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Review

Nuclear Magnetic Resonance Gas-Phase Studies of Spin-Spin Couplings in Molecules

by
Karol Jackowski
Laboratory of NMR Spectroscopy, Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
Chemistry 2025, 7(1), 16; https://doi.org/10.3390/chemistry7010016
Submission received: 19 December 2024 / Revised: 10 January 2025 / Accepted: 16 January 2025 / Published: 26 January 2025
(This article belongs to the Section Physical Chemistry and Chemical Physics)
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Abstract

:
This paper overviews gas phase experiments with respect to one fundamental part of nuclear magnetic resonance (NMR) spectra. Indirect spin-spin coupling is an important parameter of NMR spectra and is observed as the splitting of spectral signals. A molecule containing two different magnetic nuclei (e.g., hydrogen HD, HT, or DT) exhibits this interaction in an external magnetic field measured as the spin-spin coupling parameter, nJ(NN′). Modern quantum chemical methods allow the precise calculation of spin-spin coupling, but it is never easy because nJ(NN′) is modified by temperature and intermolecular interactions. Accurate calculations can be performed only for small isolated molecules. NMR spectroscopy can deliver measurements of spin-spin couplings for isolated molecules if nJ(NN′) parameters are observed in the gas phase as a function of density. The extrapolation of such measurements to the zero-density limit permits nJ0(NN′) determination free from intermolecular interactions. The latter technique can also be applied to liquid vapors in molecules like acetonitrile or water. Spin-spin couplings across one chemical bond (1J0(NN′)) are the largest and most important for theoretical modeling. The present review reports numerous 1J0(NN′) parameters recently measured by multinuclear NMR spectra of gaseous samples.

Graphical Abstract

1. Introduction

Two magnetic nuclei in a molecule can interact directly through space or indirectly via bonding electrons. The first type of interaction is much stronger and known as dipole-dipole coupling, which has been successfully explored in NMR spectra of solids and liquid crystals [1]. In fluids, direct dipole-dipole interactions are not detected because of the fast reorientation of molecules. Weaker indirect interactions are observed as the splitting of NMR signals in gases and liquids. The resultant energy E is proportional to the scalar product of the interacting nuclear spins I of N and N′ nuclei expressed by the J(NN′) parameter in Equation (1).
E = J(NN′)ININ′
Consequently, the above kind of nuclear spin interaction is called scalar or indirect spin-spin coupling [2,3]. It is possible due to the engagement of electrons in the neighborhood of N and N′ nuclei and the coupling value is independent of the external magnetic field. Since 1950, this interaction has been observed in several laboratories as the splitting of NMR signals from various chemical compounds [4,5,6]. This physical phenomenon was first named by Gutowsky et al. [7]: “Coupling among Nuclear Magnetic Dipoles in Molecules”. Later, Ramsey presented a theoretical description of spin-spin coupling in molecules with the theoretical estimation of its value in a hydrogen molecule (HD) [8]. Coupling magnitude depends on nuclear moments described by magnetogyric ratios (γA, γB) and the reduced coupling constant K(NN′), which is due only to the electronic structure of a molecule [9]. For liquids and gases, the relation between K(NN′) and J(NN′) can be written in a scalar form as follows [10]:
K(NN′) = 4π2J(NN′)/(hγAγB)
K(NN′) in SI units [1 × 1019 N A−2 m−3] can be calculated by quantum chemical methods, while J(NN′) [Hz] is directly measured from NMR spectra. The coupling constant can have a positive or negative value [11], but this information is unavailable from ordinary NMR spectra. K(NN′) has at least four contributions in non-relativistic theory: the largest and most important Fermi contact (KFC), and the smaller spin-dipole (KSD), paramagnetic spin-orbit (KPSO), and diamagnetic spin-orbit (KDSO) contributions. Modern methods of spin-spin coupling calculations were reviewed by Kowalewski [12], Helgaker et al. [13], and Faber et al. [14]. The relativistic theoretical treatment of indirect spin-spin coupling was described by Repsky et al. [15].
Indirect spin-spin coupling in molecules is complex because all details of a molecular structure must be considered. The nJ(NN′) coupling between two magnetic nuclei (N and N′) is the most distinct if it happens across one chemical bond (n = 1). Weaker splittings are observed through a few chemical bonds (n > 1), usually up to three or four bonds, but much longer interactions (n > 4) sometimes also occur [2,3]. Let us note that spin-spin couplings across a few chemical bonds are always more dependent on molecular structure. Karplus curves for 3J(HH′), 3J(CH), and 3J(CC′) couplings can serve as good examples [16]. Intermolecular interactions also modify spin-spin couplings, and nJ(NN′) measurement contains an unwanted contribution if it comes from a single NMR experiment. Observing spin-spin couplings in the gas phase can overcome these latter difficulties. Jameson and Reger [17] showed that JA(NN′) measurements in the gas phase are density-dependent. Their extrapolation to the zero-density point permits the determination of the J0A(NN′) parameter free from intermolecular interactions. For a low-density region, the density dependence of JA(NN′) is linear:
JA(NN′) = J0A(NN′) + J1A(NN′)ρA + …
where ρA is the density of the investigated gas A and J1A(NN′) is the coefficient due to bimolecular collisions. As shown [18], similar studies of the gas phase can be extended to compounds that are liquids under standard conditions when another gas B is used as the gaseous solvent:
JA(NN′) = J0A(NN′) + J1AA(NN′)ρA + J1AB(NN′)ρB + …
The ρA is usually so small that the term J1AA(NN′)ρA can be safely neglected, and Equation (4) is simplified to a new linear form:
JA(NN′) = J0A(NN′) + J1AB(NN′)ρB + …
Equations (3) and (5) can be applied to measure spin-spin coupling parameters free from intermolecular interaction (J0A(NN′)) and, therefore, equivalent to isolated molecules. Such selected results were previously reviewed in 2003 [19]. Since that time, numerous new measurements of spin-spin couplings have been observed in the gas phase, and the present review is designed to highlight these new results.

2. Spin-Spin Couplings in H2, HD, and HT Molecules

The HD hydrogen molecule is the simplest molecular object where indirect spin-spin coupling can be found and deliver information on new unknown phenomena. Nowadays, it is also an excellent object for observing how experiments and calculation methods were improved over 70 years. Table 1 presents historical data on spin-spin couplings obtained for HD molecules and new results for HT and DT molecules. Selected experimental and calculated data are shown together to highlight the progress in NMR spectroscopy. The first spectra had limited resolution because weak magnets were applied to old spectrometers. Moreover, the deuterium nucleus had spin I = 1 and the nuclear electric quadrupole moment made wider signals of 1H NMR and a lower precision spin-spin coupling reading [20]. In contrast, the initial theoretical result by Ramsey [8] was so exceptionally good that 1J(HD) = 43 Hz. Further attempts at 1J(HD) calculations were steadily successful [21,22,23]. The inclusion of geometry change in an HD molecule due to vibration allowed Kowalewski [23] to obtain 1J(HD) = 43.48 Hz exploring only the Fermi contact term (KFC) in the coupling between proton and deuteron in 1974.
For the last 40 years, a new generation of NMR spectrometers with the FT (Fourier transform) method of signal detection and superconducting magnets has been available. Experimental measurements of 1J(HD) in the gas phase became possible at any pressure and a wide range of temperatures. Comparison of the 1J(HD) parameter measured in the gas phase and liquid solution in CCl4 revealed the influence of intermolecular interactions [24]. All intermolecular effects in 1J(HD) must be removed before the spin-spin coupling parameter can be compared with the appropriate value calculated for a single HD molecule. Meanwhile, the spin-spin parameter of HD was calculated more accurately, including all rovibrational effects at a given temperature [25,26]. Recent experimental values of 1J0(HH′) for HD, HT, and DT molecules [27] have been presented together with the appropriate results of ab initio calculations [29]. Finally, experimental and calculated 1J0(HH′) couplings are fairly consistent, but still, the precision of results shown in Table 1 requires further improvements.

3. nJ0(NN′) Parameters in Light Hydrocarbons

Hydrocarbons are a gateway to the chemistry of organic compounds. Light hydrocarbons are gaseous at room temperature and can be easily investigated by 1H and 13C NMR methods [16]. Methane (CH4), ethylene (C2H4), and ethane (C2H6) were among the first gaseous compounds whose nuclear magnetic shielding was studied as the function of density by 1H and 13C NMR [30,31]. The natural abundance of the carbon-13 isotope (1.11%) [32] permits the measurement of 1J(CH) couplings in organic compounds without additional enrichment in 13C atoms. On the other hand, the enrichment of hydrocarbons in carbon-13 and deuterium atoms permits more accurate studies of molecules by 1H and 13C NMR. Bennett et al. [33] observed 1J(CH) and 1J(CD) spin-spin couplings in the gas phase, and their experiments provided the temperature dependence of investigated parameters ranging from 200 to 370 K; their research was performed for CH4, CH3D, CHD3, and CD4, revealing 1H/2H isotope effects in spin-spin couplings as well. Enriched carbon-13 methane was also used to measure its 1J0(CH) value [34], as shown in Table 2.
Pure acetylene cannot be compressed because it is explosive at high pressure. Small amounts of 1,2-13C-enriched acetylene were studied in gaseous mixtures in xenon or carbon dioxide when gaseous solvents (Xe or CO2) were used with various densities [35]. The 1,2-13C-acetylene gave the AA′XX′ spin system, of which the AA′ and XX′ parts were separately observed by 1H and 13C NMR, respectively. As a result, four spin-spin couplings were measured: 1J(CH), 1J(CC), 2J(CH), and 3J(HH′). The application of Equation (5) facilitated obtaining appropriate nJ0 values, as shown in Table 2. The same methods were applied to measure nJ0 values from ethylene-13C2 (AA′A″A‴XX′) and ethane-13C2 (A3A′3XX′ spin system) using 13C NMR spectra [36]. Interestingly, similar results could also be obtained from 1H NMR spectra for the same 13C-enriched hydrocarbons. This method was first used for appropriate measurements in liquid carbon tetrachloride [37] and liquefied pure hydrocarbons at −70 °C [38]. Results in Table 2 show how spin-spin couplings in methane, acetylene, ethylene, and ethane resisted intermolecular interactions. The 1J(CC) and less 1J(CH) of acetylene-13C2 are perhaps exceptional because their values changed by more than 1 Hz when 13C2H2 was transferred from a gaseous to a liquid state. Results in Table 2 also reveal the large magnitude of spin-spin couplings across one chemical bond, which was dominant in all experimental results among the nJ(NN′) values here.
Table 2. Selected examples of spin-spin coupling measurements [Hz] in methane, acetylene, ethylene, and ethane molecules.
Table 2. Selected examples of spin-spin coupling measurements [Hz] in methane, acetylene, ethylene, and ethane molecules.
Molecule1J(CH)1J(CC)2J(CH)2J(HH′)3Jcis(HH′)3Jtrans(HH′)NMR
Method		Ref.
CH4125.304
125.31 		13C: 1J
13C; 1J0		[33]
[34]
C2H2247.56
248.4
249.0		174.78
171.5
171.6		50.14
49.4
49.3		 9.62
9.5
9.55		13C; 1J0
1H; in CCl4
1H; pure liq.		[35]
[37]
[38]
C2H4156.03
156.3
156.4		67.92
67.6
67.6		−2.55
−2.4
−2.4		2.53
2.3		11.81
11.7
11.7		19.18
19.0
19.1		13C; 1J0
1H; in CCl4
1H; pure liq.		[36]
[37]
[38]
C2H6124.97
124.9
125.3		35.00
34.6
34.4		−4.80
−4.5
−4.5		 8.09
8.0
8.0		13C; 1J0
1H; in CCl4
1H; pure liq.		[36]
[37]
[38]

4. nJ0(NN′) Values Measured for Vapors of Liquids

Numerous liquids (A) have sufficient vapor pressure for NMR experiments in the gas phase. Unfortunately, their gaseous molecules exhibit distinct intermolecular interactions that can change the magnitude of observed spin-spin couplings. Using any gaseous “inert” solvent (B; like Xe, SF6, CO2, etc.), one can solve the problem and successfully apply Equation (5) for the determination of spin-spin coupling in the isolated A molecule, nJ0A(NN′). Such experiments were first completed with acetonitrile (CH3CN) enriched in carbon-13 and nitrogen-15 isotopes [39,40]; Table 3 presents these results.
In contrast to results for light hydrocarbons, spin-spin couplings across one chemical bond of acetonitrile (1J0) are very sensitive to intermolecular interactions. In liquid acetonitrile and acetone, 1J(CH) increases by more than 2 Hz relative to the value in an isolated molecule, and 1J(CC) and 1J(NC) decrease by over 1 Hz. Spin-spin couplings across two and three chemical bonds are smaller and more stable, cf. values of 2J0(CH) and 3J0(NH). However, intermolecular effects are seen in all spin-spin couplings of CH3CN in liquid solutions.
Studies of spin-spin couplings of liquid vapors in the gas phase are promising because they can deliver nJ0(NN′) parameters of isolated molecules that can be immediately compared with results from quantum chemical calculations. As a result, this method has been applied in many later investigations of magnetic shielding and spin-spin couplings for methanol [43], water [44], acetaldehyde [45], and ethanol [46]. In all the above studies, the enrichment of investigated molecules in NMR active isotopes was necessary. Water is the most important chemical in our environment and crucial for life. Spectral NMR parameters of water are important in physical chemistry, but not easily available. 1J0(OH) coupling values were mostly measured in liquid solutions for a long time. Table 4 summarizes results obtained for 1H-17O spin-spin coupling of H2O molecules in various NMR experiments.
As seen in Table 1, 1J(17O,1H) spin-spin coupling in water molecules is sensitive to intermolecular interactions, especially to the hydrogen bonding system in liquid water. The 1J(17O,1H) parameter is diminished by over 10% when an isolated H217O molecule is transferred to the liquid phase. In vapor or cyclohexane solution, 1J(17O,1H) coupling is more similar to that in the isolated molecule. The effect of hydrogen bonds on the H217O molecule is pronounced because the single H217O molecule encapsulated in a fullerene cage gives 1J(17O,1H) = −77.9 Hz [53], only slightly changed from the 1J0(17O,1H) equal to −78.2 Hz [44].

5. J0(NN′) Couplings Across One Chemical Bond

All results shown in Table 1, Table 2, Table 3 and Table 4 confirm that spin-spin couplings across one chemical bond are larger and more distinct than couplings across a few bonds. This means they are more valuable as experimental standards to benchmark quantum chemical calculations. It is an important problem because calculations of spin-spin coupling are rather difficult, and the consistency between calculated and measured 1J0(NN′) values is never fully satisfactory; the group of CH4-nFn molecules can serve as an example [54]. Table 5 presents the collection of 1J0(NN′) parameters, which can be useful for further developments in quantum calculations towards indirect spin-spin coupling in molecules.

6. Conclusions

The present review paper provides an updated list of nJ0(NN′) experimental data for numerous molecules. It shows how difficult it is to obtain a satisfactory agreement between measured and calculated results of spin-spin coupling even for the smallest molecules: HD, HT, and DT. For larger molecules, this problem is even more complex and requires better methods of calculation. For this reason, comparison of experimental and calculated nJ values was limited in this review to hydrogen molecules. The discrepancy between calculated and experimental nJ(NN′) values for larger molecules is always more significant [54]. Let us note the continuous progress in calculations of spin-spin couplings that also include vibration corrections [66] and solvent effects [67,68]. Quantum chemical experts should decide which approximation is best for spin-spin calculations in various groups of chemical compounds. Fast improvements in electronics and computer capabilities give us hope for better precision in nJ quantum chemical calculations soon. All the experimental nJ0(NN′) data in Table 1, Table 2, Table 3, Table 4 and Table 5 of this review can be benchmarks for calculated spin-spin couplings in isolated molecules. The convergence of experimental and calculated 1J(H,H′) values for hydrogen molecules is well illustrated in Table 1. Other nJ(N,N′) from Table 2, Table 3 and Table 4 reveal the scale of intermolecular effects in spin-spin couplings. The observed intermolecular effects in spin-spin couplings were negligibly small for hydrocarbons, but rather significant for other molecules. Therefore, reliable NMR experimental data like 1J0(NN′) are always important. Fortunately, modern spectrometers and easy access to chemicals enriched in active NMR isotopes are promising for future research. As shown in Section 4, NMR investigations in the gas phase are already possible for numerous compounds that are real liquids under standard conditions. We can expect that similar experiments will also be available for some solid materials in the future. As presented, the amount of spin-spin coupling data from the gas phase is fairly large. Table 5 contains only the most important 1J0(NN′) parameters. All other nJ0(NN′) values can be easily found in the original papers. Let us hope that the present collection of 1J0(NN′) experimental parameters will be helpful for further studies on indirect spin-spin coupling.

Funding

This research received no external funding.

Conflicts of Interest

The author declares no conflict of interest.

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Table 1. Spin-spin couplings in hydrogen molecules. Milestones in NMR experiments and quantum chemical calculations for precisely determining 1J0(HH′) values.
Table 1. Spin-spin couplings in hydrogen molecules. Milestones in NMR experiments and quantum chemical calculations for precisely determining 1J0(HH′) values.
Molecule1J(HH′) [Hz]Method of MeasurementYearReference
HD45.5exp. HD gas; NMR spectra1952[20]
HD43theoretically estimated 1953[8]
HD35.217calculated1958[21]
HD42.7(5)calculated1969[22]
HD43.48calc.; vibrations included 1974[23]
HD43.115(12)exp. HD gas; NMR spectra1976[24]
HD42.64dissolved in CCl41976[24]
HD42.79calc.; rovib. included at 40 K 1988[25]
HD43.31(5)calc.; rovib. included at 300 K2012[26]
HD43.26(6)HD gas; NMR spectra, J0(1H,2H)2012[26]
HD43.12HD gas; NMR spectra, J0(1H,2H)2016[27]
HD43.31(5)calc.; rovib. included at 300 K2016[27]
HD43.112(5)HD gas; NMR spectra2018[28]
HD43.3067(9)calc.; rovib. included at 300 K2018[29]
HT299.06(36)HT gas; NMR spectra, J0(1H,3H)2016[27]
HT300.24(35)calc.; rovib. included at 300 K2016[27]
HT300.117(6)calc.; rovib. included at 300 K2018[29]
DT45.56(2)DT gas; NMR spectra, J0(2H,3H)2016[27]
DT45.67(5)calc.; rovib. included at 300 K2016[27]
DT45.6506(9)calc.; rovib. included at 300 K2018[29]
Table 3. Spin-spin couplings [Hz] in acetonitrile enriched in 13C and 15N isotopes.
Table 3. Spin-spin couplings [Hz] in acetonitrile enriched in 13C and 15N isotopes.
Solvent1J(CH)1J(CC)1J(NC)2J(CH)3J(NH)Ref.
SF6 gas; J0(NN′)134.04(2)60.12(5)−16.20(1)−10.18(2)−1.34(2)[39,40]
C6H12, liquid134.90(10) −16.55(8)−9.96(8)−1.65(8)[39]
(CH3)2CO, liquid136.00(10)56.89(8)−17.22(6)−9.92(7)−1.68(7)[40]
(CD3)2CO, liquid136.25(10)56.94(4)−17.53(10)−9.94(4)−1.69(2)[41]
CH3CN, liquid136.27(6)56.99(5)−17.55(5)−9.97(4)−1.70(4)[39]
C6F6, liquid135.73(1)58.0(2) −9.94(2)−1.69(2)[42]
Nematic phase135.7(2)57.7(3) [42]
Table 4. Various measurements of 1J(17O,1H) spin-spin coupling in the H217O molecule.
Table 4. Various measurements of 1J(17O,1H) spin-spin coupling in the H217O molecule.
Experimental Method1J(17O,1H) [Hz]YearReference
3% in liquid acetone−73.5 ± 2.11962[47]
10% in liquid acetone−82 ± 11967[48]
Vapor of H217O−79 ± 21967[49]
Liquid H217O−89.8 ± 2.31974[50]
0.1% in liquid cyclohexane-d12 −78.70 ± 0.021987[51]
0.5% in liquid nitromethane-d3 −80.6 ± 0.11997[52]
H217O@C60−77.92017[53]
1J0(17O,1H), gas phase−78.2 ± 0.12018[44]
Table 5. Selected examples of spin-spin couplings across one chemical bond, 1J0(NN′) a.
Table 5. Selected examples of spin-spin couplings across one chemical bond, 1J0(NN′) a.
NMR Experiment
in the Gas Phase b		MoleculeSpin-Spin Coupling1J0(N, N′) a,c [Hz]Reference
1H and 2H HD1H–2H43.12[26,27]
1H and 3H HT1H–3H299.06(36)[27]
2H and 3H DT2H–3H45.56(2)[27]
13C13CH413C–1H125.31(1)[34]
1H and 13C13CH3D13C–1H124.948 *[33]
13C13CH3D13C–2H19.224 *[33]
1H and 13C13CHD313C–1H124.262 *[33]
13C13CHD313C–2H19.113 *[33]
1H and 13C13CD413C–2H19.056 *[33]
1H and 17OH217O17O–1H−78.2(1)[44]
1H and 13C13CH313CHO13C–1H126.32(2)[45]
1H and 13C13CH313CHO13C–13C40.24(8)[45]
1H and 13C13CH313CHO13C–1H169.78(6)[45]
1H and 13C13CH313CH2OH13C–1H125.09(15)[46]
1H and 13C13CH313CH2OH13C–13C37.72(28)[46]
1H and 13C13CH313CH2OH13C–1H140.12(14)[46]
1H and 17OCH3CH217OH17O–1H−78.22(5)[46]
1H and 15N; 303 K15NH315N–1H−61.54(3) *[55]
1H and 15N; 303 K15NH2D15N–1H−61.46(3) *[55]
15N; 303 K15NH2D15N–2H−9.49(10) *[55]
1H and 15N; 303 K15NHD215N–1H−61.37(3) *[55]
15N; 303 K15NHD215N–2H−9.50(10) *[55]
15N; 303 K15ND315N–2H−9.49(10) *[55]
1H and 13C; 298 K13CH3F13C–1H147.37(5)[56]
13C and 19F; 298 K13CH3F13C–19F−163.10(5)[56]
13C and 19F13CH3F13C–19F−163.00(2)[57]
13C; 298K13CD3F13C–2H 22.45(5)[58]
13C and 19F13CD3F13C–19F−163.72(5)[58]
1H and 13C13CH2F213C–1H180.42(5)[59]
1H and 13C13CH2F213C–1H180.38(4)[57]
13C and 19F13CH2F213C–19F−234.55(5)[59]
13C and 19F13CH2F213C–19F−233.91(11)[57]
1H and 13C13CHF313C–1H235.63(5)[60]
1H and 13C13CHF313C–1H235.26(9)[57]
13C and 19F13CHF313C–19F−272.29(5)[60]
13C and 19F13CHF313C–19F−272.18(7)[57]
13C and 19F13CF413C–19F−258.32(9)[56]
1H and 13C13CH3Cl13C–1H147.58(6)[56]
1H and 13C13CH3Br13C–1H 149.45(7)[61]
1H and 13C13CH3I13C–1H149.38(2)[62]
11B and 19F BF311B–19F 20.0(2)[63]
31P and 1HPH331P–1H176.18(2)[64]
29Si and 1HSiH429Si–1H−201.01(2)[34]
73Ge and 1HGeH473Ge–1H−96.97(2)[34]
33S and 19FSF633S–19F250.1(4)[65]
(a) Parameters mostly from experimental data extrapolated to the zero-density point; some parameters are from single measurements at very low gas pressure and appropriately marked (*). Results for C2H2, C2H4, C2H6, and CH3CN are separately presented in Table 2 and Table 3. (b) Available methods for measurements and result verification. (c) Only one better result was chosen when the authors provided data from a few similar experiments.
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Jackowski, K. Nuclear Magnetic Resonance Gas-Phase Studies of Spin-Spin Couplings in Molecules. Chemistry 2025, 7, 16. https://doi.org/10.3390/chemistry7010016

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Jackowski K. Nuclear Magnetic Resonance Gas-Phase Studies of Spin-Spin Couplings in Molecules. Chemistry. 2025; 7(1):16. https://doi.org/10.3390/chemistry7010016

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Jackowski, K. (2025). Nuclear Magnetic Resonance Gas-Phase Studies of Spin-Spin Couplings in Molecules. Chemistry, 7(1), 16. https://doi.org/10.3390/chemistry7010016

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