³S NMR, mainly due to the lack of experimental data used to benchmark such calculations.

Generally, for the heavy elements, the available methods for the prediction of NMR parameters based on the Schrödinger equation become insufficient. In this case, the average orbital velocities of electrons in the vicinity of nuclei are close to the speed of light, giving rise to so-called relativistic effects such as spin-orbit coupling, also known as zitterbewegung (Darwin term), and mass-velocity correction, which can essentially affect NMR spectroscopic parameters. In general, relativistic effects on the NMR parameters become noticeable for the atoms beginning with the third period of the Periodic Table; however, for sulfur, such effects are expected (but not yet documented) to be fairly negligible. In one of the early papers, Kupka and coworkers [50] reported DFT calculations of ³³S NMR chemical shifts supported by experimental Raman and NMR data for thiophene and 3-methylthiophene. The Raman spectra of liquid thiophene were re-examined, and the performance of a hybrid B3PW91 functional used in combination with Pople’s basis set 6-311++G(d,p) was benchmarked at the ab initio restricted Hartree-Fock method.

In a much later paper by the same leading author [51], the ³³S nuclear isotropic shielding constants of 2-thiouracil were calculated at the B3LYP/aug-ccpVXZ and B3LYP/aug-cc-pCVXZ levels of theory. Figure 19 compares the convergence patterns of the ³³S isotropic shieldings for 2-thiouracil calculated at the B3LYP level with the aug-cc-pVXZ and aug-cc-pCVXZ basis sets. For the first family of basis sets, a considerable scatter of calculated values was observed, while a smooth convergence was found for the latter one. The same behavior was noticed when the Locally Dense Basis Set (LDBS) approach was employed. The change in estimated Complete Basis Set (CBS) values due to the LDBS approach was found to be about 10% of the CBS value when all atoms were described with the aug-cc-pVXZ or aug-cc-pCVXZ basis sets.

Bagno in his early paper [52] reported ³³S NMR chemical shifts of a wide series of organic and inorganic sulfur-containing compounds, calculated at the DFT-GIAO level using the 6-311++G(2d,2p) basis set. Theoretical values were found to be in good agreement with the available experiment, with a few exceptions (mostly those for the charged species); see

Table 5. ³³S NMR chemical shifts (δ, ppm) of organic and inorganic sulfur compounds calculated at the DFT-GIAO/6-311++G(2d,2p) level as compared to the experiment. Compiled from Bagno [52].

Cmpd.	33S NMR Chemical Shift, ppm		Cmpd.	33S NMR Chemical Shift, ppm
	Calc	Exp		Calc	Exp
OCS	−650	−594	SO2Cl2	−25	−46
Et2S2	−392	−501	Me2SO2	60	−12
thiophene	−168	−119	Me2SO2NMe2	−50	−9
H2S	−565	−503	MeSO3H	−40	−6
MeSH	−508	−458	MeSO3−	−40	−5
Me2S	−465	−428	MeSO2OMe	−35	2
Et–N=C=S	−640	−340	Na2S2O3	33	33
CS2	−386	−332	SOCl2	173	224
SF6	−253	−177	Ph–N=S=O	356	261
Me2SO	−100	−101	SO2	462	375

. Seven years later, Chesnut and Quin [53] reported a number of sulfur chemical shieldings (σ, ppm) evaluated at the scaled correlation level, including density functional theory, B3LYP/6-311+G(nd,p)//B3LYP/6-311+G(d,p), and modified MP2/6-311+G(nd,p) estimated infinite order Møller-Plesset theory with n = 2, the latter abbreviated as EMPI. The results of the ³³S NMR chemical shieldings are exemplified in

Table 6. The ³³S NMR chemical shieldings (σ, ppm) of typical organic and inorganic sulfur compounds calculated at the DFT level (B3LYP/6-311+G(2d,p)//B3LYP/6-311+G(d,p), scaled by k = 0.871, and at the EMPI (RHF plus MP2/6-311+G(d,p)//MP2/6-311+G(d,p)) level, as compared to the experiment. Compiled from Chesnut and Quin [53].

Cmpd.	Method of Calculation		Exp
	Pure DFT	EMPI
OCS	797.3	803.2	817
C2H4S	771.2	822.2	776
H2S	733.0	747.3	707.7
C6H5NCS	727.3		774
CH3SH	653.2	677.2	663.0
(CH3)2S	593.7	624.8	631
CH3SCN	580.2	595.0	573
CS2	558.4	552.4	536.1
C6H5SH	536.9		536
Tetrahydrothiophene	534.4	571.5	547
C2H4SO	437.6	426.3	416
C2H4SO2	351.7	295.8	291
SF6	339.9	340.9	379.9
Thiophene	328.5	309.6	324
C6H5SO2H	290.1		222
(CH3)2SO2	267.7	208.9	216
(CH3)2SO	257.0	202.0	219
Cl2SO2	236.7	183.0	249.4
C2H5SOCl	−39.1		−14
Cl2SO	−67.2	−84.6	−19
SO2	−157.1	−235.0	−169.7

. Calculations spanned over the range of available sulfur shieldings showed an agreement with the experiment of about 3% of the whole shielding range (Figure 20). For the EMPI method, the authors used a particular mixture of RHF and MP2 approaches. In many cases, the Møller-Plesset series of corrections appeared to converge in a manner that allowed the infinite series to be summed, so that the EMPI shieldings could be represented by a particular combination of the RHF and MP2 contributions. The ³³S NMR chemical shifts for fluoride, chloride, and bromide of the trimethylsulfonium ion and the S-methyltetrahydrothiophenium ion, in addition to the corresponding free cations, were also calculated within the same scaled DFT and EMPI approaches [54]. Experimental values were found to agree with the calculated values with the standard deviation of 35 ppm (3.5% of the shielding range) established in the previous paper [53] for a larger variety of sulfur compounds (Table 6).

Musio and Sciacovelli [55] calculated sulfur isotropic absolute shielding constants at the DFT level of theory (B3LYP/6-311++G(2d,p)) in the series of 2-substituted sodium ethanesulfonates, X–CH₂–CH₂–SO₃Na (X = H, CH₃, OH, SH, NH₂, Cl, Br, NH₃⁺). The diamagnetic contribution to the sulfur shielding constant was found to be constant, so that the observed deshielding of the ³³S resonance induced by the electron-removing substituents could be primarily related to the variations of the paramagnetic contribution. It was also demonstrated that oxygen lone pairs and sulfur core 2p electrons could play an active role in determining the paramagnetic contribution to sulfur shielding. With regard to the linewidth variations, they could be ascribed primarily to changes in the nuclear quadrupole coupling constants. The same authors [56] calculated the ³³S nuclear quadrupole coupling constants of 3- and 4-substituted benzenesulphonates and related charged species (both cations and anions) in the gas phase and in solution. The inclusion of the solvent effect in the calculations was found to be mandatory to reproduce experimental data. The solvent effect on the sulfur electric field gradient was shown to be due to electrostatic interactions. It was also shown that solvent interactions annihilated the Coulomb effect of the charge of the substituent and that those interactions caused a redistribution of electron density around the sulfur nucleus.

9.2. Computational ³³S NMR in the Solid State

For computational ³³S NMR in the solid-state, the available software and computational methods, the lineshape analysis and simulation of experimental data, together with the first principles calculations of NMR parameters, are of utmost importance. Some practical observations gained from a wide application of those approaches include, first of all, the choice of basis set and cluster approximation. Starting from a crystal structure, it is the accuracy of the unit cell parameters and atomic positions within the cell that determine the accuracy of calculated NMR parameters. The Gauge-Including Projector Augmented Wave (GIPAW) approach and its different modifications are particularly effective in reproducing NMR parameters. Although these approaches were initially aimed at periodic systems, there have been adaptations that allow parameters to be calculated when there is some atomic disorder in solid solutions and even in glasses. In particular, for glasses, Molecular Dynamics (MD) is effectively used to model the glass formation process, with the structural model further refined using DFT calculations, which then act as the input into GIPAW computation. For more details, see the recent review by Smith [31].

Wagler and coauthors [36] reported the solid-state ³³S MAS NMR spectra of a variety of inorganic sulfates recorded at magnetic fields ranging from 4.7 to 18.8 T and magic angle spinning (MAS) at the natural abundance of the ³³S isotope. A number of factors were considered when analyzing spectral linewidths, including magnetic field inhomogeneity, dipolar coupling, chemical shift anisotropy, chemical shift dispersion, and quadrupolar coupling. DFT calculations of the electric field gradient tensors revealed that the most significant contribution to the asymmetric electric field gradient around the sulfur nucleus was provided by the closest atoms, so that a general correlation could be observed between calculated and experimentally determined nuclear electric quadrupolar coupling constants.

Sutrisno et al. [57] demonstrated that a series of layered transition metal disulfides display a wide range of ³³S quadrupole coupling constants and chemical shift anisotropy values. It was shown that the wide-line natural abundance solid-state NMR spectra of ³³S in a less symmetric environment could readily be obtained at the ultrahigh magnetic field of 21.1 T and that, surprisingly, these closely related materials displayed a wide range of ³³S quadrupole coupling constant and chemical shift anisotropy values, both experimental and calculated (Figure 21).

Moudrakovski et al. [58] performed the assignment of various sites and the relative orientations of the electron field gradient (EFG) tensors by means of quantum chemical calculations using the DFT method and Gauge Independent Atomic Orbitals (GIAO) on molecular clusters of about 100 to 120 atoms. CASTEP, a leading code for calculating the properties of materials from first principles, was used, which is specifically designed for periodic boundary conditions and a gauge-including projector-augmented wave pseudopotential approach. Although only semiquantitative agreement was observed between the experimental and calculated parameters, the calculations of ³³S QCPMG spectra for K₂S₂O₇ and K₂S₂O₈ (Figure 22) appeared to be very useful in the interpretation of the experimental data.

O’Dell and Ratcliffe [59] reported the crystal structure for taurine shown in Figure 23a. It was found that the most shielded component of the chemical shift anisotropy tensor, σ₃₃, was aligned within 3° of the S-C bond, with σ₁₁ pointing in the approximate direction of the S-O² bond, while the largest component of the EFG tensor, V₃₃, was aligned very close to the S-O¹ bond (<5°), with V₂₂ pointing in the approximate direction of the S-O² bond. A combination of density functional and optimal control theory has been used by the authors to generate amplitude- and phase-modulated excitation pulses tailored specifically for the ³³S nuclei, based on one of several reported crystal structures. This allowed the authors to perform accurate determinations of the ³³S NMR interaction parameters at natural abundance and at a moderate magnetic field strength of 11.7 T. The ³³S NMR parameters were then used to assess the accuracy of various proposed crystal structures specified in Figure 23b,c. Very recently, Masuda et al. [9] performed experimental (Figure 12) and computational studies of polycrystalline ³³S-labeled taurine. The ³³S chemical shift anisotropy parameters agree with those reported by O’Dell and Ractliffe [59]. It was concluded, however, that the orientations of the ³³S electric field gradient and chemical shift tensors cannot be determined accurately since even small changes in the local asymmetry of the -${\mathrm{S}\mathrm{O}}_3^{-}$ group could introduce significant inconsistencies among the computational methods and molecular structures used.

Pallister and coauthors [60] applied a combination of solid-state NMR, first principles calculations, and single crystal XRD to relate solid-state ³³S NMR parameters obtained from a series of anhydrous sulfates of the elements of groups I–III. It was shown that the experimental ³³S NMR spectra, exemplified in Figure 24, for Cs₂SO₄, and Rb₂SO_4, were dominated by the quadrupolar interactions. Magnetic shielding constants and quadrupolar parameters for sulfur atoms were calculated using the plane wave pseudo-potential DFT. All calculated NMR parameters were found to be in very good agreement with the experimental results, which helped in the assignment of the stationary spectra. Indeed, reported correlations between ³³S experimentally determined chemical shifts and calculated isotropic shielding constants and quadrupolar coupling constants were characterized by correlation coefficients R² of 0.93–0.95 (Figure 25). Such a combined computational-experimental solid-state ³³S NMR approach could aid in the assessment and interpretation of the unique crystallographic data.

Halat and coauthors [34] reported ultra-wideline, high-field natural abundance solid-state ³³S NMR spectra of the Li-ion battery conversion electrode NbS₃, emphasizing the fact that it was the first ³³S NMR study of a compound containing disulfide units. The large quadrupolar coupling parameters of about 31 MHz reported were consistent with the values obtained from the performed DFT calculations. As an illustration, several experimental and calculated at the DFT level ³³S NMR spectra of NbS₃ are presented in Figure 26.

Yamada and coworkers [45] performed experimental and theoretical investigations of the sulfur-33 EFG tensor of disulfide and trisulfide sulfur-sulfur bonds in the corresponding dibenzyl compounds. The orientations of the ³³S EFG tensor were obtained by quantum chemical calculations. It was found that the largest EFG tensor component, V_ZZ, was approximately perpendicular to the molecular plane, while the smallest component, V_XX, was approximately 41° off the C-S bond. Extensive quantum chemical calculations were systematically performed by the authors to investigate the dependences of the ³³S EFG tensors on changes in torsion angles in disulfide and trisulfide bonds (the latter are shown in Figure 27), indicating that analysis of the ν_Q and C_Q values potentially makes it possible to assign the secondary structures of crosslinking in rubber.

Yamada [44] reported four ³³S quadrupolar frequencies of the ³³S-enriched elemental sulfur, α-S₈, which were observed in the range of 23.122–23.280 MHz at 140 K and assigned based on the results of the quantum chemical calculations. The two-dimensional nutation echo ³³S NQR techniques were carried out for each quadrupolar frequency, providing the ³³S EFG tensor with the following information: the quadrupolar coupling constant and the asymmetry parameter. Quantum chemical calculations were also performed to complete the spectral assignment and to obtain the ³³S EFG tensor orientations with respect to the molecular frame. As shown in Figure 28, the nutation NQR spectrum of α-S₈ exhibits a powder pattern with three sharp singularities, denoted as ν1, ν2, and ν3 (ν1 < ν2 < ν3), and these frequencies can be used to obtain ν_Q in a straightforward way.

Bellan and coauthors [39] reported ³³S solid-state NMR experiments at ultra-high fields and DNP experimental data coupled with DFT calculations, which allowed, for the first time, to propose a structural model of ZnS nanoplatelets in full agreement with the observed optical and conductive properties. This study represented a step toward the use of NMR spectroscopy coupled with DFT calculations for a better understanding of the structure-property relationship of the metal sulfide nanomaterials.

The most recent paper by Kupka and coauthors [61] described the crystal and molecular structures of three new thiosulfonates. Theoretical analysis of molecular structure and vibrational IR, Raman, and NMR spectra was carried out. Theoretical structures closely resemble their geometry in the solid state. A profound influence of the substituent effect of amino and acetamido groups on the SO₂S moiety in the p-position of the phenyl group was derived from theoretically computed quantitative aromaticity indexes based on geometric, magnetic, and electronic criteria. The substituent effect in the studied molecules, leading to chinoid structures of the phenyl ring and shortening of the C_Ar-S bonds, was clearly pronounced both in crystal and DFT-calculated geometries. In addition, the presence of the oxygen-lone electron pairs on one side of the phenyl group was found to provide different aromaticities above and below the ring plane.

Combination of NMR studies at various magnetic fields, various signal enhancement techniques, line shape analysis/simulation of experimental data, and first principles calculations resulted in several isotropic, δ_iso, and nuclear quadrupole coupling constants C_Q and n_Q, which are compiled in

Table 7. Isotropic ³³S chemical shifts, δ_iso, and nuclear quadrupole coupling constants $C_Q$ and $n_Q$ in the solid state (in brackets are the chemical shifts relative to CS₂ at 0 ppm).

Compound	δiso ppm	CQ MHz	nQ
Li2S a	−680
Na2S a	−671
CdS (wurtzite) a	−617
ZnS (wurtzite) a	−564
MgS a	−507
SrS a	−290.2
BaS a	−42
Na2$\mathrm{S}{\mathrm{O}}_4$ a	−3	0.82
Cs2$\mathrm{S}{\mathrm{O}}_4$ a	2	0.97
Ca$\mathrm{S}{\mathrm{O}}_4$ a	−7	1.0
CaSO4·2H2O a	−4	0.77
Na2Ca$(\mathrm{S}{\mathrm{O}}_4{)}_2$ a	5	0.71
Na2Mg(SO4)2·4H2O a	−12	2.2
(NH4)Al(SO4)2·12H2O a	0	0.53
TlAl(SO4)2·12H2O a	−1	0.56
CsAl (SO4)2·12H2O a	−2	0.53
Li2${\mathrm{S}\mathrm{O}}_4$ b	−2.1 (0.5) [330.9 (0.5)]	0.877 (0.050)	0.91 (0.05)
Na2${\mathrm{S}\mathrm{O}}_4$ b	7.1 (1.0) [340.1 (1.0)]	0.655 (0.050)	0.0 (0.10)
K2${\mathrm{S}\mathrm{O}}_4$ b	2.7 (0.5) [335.7 (0.5)]	0.959 (0.030)	0.42 (0.05)
Rb2${\mathrm{S}\mathrm{O}}_4$ b	3.4 (0.6) [336.4 (0.6)]	0.860 (0.050)	0.42 (0.10)
Cs2${\mathrm{S}\mathrm{O}}_4$ b	2.9 (1.0) [335.9 (1.0)]	0.813 (0.050)	0.4 (0.10)
(NH4)2${\mathrm{S}\mathrm{O}}_4$ b	1.1 (0.4) [334.1 (0.4)]	0.520 (0.050)	0.85 (0.20)
a-Mg ${\mathrm{S}\mathrm{O}}_4$ b	−19.9 (2.0 [313.1 (2.0)]	2.14 (0.05)	0.91 (0.05)
Ca${\mathrm{S}\mathrm{O}}_4$ b	−6.8 (0.5) [326.2 (0.5)]	0.86 (0.05)	0.48 (0.10)
Sr${\mathrm{S}\mathrm{O}}_4$ b	−2.6 (1.0) [330.4 (1.0)]	1.31 (0.05)	0.84 (0.10)
Ba${\mathrm{S}\mathrm{O}}_4$ b	−2.6 (2.0) [330.4 (2.0)]	1.76 (0.05)	0.68 (0.05)
Al2(SO4${)}_3$ b	−52.3 (2.0) [280.7 (2.0)]	2.32 (0.05)	0.55 (0.05)
(NH4)Al(SO4)2·12H2O b	−2.6 [330.4]	0.106 (0.005)	0.05 (0.05)
KAl(SO4)2·12H2O b	−1.2 [331.4]	0.633 (0.005)	0.20 (0.05)
KH${\mathrm{S}\mathrm{O}}_4$ b	−3(<50) [330 (<50)]	10.6	0.37
K2S2${\mathrm{O}}_7$ b	−13(<50) [320 (<50)]	16.2	0.1
K2S2${\mathrm{O}}_8$ b	−3(<50) [330 (<50)]	15.9	0.1
[C2H5)4N] [ReS4] c S1	474.5 [807.5]	2.27 (0.05)	0.00
	433.4 [766.4]	2.48 (0.05)	0.18 (0.05)
ZnS (nanoplatelets) d	−621	5.2	0.40
Nb${\mathrm{S}}_3$ e S1 S2−	−353 [−20]	4.4	0.38
S2	−576 [−243]	6.5	0.82
S3 ${\mathrm{S}}_2^{2-}$	−289 [40]	30.3	0.04
S4	−220 [113]	30.5	0.27
S5	−275 [58]	30.1	0.05
S6	−221 [112]	30.3	0.29
[33S]-taurine f	−2 (3)	1.39 (6)	0.65 (4)
α—${\mathrm{S}}_8$ g		43.68	0.57
α—${\mathrm{S}}_8$ h		44.6 (5)–45.7 (4)	0.30 (10)–0.49 (7)
[33S]-S-4 phenyl 4-toluene thiosulfonate i		42.1	0.8
[33S]-dibenzyl disulfide j		46.8 (6)	0.98 (7)

^a Complied from the review of Hinton [1]; ^b Complied from the review of Smith [31]; ^c Ref. [46]; ^d Ref. [39]; ^e Ref. [34]; ^f Ref. [9]; ^g Ref. [43]; ^h Ref. [44]; ⁱ Ref. [62]; ^j Ref. [45].

. Chemical shifts of metal sulfides exhibited an extremely large chemical shift range of over 600 ppm (Figure 7), which was explained in terms of the crystalline ionicities and the effects of orbital overlap [1]. DFT calculations by Laskowski and Blaha [62] showed that the variation of δ(³³S) in sulfides is mainly related to the presence of metal d states and their variation in the energy position within the conduction bands. The sulfate chemical shifts exhibit a narrow range of ~80 ppm, which is rather similar to that in solution, but with a wider range of C_Q values of 0.53 to 2.3 MHz (Table 7). C_Q values increase significantly to 10.6 MHz in KHSO₄, 15.9 MHz in K₂S₂O_8, and 16.2 MHz in K₂S₂O₇.

10. Conclusions and Prospects for Future Research

From the present review, it becomes evident that the number of reports of ³³S NMR in solution and, to a lesser extent, in the solid state is extremely sparse. Nevertheless, several technical and methodological advances and the availability of elemental ³³S (99.8 atom %) as the starting material for isotope enrichment are expected to give a significant impetus to ³³S NMR, which are summarized below.

(1)

Ultra-high-field instrumentation and high-sensitivity detection schemes will significantly enhance sensitivity and resolution in the case of: (i) small molecular-weight biological molecules with sulfur in a highly symmetric environment, which can be detected in enzymatic reaction products and in metabolomic studies [13]. (ii) Ligands, with C_Q (³³S) «10 MHz, bound to macromolecules and utilization, outside the extreme narrowing condition, of the m = 1/2 → m = −1/2 component, which is expected to result in significantly narrower resonances than the other component. Nevertheless, the prospect of recording meaningful NMR spectra for sulfur amino acid residues in proteins is rather poor. The use of ⁷⁷Se as a substitution for sulfur for ¹H detection in ⁷⁷Se NMR is, probably, the method of choice [30]. (iii) Solid state since the second-order quadrupolar line width of the m = 1/2 → m = −1/2 central transition decreases linearly with the magnetic field [36]. In addition, significant sensitivity enhancement is expected with the use of selective polarization transfer between the four ³³S energy levels [37].

(2)

Spin-echo experiments of the broad band excitation of static solids and refocusing at several frequencies can be successfully used to map out line shapes resulting from sulfur sites with C_Q (³³S) > 10 MHz.

(3)

Dynamic nuclear polarization (DNP) NMR would allow orders of magnitude sensitivity enhancement [39] and, thus, ³³S NMR studies at natural abundance within a reasonable experimental time.

(4)

The indirectly detected satellite transition via saturation of the proton reservoir (PROSPR) method and its variants [42,48] are expected to open new avenues of applications in investigating dynamic processes over a wide range of time scales.

(5)

Zero-field NMR (NQR) and frequency/field-swept NMR. Although this method may sound rather esoteric for ultra-high-field NMR spectroscopists, it should be emphasized that successful spectra were recorded using zero-field NMR of selectively enriched ³³S organosulfur compounds and models of cross-linked structures in rubber, with C_Q values in the range of 42 to 46 MHz [43,44,45,63,64].

(6)

The widespread availability of software and computational methods, the line-shape analysis and simulation of experimental data, and the great potentialities of ab initio calculations of NMR parameters will provide excellent means for structural and electronic information at the atomic level.

It should be emphasized, however, that for solid-state DNP-NMR experiments, specialized instrumentation is required, which is commercially available, or several components are necessary to upgrade more conventional wide-bore NMR instruments. Commercial zero-field NQR and frequency/field-swept NMR instruments are not widely spread and, in several cases, are available in specialized laboratories [45]. Fortunately, the highly promising indirectly detected satellite transition via saturation of the proton reservoir (PROSPR) method and its variants [42,48] can be applied with conventional NMR instrumentation with modest hardware modifications at room temperature,

It is hoped that the present review will encourage a wide range of researchers to utilize ³³S NMR spectroscopy as a powerful tool to provide structural, electronic, and dynamic information in a wide range of chemical, geological, and industrial applications.