3He NMR: from free gas to its encapsulation in fullerene

Measurements of Nuclear Magnetic Shielding in Molecules

The origin of nuclear magnetic shielding in diamagnetic molecules is discussed, pointing out various contributions to the shielding from electrons and the effects of intra- and intermolecular interactions. In NMR practice, chemical shifts are determined first as the measure of shielding in observed samples. The descriptions of shielding and chemical shifts are not fully consistent. Gas phase studies permit the withdrawal of intermolecular contributions from shielding and obtaining the magnetic shielding data in isolated molecules. The shielding determination in molecules is possible using at least three methods delivering the reference shielding standards for selected nuclei. The known shielding of one magnetic nucleus can be transferred to other nuclei if the appropriate nuclear magnetic moments are available with satisfactory accuracy. It is possible to determine the nuclear magnetic dipole moments using the most advanced ab initio shielding calculations jointly with the NMR frequencies measurements for small-sized isolated molecules. Helium-3 gas is postulated as all the molecules' primary and universal reference standard of shielding. It can be easily applied using common deuterium lock solvents as the secondary reference standards. The measurements of absolute shielding are available for everyone with the use of standard NMR spectrometers.

An overview of Helium-3 NMR: Recent developments and applications

The present review is focused on experimental and theoretical methods together with applications of helium NMR in chemistry and biochemistry. It comprises two main sections, the first dealing with standardization and instrumentation for 3He NMR spectroscopy and the second dealing with its practical applications, mainly those in general and organic chemistry with a special emphasis on the rapidly developing and exciting area of fullerenes encapsulating helium atoms. Several general applications of 3He NMR spectroscopy in physical chemistry and biomedicine are also briefly discussed.

Direct measurement of the 3He+ magnetic moments

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics^1-3, nuclear and atomic structure^4,5, magnetometry and metrology⁶, as well as chemistry and medicine^7,8. In particular, ³He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry^6,9. This requires a high-accuracy value for the ³He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon^10,11. Here we investigate the ³He⁺ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of ³He⁺ [Formula: see text], the zero-field hyperfine splitting [Formula: see text] Hz and the bound electron g-factor [Formula: see text]. The latter is consistent with our theoretical value [Formula: see text] based on parameters and fundamental constants from ref. ¹². Our measured value for the ³He⁺ nuclear g-factor enables determination of the g-factor of the bare nucleus [Formula: see text] via our accurate calculation of the diamagnetic shielding constant¹³ [Formula: see text]. This constitutes a direct calibration for ³He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value¹⁴ and enables us to determine the Zemach radius¹⁵ to [Formula: see text] fm.

QED Effect on the Nuclear Magnetic Shielding of ^{3}He

The leading quantum electrodynamic corrections to the nuclear magnetic shielding in one- and two-electron atomic systems are obtained in a complete form, and the shielding constants of ^{1}H, ^{3}He^{+}, and ^{3}He are calculated to be 17.735 436(3)×10^{-6}, 35.507 434(9)×10^{-6}, and 59.967 029(23)×10^{-6}, respectively. These results are orders of magnitude more accurate than previous ones, and, with the ongoing measurement of the nuclear magnetic moment of ^{3}He^{+} and planned ^{3}He^{2+}, they open the window for high-precision absolute magnetometry using ^{3}He NMR probes. The presented theoretical approach is applicable to all other light atomic and molecular systems, which facilitates the improved determination of magnetic moments of any light nuclei.

On the aromaticity of uracil and its 5-halogeno derivatives as revealed by theoretically derived geometric and magnetic indexes

The problem of aromaticity in heterocyclic rings of uracil and its 5-halogenoderivatives (5XU) was analyzed theoretically by calculating modified harmonic oscillator model of aromaticity (HOMA) for Heterocycle Electron Delocalization (HOMHED), nucleus-independent chemical shift parameters (NICS) and the so-called scan experiments, using helium-3 atom as a magnetic probe. The impact of halogen electronegativity on C5 atom’s NBO charges was also investigated. Water, as a polar environment, has a negligible impact on 5XU aromaticity. The most stable diketo tautomer shows a very low aromaticity while the “rare” dihydroxy form (tautomer No 6) is aromatic and resembles benzene. This is in agreement with traditional drawing of chemical formula of uracil’s six-membered ring, directly showing three alternating single and double bonds in its tautomer No 6. No good correlation between magnetic and geometric indexes of aromaticity for the studied 5XU tautomers was found. Linear correlation between the magnitude of NICS minimum, as well as the distance of the minimum above uracil ring plane center from 3He NMR chemical shift scan plot with respect to halogen electronegativity were observed. A strong linear dependence of magnetic index of aromaticity and the electronegativity of 5X substituent was observed.

Explorations of Magnetic Properties of Noble Gases: The Past, Present, and Future

In recent years, we have seen spectacular growth in the experimental and theoretical investigations of magnetic properties of small subatomic particles: electrons, positrons, muons, and neutrinos. However, conventional methods for establishing these properties for atomic nuclei are also in progress, due to new, more sophisticated theoretical achievements and experimental results performed using modern spectroscopic devices. In this review, a brief outline of the history of experiments with nuclear magnetic moments in magnetic fields of noble gases is provided. In particular, nuclear magnetic resonance (NMR) and atomic beam magnetic resonance (ABMR) measurements are included in this text. Various aspects of NMR methodology performed in the gas phase are discussed in detail. The basic achievements of this research are reviewed, and the main features of the methods for the noble gas isotopes: 3He, 21Ne, 83Kr, 129Xe, and 131Xe are clarified. A comprehensive description of short lived isotopes of argon (Ar) and radon (Rn) measurements is included. Remarks on the theoretical calculations and future experimental intentions of nuclear magnetic moments of noble gases are also provided.

Local aromaticity mapping in the vicinity of planar and nonplanar molecules

We report on nucleus-independent magnetic shielding (NICS) scans over the centers of six- and five-membered rings in selected metal phthalocyanines (MPc) and fullerene C60 for more accurate characterization of local aromaticity in these compounds. Detailed tests were conducted on model aromatic molecules including benzene, pyrrole, indole, isoindole, and carbazole and subsequently applied to H₂ Pc, ZnPc, Al(OH)Pc, and CuPc. Similar behavior of three selected magnetic probes, Bq, ³ He, and ⁷ Li⁺ , approaching perpendicularly the ring centers, was observed. For better visualization of shielding zone over the centers of aromatic rings, we introduced a simple mathematical procedure: the first and second derivatives of scan curves with respect to magnetic probe position enabled their additional examination. It allowed an easier localization of curve minimum and discrimination between areas in space varying by the magnetic field magnitude and to illustrate local aromaticity of two different kinds of rings in MPc with better resolution. Our results supported earlier reports on very low aromaticity indexes of pyrrole ring incorporated into MPc and significant aromaticity of the central macrocycle. No direct dependence between harmonic oscillator model of aromaticity and NICS was observed. Instead, a correlation between position of scan curve minimum and its magnitude were observed. In addition, the NICS values and ³ He chemical shifts in the middle of neutral C60 and C60^6- anion agreed well with the reported experimental NMR values for He@C60 and He@C60^6- .

Method and basis set dependence of the NICS indexes of aromaticity for benzene

The role of theory level in prediction of benzene magnetic indexes of aromaticity is analysed and compared with calculated nuclear magnetic shieldings of ³ He used as NMR probe. Three closely related nucleus-independent chemical shift (NICS) based indexes were calculated for benzene at SCF-HF, MP2, and DFT levels of theory and the impact of basis set on these quantities was studied. The changes of benzene NICS(0), NICS(1), and NICS(1)zz parameters calculated using SCF-HF, MP2 and several density functionals were within 1 to 3 ppm. Similar deviations between magnetic indexes of aromaticity were observed for values calculated with selected basis sets. Only very small effect of polar solvent on benzene aromaticity was predicted. The ³ He nuclear magnetic isotropic shielding (σ) and its zz-components (σ_zz ) of helium atom approaching the centre of benzene ring from above produced similar curves versus benzene-He distance to NICS parameters calculated for similarly moving Bq ghost atom. We also propose an experimental verification of NICS calculations by designing the ³ He NMR measurement for benzene saturated with helium gas or in low temperature matrices.

(129) Xe and (131) Xe nuclear magnetic dipole moments from gas phase NMR spectra

(3) He, (129) Xe and (131) Xe NMR measurements of resonance frequencies in the magnetic field B0=11.7586 T in different gas phase mixtures have been reported. Precise radiofrequency values were extrapolated to the zero gas pressure limit. These results combined with new quantum chemical values of helium and xenon nuclear magnetic shielding constants were used to determine new accurate nuclear magnetic moments of (129) Xe and (131) Xe in terms of that of the (3) He nucleus. They are as follows: μ((129) Xe) = -0.7779607(158)μN and μ((131) Xe) = +0.6918451(70)μN . By this means, the new 'helium method' for estimations of nuclear dipole moments was successfully tested. Gas phase NMR spectra demonstrate the weak intermolecular interactions observed on the (3) He and (129) Xe and (131) Xe shielding in the gaseous mixtures with Xe, CO2 and SF6 .

3He NMR studies on helium-pyrrole, helium-indole, and helium-carbazole systems: a new tool for following chemistry of heterocyclic compounds

The (3)He nuclear magnetic shieldings were calculated for free helium atom and He-pyrrole, He-indole, and He-carbazole complexes. Several levels of theory, including Hartree-Fock (HF), Second-order Møller-Plesset Perturbation Theory (MP2), and Density Functional Theory (DFT) (VSXC, M062X, APFD, BHandHLYP, and mPW1PW91), combined with polarization-consistent pcS-2 and aug-pcS-2 basis sets were employed. Gauge-including atomic orbital (GIAO) calculated (3)He nuclear magnetic shieldings reproduced accurately previously reported theoretical values for helium gas. (3)He nuclear magnetic shieldings and energy changes as result of single helium atom approaching to the five-membered ring of pyrrole, indole, and carbazole were tested. It was observed that (3)He NMR parameters of single helium atom, calculated at various levels of theory (HF, MP2, and DFT) are sensitive to the presence of heteroatomic rings. The helium atom was insensitive to the studied molecules at distances above 5 Å. Our results, obtained with BHandHLYP method, predicted fairly accurately the He-pyrrole plane separation of 3.15 Å (close to 3.24 Å, calculated by MP2) and yielded a sizable (3)He NMR chemical shift (about -1.5 ppm). The changes of calculated nucleus-independent chemical shifts (NICS) with the distance above the rings showed a very similar pattern to helium-3 NMR chemical shift. The ring currents above the five-membered rings were seen by helium magnetic probe to about 5 Å above the ring planes verified by the calculated NICS index.

Modeling 21Ne NMR parameters for carbon nanosystems

The potential of nuclear magnetic resonance (NMR) technique in probing the structure of porous systems including carbon nanostructures filled with inert gases is analysed theoretically using accurate calculations of neon ((21) Ne) nuclear magnetic shieldings. The CBS estimates of (21) Ne NMR parameters were performed for single atom, its dimer and neon interacting with acetylene, ethylene and 1,3-cyclopentadiene. Several levels of theory including restricted Hartree-Fock (RHF), Møller-Plesset perturbation theory to the second order (MP2), density functional theory (DFT) with van Voorhis and Scuseria's t-dependent gradient-corrected correlation functional (VSXC), coupled cluster with single and doubles excitations (CCSD), with single, doubles and triples included in a perturbative way (CCSD(T)) and single, doubles and tripes excitations (CCSDT) combined with polarization-consistent aug-pcS-n series of basis sets were employed. The impact of neon confinement inside selected fullerene cages used as an NMR probe was studied at the RHF/pcS-2 level of theory. A sensitivity of neon probe to the proximity of multiple CC bonds in C2 H2 , C2 H4 , C5 H6 and inside C28 , C30 , C32 , C34 and C60 fullerenes was predicted from (21) Ne NMR parameters' changes. Copyright © 2013 John Wiley & Sons, Ltd.