Nuclear Magnetic Moments Research Articles

Characteristic nuclear spin-induced optical rotation in oxygen-containing organic molecules.

Nuclear spin-induced optical rotation (NSOR) is a nuclear magneto-optic effect that manifests itself as a rotation of the plane of polarization of linearly polarized light. The effect is induced by ordered nuclear magnetic moments within a molecule. NSOR is sensitive to specific, localized interactions. Hence, the connection between the local chemical environment and the corresponding NSOR signal is crucial to understand. Despite the fact that contributions to better understand the connection have been made, the general systematics still remain unknown. In this paper, NSOR in oxygen compounds is investigated systematically to better understand the impact of oxygen atoms on the NSOR signal. NSOR signals are computed using density-functional theory methods for five different classes of oxygen compounds. The ability of NSOR to distinguish different molecules and individual nuclei in the molecules is studied and the information provided by NSOR is compared to conventional NMR spectroscopy. The results reveal that NSOR is capable of chemical distinction between nuclei and molecules, and by using NMR and NSOR together it is possible to distinguish nuclei near the oxygen atom.

Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm’s hidden variables

In this paper, we outline the research conducted by the first named author and his associates on the axiom-preserving, thus isotopic completion of quantum mechanics into hadronic mechanics according to the historical legacy by A. Einstein, B. Podolsky and N. Rosen that quantum mechanics is not a complete theory and review the ensuing exact representation of the magnetic moment and spin of the Deuteron in its ground state thanks to the isotopic completion of Pauli’s matrices with an explicit and concrete content of D. Bohm’s hidden variablelambda. We then outline the independent studies conducted by the second named author on the representation of the conventional Pauli’s matrices via geometric Clifford algebras. We finally show that the combination of the two studies allows a mathematically rigorous, numerically exact and time invariant geometric representation of the magnetic moment, spin and hidden variable of the Deuteron in its ground state.

P,T -odd energy shifts of the YbOH173 molecule

The energy shift in molecular spectra due to interaction of nuclear magnetic quadrupole moment ($M$) with electrons is equal to $\delta E_M = MW_M P_{ M}$, where $W_M$ is a constant determined by the electronic structure of the molecule and $P_{ M}$ is a dimensionless constant. We extended the method for calculation of parity nonconservation effects in triatomic molecules developed in Ref. [A. Petrov and A. Zakharova, Phys. Rev. A ${\bf 105}$, L050801 (2022)] to the case of $P_{ M}$ constant and applied it to $^{173}$YbOH in the first excited $v=1$ bending mode. Results of our calculations are required for the extraction of the $M$ value from the YbOH experiment.

Re-Evaluation of the Nuclear Magnetic Octupole Moment of 209Bi

We modified the Hfs92 code of the GRASP package in order to describe the magnetic octupole hyperfine interaction. To illustrate the utility of the modified code, we carried out state-of-the-art calculations of the electronic factors of the magnetic octupole hyperfine interaction constants for levels in the ground configuration of the Bi atom. The nuclear magnetic octupole moment of the 209Bi isotope was extracted by combining old measurements of the hyperfine structures of 6p34S3/2o [Hull, R.; Brink, G. Phys. Rev. A 1970, 1, 685] and 2P3/2o [Landman, D.A.; Lurio, A. Phys. Rev. A 1970, 1, 1330] using the atomic-beam magnetic-resonance technique with our theoretical electronic factors. The present extracted octupole moment was consistent with all the available values but the one obtained in the single-particle nuclear shell model approximation. This observation supports the previous finding that nuclear many-body effects, such as the core polarization, significantly contribute to the nuclear magnetic octupole moment in the case of 209Bi.

Refined nuclear magnetic dipole moment of rhenium: Re185 and Re187

The refined values of the magnetic dipole moments of $^{185}$Re and $^{187}$Re nuclei are obtained. For this, we perform a combined relativistic coupled cluster and density functional theory calculation of the shielding constant for the ReO$_4^-$ anion. In this calculation, we explicitly include the effect of the finite nuclear magnetization distribution in the single-particle nuclear model using the Woods-Saxon potential for the valence nucleon. By combining the obtained value of the shielding constant $\sigma=4069(389)$~ppm with the available experimental nuclear magnetic resonance data we obtain the values: $\mu(^{185}{\rm Re})=3.1567(3)(12) \mu_N, \mu(^{187}{\rm Re})=3.1891(3)(12) \mu_N$, where the first uncertainty is the experimental one and the second is due to theory. The refined values of magnetic moments are in disagreement with the tabulated values, $\mu(^{185}{\rm Re})=3.1871(3) \mu_N, \mu(^{187}{\rm Re})=3.2197(3) \mu_N$, which were obtained using the shielding constant value calculated for the atomic cation Re$^{7+}$ rather than the molecular anion. The updated values of the nuclear magnetic moments resolve the disagreement between theoretical predictions of the hyperfine structure of H-like rhenium ions which were based on the tabulated magnetic moment values and available experimental measurements. Using these experimental data we also extract the value of the parameter of nuclear magnetization distribution introduced in [J. Chem. Phys. \textbf{153}, 114114 (2020)], which is required to predict hyperfine structure constants for rhenium compounds.

Calculation of energies and hyperfine-structure constants of U+233 and U233

We carried out calculations of the energies and magnetic dipole hyperfine-structure constants of the low-lying states of $^{233}\mathrm{U}^{+}$ and $^{233}\mathrm{U}$ using two different approaches. With six valence electrons and a very heavy core, uranium represents a major challenge for precision atomic theory even using large-scale computational resources. The first approach combines configuration interaction (CI) with a method allowing us to include core-valence correlations to all orders of the perturbation theory over residual Coulomb interaction. The second approach is a pure CI method which allows the use of different initial approximations. We present a detailed analysis of all calculated properties and discuss the advantages and disadvantages of each of these methods. We report a preliminary value of the U nuclear magnetic moment and outline the need for further experiments.

Nuclear DFT analysis of electromagnetic moments in odd near doubly magic nuclei

We use the nuclear density functional theory to determine nuclear electric quadrupole and magnetic dipole moments in all one-particle and one-hole neighbours of eight doubly magic nuclei. We align angular momenta along the intrinsic axial-symmetry axis with broken time-reversal symmetry, which allows us to explore fully the self-consistent charge, spin, and current polarisation. Spectroscopic moments are determined for symmetry-restored wave functions and compared with available experimental data. We find that the obtained polarisations do not call for using quadrupole- or dipole-moment operators with effective charges or effective g-factors.

Valence state of chromium ions in the half-metallic ferromagnet CrO2 probed by Cr53 NMR

We have performed $^{53}\mathrm{Cr}$ NMR measurements on a high-purity polycrystalline sample to investigate the static and dynamic properties of a half-metallic ferromagnet ${\mathrm{CrO}}_{2}$. Two $^{53}\mathrm{Cr}$ NMR lines, corresponding to magnetically nonequivalent Cr nuclei, were observed in the ferromagnetic phase of ${\mathrm{CrO}}_{2}$ despite all of the Cr ions being situated on the crystallographic equivalent sites. We measured the temperature dependences of the $^{53}\mathrm{Cr}$ spin-lattice relaxation rate ${({T}_{1})}^{\ensuremath{-}1}$ in the ferromagnetic phase for the temperature range $T=4.2--360\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. It was found that in the range of low temperatures ($T\ensuremath{\le}60\phantom{\rule{0.28em}{0ex}}\mathrm{K}$) the relaxation of nuclear magnetic moments is determined mainly by the orbital contribution proportional to the temperature, conditioned by the fluctuation of the orbital currents of $d$-band electrons. At temperatures $T>60\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, the main mechanism leading to the nuclear spin-lattice relaxation is a three-magnon process of scattering at which the relaxation of the nuclear spin is accompanied by the absorption of a magnon and the creation of two magnons. Based on the analysis of temperature dependences of ${({T}_{1})}^{\ensuremath{-}1}$ for two nonequivalent Cr ions, we found that their valence state is the same and corresponds to valence ${\mathrm{Cr}}^{4+}$, whereas the difference of resonance frequencies for these ion nuclei is conditioned by the different magnetic local fields in their location.

Ammonia: The molecule for establishing 14N and 15N absolute shielding scales and a source of information on nuclear magnetic moments.

Multinuclear Nuclear Magnetic Resonance (NMR) studies of the gaseous mixtures 3He/14NH3 and 3He/15NH3 are reported. Precise analysis of the 3He, 14N, 15N, and 1H resonance frequencies show a linear dependence on the gas density. Extrapolation of these results to the zero-pressure limit gives ν0(1H), ν0(14N), and ν0(15N) resonance frequencies of the isolated ammonia molecule at 300K. The analogous value for 3He atoms in gaseous mixtures ν0(3He) was measured as well. The application of a new scheme to introduce the most important electronic effects on NMR shieldings, together with highly accurate quantum chemical shielding calculations, allows the 14/15N and 1H shielding of the isolated ammonia molecule to be obtained with the greatest accuracy and precision. For the first time, these studies were carried out on ammonia within the so-called four-component relativistic framework. The NMR frequency comparison method provides an approach for determining the 14N and 15N nuclear magnetic moments. The new shielding parameters in ammonia were used for re-evaluation of the entire nitrogen absolute shielding scale. Additionally, the absolute shielding values of several gaseous compounds and secondary reference substances in liquids were presented. It was established that 14N and 15N absolute shielding constants in 14NH3 and 15NH3 are very similar and only differ by less than 0.01 ppm, which is not usually measurable in NMR experiments. Precise calculations of 14N and 15N dipole moments were also made from these accurate shielding values.

Distinguishing “Through-Space” from “Through-Bonds” Contribution in Indirect Nuclear Spin–Spin Coupling: General Approaches Applied to Complex JPP and JPSe Scalar Couplings

We present herein two complementary theoretical approaches for analyzing the transmission pathways of indirect nuclear spin-spin couplings in high-resolution nuclear magnetic resonance. This phenomenon is notably conceptually poorly understood in complex experimental situations in which both nonbonded ["through-space" (TS)] and more "classical" bonding ("through-bond") spin-spin coupling pathways are potentially involved. The computational approaches we propose allow the visualization and discussion of individual transmission pathways and estimation of their relative weight from numerical contributions to the spin-spin coupling constant J-value. The first approach is based on the analysis of contributions limited to occupied molecular orbitals [focused on occupied molecular orbitals (FOMO)]. The second approach encompasses the consideration of both occupied and vacant orbitals [global molecular orbital contributions (GMOC)], and, besides the contributions from individual pathways, also considers their cross contributions. Both approaches are applicable to large systems with complex interactions of nuclear magnetic moments. Herein, we have first applied the FOMO and GMOC computational approaches to simple diphosphine models and then extended the analysis to JPP and JPSe experimentally measured in a constrained selenated (diphosphino)naphthalene compound. The new computational tools contributed evidence for the importance of the single lone pair not only from phosphorus but also from selenium in TS spin-spin transmission. It evidenced and modeled for the first time the existence of spin-spin transmission pathways mixing classical covalent bonding parts with a lone pair overlap of proximate heteroatoms (P and Se).

Direct measurement of the 3He+ magnetic moments

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics1–3, nuclear and atomic structure4,5, magnetometry and metrology6, as well as chemistry and medicine7,8. In particular, 3He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry6,9. 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 billon10,11. Here we investigate the 3He+ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of 3He+{g}_{I}^{{prime} }=-,4.2550996069(30{)}_{{rm{stat}}}(17{)}_{{rm{sys}}}, the zero-field hyperfine splitting {E}_{{rm{HFS}}}^{exp }=-,8,,665,,649,,865.77{(26)}_{{rm{stat}}}{(1)}_{{rm{sys}}} Hz and the bound electron g-factor {g}_{e}^{{rm{exp }}}=-,2.00217741579(34{)}_{{rm{stat}}}(30{)}_{{rm{sys}}}. The latter is consistent with our theoretical value {g}_{e}^{{rm{theo}}}=-,2.00217741625223(39) 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 {g}_{I}=-,4.2552506997(30{)}_{{rm{stat}}}(17{)}_{{rm{sys}}}(1{)}_{{rm{theo}}} via our accurate calculation of the diamagnetic shielding constant13{sigma }_{{}^{3}{mathrm{He}}^{+}}=0.00003550738(3). 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 {r}_{Z}=2.608(24) fm.

Contribution of the Weinberg-type operator to atomic and nuclear electric dipole moments

The contribution of the CP violating three-gluon Weinberg operator, frac{1}{3!}w{f}^{abc}{epsilon}^{nu rho alpha beta}{G}_{mu nu}^a{G}_{alpha beta}^b{G}_{rho}^{cmu} , to the atomic and nuclear EDMs is estimated using QCD sum rules. After calculating the transition matrix element between the pion and the vacuum through the Weinberg operator, we obtain the long-range CP-odd nuclear force by determining the isovector CP-odd pion-nucleon vertex, using chiral perturbation theory at NLO. The EDMs of 199Hg, 129Xe, and 225Ra atoms, as well as those of 2H and 3He nuclei are finally given including comprehensive uncertainty analysis. While the leading contribution of the 199Hg EDM is given by the intrinsic nucleon EDM, that of 129Xe atom may be dominated by the one-pion exchange CP-odd nuclear force generated by the Weinberg operator. From current experimental data of the 199Hg atomic EDM, we obtain an upper limit on the Weinberg operator magnitude of |w| < 4 × 10−10GeV−2 if we assume that it is the only source of CP violation at the scale μ = 1 TeV.

Dark magnetic dipole property in fermionic absorption by nucleus and electrons

The fermionic dark matter (DM) absorption by nucleus or electron targets provides a distinctive signal to search for sub-GeV DM. We consider a Dirac fermion DM charged under a dark gauge group and with the dark magnetic dipole operator. The DM field mixes with right-handed neutrino and interacts with the ordinary electromagnetic charge current via the kinetic mixing term of gauge fields. As a result, the incoming DM is absorbed and converted into neutrino in final state through the dipole-charge interaction. For the DM absorption by nucleus, the recoil energy spectrum exhibit a peak at {m}_{upchi}^2/2{m}_N for each isotope in the target. XENON1T can probe the DM mass above 27 MeV and the projected constraint on the inelastic DM-nucleon cross section becomes 10−49 cm2. CRESSTIII with lower energy threshold would be sensitive to the DM mass above 2 MeV. We also check that the contribution from the nuclear magnetic dipole is negligible for 131Xe target. The absorption of DM by bound electron target induces ionization signal and is sensitive to sub-MeV DM mass. The involvement of the ionization form factor spreads out the localized recoil energy. We show the future prospect for the constraint on the magnetic dipole coupling from the electron ionization of 131Xe.

Probing Nuclear Dipole Moments and Magnetic Shielding Constants through 3-Helium NMR Spectroscopy

Multinuclear NMR studies of the gaseous mixtures that involve volatile compounds and 3He atoms are featured in this review. The precise analyses of 3He and other nuclei resonance frequencies show linear dependencies on gas density. Extrapolation of the gas phase results to the zero-pressure limit gives the ν0(3He) and ν0(nX) resonance frequencies of nuclei in a single 3-helium atom and nuclei in molecules at a given temperature. The NMR frequency comparison method provides an approach for determining different nuclear magnetic moments. The application of quantum chemical shielding calculations, which include a more complete and careful theoretical treatment, allows the shielding of isolated molecules to be achieved with great accuracy and precision. They are used for the evaluation of nuclear moments, without shielding impacts on the bare nuclei, for: 10/11B, 13C, 14N, 17O, 19F, 21Ne, 29Si, 31P, 33S, 35/37Cl, 33S, 83Kr, 129/131Xe, and 183W. On the other hand, new results of nuclear moments were used for the reevaluation of absolute nuclear magnetic shielding in the molecules under study. Additionally, 3He gas in water solutions of lithium and sodium salts was used for measuring 6/7Li and 23Na magnetic moments and reevaluating the shielding parameters of Li+ and Na+ water-solvated cations. In this paper, guest 3He atoms that play a role in probing the electron density in many host macromolecules are also presented.

Nuclear-induced dephasing and signatures of hyperfine effects in isotopically purified C13 graphene

The hyperfine interaction between the spins of electrons and nuclei is both a blessing and a curse. It can provide a wealth of information when used as an experimental probing technique but it can also be destructive when it acts as a dephasive perturbation on the electronic system. In this work, we fabricated large scale single and multilayer isotopically-purified $^{13}$C graphene Hall bars to search for interaction effects between the nuclear magnetic moments and the electronic system. We find signatures of nuclei with a spin in the analysis of the weak localization phenomenon that shows a significant dichotomy in the scattering times of monolayer $^{12}$C and $^{13}$C graphene close the Dirac point. Microwave-induced electron spin flips were exploited to transfer momentum to the nuclei and build-up a nuclear field. The presence of a very weak nuclear field is encoded in a modulation of the electron Zeeman energy which shifts the energy for resonant absorption and reduces the $g$-factor.

Nuclear magnetic shielding in HD and HT

We perform a calculation of the nuclear magnetic shielding in HD and HT molecules, with complete and perturbative accounts for nuclear masses. From the difference in shielding, we obtain the deuteron and triton magnetic moments in agreement with the CODATA value, with the accuracy limited only by nuclear magnetic resonance measurements. Most importantly, our calculations indicate a potential for improved determination of nuclear magnetic moments.

Laser-coolable AcOH+ ion for CP -violation searches

The ${\mathrm{AcOH}}^{+}$ molecular ion is identified as a prospective system to search for $\mathcal{CP}$-violation effects. According to our study ${\mathrm{AcOH}}^{+}$ belongs to the class of laser-coolable polyatomic molecular cations implying a large coherence time in the experiments to study symmetry-violating effects of fundamental interactions. We perform both nuclear and high-level relativistic coupled cluster electronic structure calculations to express the experimentally measurable $\mathcal{T},\mathcal{P}$-violating energy shift in terms of fundamental quantities such as the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment ($e\mathrm{EDM}$) and dimensionless scalar-pseudoscalar nuclear-electron interaction constant. We further express nuclear MQM in terms of the strength constants of $\mathcal{CP}$-violating nuclear forces: quantum chromodynamics vacuum angle $\overline{\ensuremath{\theta}}$ and quark chromo-EDMs. The equilibrium structure of ${\mathrm{AcOH}}^{+}$ in the ground and the four lowest excited electronic states was found to be linear. The calculated Franck-Condon factors and transition dipole moments indicate that the laser cooling using an optical cycle involving the first excited state is possible for the trapped ${\mathrm{AcOH}}^{+}$ ions with the Doppler limit estimated to be $\ensuremath{\sim}$4 nK. The lifetime of the ($0,{1}^{1},0$) excited vibrational state considered as a working one for MQM and $e\mathrm{EDM}$ search experiments is estimated to be $\ensuremath{\sim}0.4$ s.

A Method for the Variational Calculation of Hyperfine-Resolved Rovibronic Spectra of Diatomic Molecules.

An algorithm for the calculation of hyperfine structure and spectra of diatomic molecules based on the variational nuclear motion is presented. The hyperfine coupling terms considered are Fermi-contact, nuclear spin-electron spin dipole–dipole, nuclear spin–orbit, nuclear spin-rotation, and nuclear electric quadrupole interactions. Initial hyperfine-unresolved wave functions are obtained for a given set of potential energy curves and associated couplings by a variation solution of the nuclear-motion Schrödinger equation. Fully hyperfine-resolved parity-conserved rovibronic Hamiltonian matrices for a given final angular momentum, F, are constructed and then diagonalized to give hyperfine-resolved energies and wave functions. Electric transition dipole moment curves can then be used to generate a hyperfine-resolved line list by applying rigorous selection rules. The algorithm is implemented in Duo, which is a general program for calculating spectra of diatomic molecules. This approach is tested for NO and MgH, and the results are compared to experiment and shown to be consistent with those given by the well-used effective Hamiltonian code PGOPHER.

New Tetra-dentate Schiff Base Ligand N2O2 and Its Complexes with Some of Metal Ions: Preparation, Identification, and Studying Their Enzymatic and Biological Activities

In present work, new tetra-dentate ligand, titled 3,5-bis ((E)-5-Bromo-2-hydroxy benzylidene amino) benzoic acid (H3L), was prepared via an acid-catalyzed condensation process. New four metallic ligand complexes with Co(II), Ni(II), Cu(II) and Zn(II) ions, were also prepared from the refluxing of equivalent moles. Ligand's structure and its complexes; were confirmed by numerous characterization methods, including Ultraviolet-Visible, Infrared, Mass Spectrometer, 1H and 13C Nuclear Magnetic Resonance spectra, atomic absorption, magnetic moments, and molar conductivity measurements. The results of the spectroscopic analyzes proved that the prepared ligand acts as tetradentate bi-ionic ligand and it was bonded to the metal ions by two nitrogen atoms of the two azomethine groups and by two oxygen atoms of the two phenolic hydroxyl groups after losing their two protons. Octahedral structure proposed to all prepared complexes. The (anti-bacterial) and (anti-fungal) activities of these compound were screened against (E. coli, S. aureus, Klebsiella spp., S. epidermidis,), and (Candida albicans). The results indicated that these compounds have moderated inhibition behavior. The activity of the prepared compounds against Acetyl Choline Esterase Enzyme (AChE) have also studied and the obtained data indicated the presence of different inhibition behavior.

Precision measurement of the magnetic octupole moment in 45Sc as a test for state-of-the-art atomic- and nuclear-structure theory

We report on measurements of the hyperfine A,B and C-constants of the 3d4s2D5/22 and 3d4s2D3/22 atomic states in 45Sc. High-precision atomic calculations of the hyperfine fields of these states and second-order corrections are performed, and are used to extract C5/2=−0.06(6)kHz and C3/2=+0.04(3)kHz from the data. These results are one order of magnitude more precise than the available literature. From the combined analysis of both atomic states, we infer the nuclear magnetic octupole moment Ω=−0.07(53)μNb, including experimental and atomic structure-related uncertainties. With a single valence proton outside of a magic calcium core, scandium is ideally suited to test a variety of nuclear models, and to investigate in-depth the many intriguing nuclear structure phenomena observed within the neighbouring isotopes of calcium. We perform nuclear shell-model calculations of Ω, and furthermore explore the use of Density Functional Theory for evaluating Ω. From this, mutually consistent theoretical values of Ω are obtained, which are in agreement with the experimental value. This confirms atomic structure calculations possess the accuracy and precision required for magnetic octupole moment measurements, and shows that modern nuclear theory is capable of providing meaningful insight into this largely unexplored observable.