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Kozioł K, Aucar IA, Gaul K, Berger R, Aucar GA. Relativistic and quantum electrodynamics effects on NMR shielding tensors of TlX (X = H, F, Cl, Br, I, At) molecules. J Chem Phys 2024; 161:064307. [PMID: 39132800 DOI: 10.1063/5.0213653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Accepted: 07/22/2024] [Indexed: 08/13/2024] Open
Abstract
The results of relativistic calculations of nuclear magnetic resonance shielding tensors (σ) for the thallium monocation (Tl+), thallium hydride (TlH), and thallium halides (TlF, TlCl, TlBr, TlI, and TlAt) are presented as obtained within a four-component polarization propagator formalism and a two-component linear response approach within the zeroth-order regular approximation. In addition to a detailed analysis of relativistic effects performed in this work, some quantum electrodynamical (QED) effects on those nuclear magnetic resonance shieldings and other small contributions are estimated. A strong dependence of σ(Tl) on the bonding partner is found, together with a very weak dependence of QED effects with them. In order to explain the trends observed, the excitation patterns associated with relativistic ee (or paramagnetic-like) and pp (or diamagnetic-like) contributions to σ are analyzed. For this purpose, the electronic spin-free and spin-dependent contributions are separated within the two-component zeroth-order regular approximation, and the influence of spin-orbit coupling on involved molecular orbitals is studied, which allows for a thorough understanding of the underlying mechanisms.
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Affiliation(s)
- Karol Kozioł
- Narodowe Centrum Badań Jadrowych (NCBJ), Andrzeja Sołtana 7, 05-400 Otwock-Świerk, Poland
| | - I Agustín Aucar
- Instituto de Modelado e Innovación Tecnológica (UNNE-CONICET), Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Avda. Libertad, 5460 Corrientes, Argentina
- Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, 9747 AG Groningen, The Netherlands
| | - Konstantin Gaul
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Robert Berger
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Gustavo A Aucar
- Instituto de Modelado e Innovación Tecnológica (UNNE-CONICET), Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Avda. Libertad, 5460 Corrientes, Argentina
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Dickopf S, Sikora B, Kaiser A, Müller M, Ulmer S, Yerokhin VA, Harman Z, Keitel CH, Mooser A, Blaum K. Precision spectroscopy on 9Be overcomes limitations from nuclear structure. Nature 2024; 632:757-761. [PMID: 39143212 PMCID: PMC11338825 DOI: 10.1038/s41586-024-07795-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2024] [Accepted: 07/05/2024] [Indexed: 08/16/2024]
Abstract
Many powerful tests of the standard model of particle physics and searches for new physics with precision atomic spectroscopy are hindered by our lack of knowledge of nuclear properties. Ideally, these properties may be derived from precise measurements of the most sensitive and theoretically best-understood observables, often found in hydrogen-like systems. Although these measurements are abundant for the electric properties of nuclei, they are scarce for the magnetic properties, and precise experimental results are limited to the lightest of nuclei1-4. Here we focus on 9Be, which offers the unique possibility to use comparisons between different charge states available for high-precision spectroscopy in Penning traps to test theoretical calculations typically obscured by nuclear structure. In particular, we perform high-precision spectroscopy of the 1s hyperfine and Zeeman structure in hydrogen-like 9Be3+. We determine the effective Zemach radius with an uncertainty of 500 ppm, and the bare nuclear magnetic moment with an uncertainty of 0.6 parts per billion- uncertainties unmatched beyond hydrogen. Moreover, we compare our measurements with the measurements conducted on the three-electron charge state 9Be+ (ref. 5), which enables testing the calculation of multi-electron diamagnetic shielding effects of the nuclear magnetic moment at the parts per billion level. Furthermore, we test the quantum electrodynamics methods used for the calculation of the hyperfine splitting. Our results serve as a crucial benchmark for transferring high-precision results of nuclear magnetic properties across different electronic configurations.
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Affiliation(s)
- Stefan Dickopf
- Max Planck Institute for Nuclear Physics, Heidelberg, Germany.
| | - Bastian Sikora
- Max Planck Institute for Nuclear Physics, Heidelberg, Germany
| | | | - Marius Müller
- Max Planck Institute for Nuclear Physics, Heidelberg, Germany
| | - Stefan Ulmer
- Institute for Experimental Physics, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
- Ulmer Fundamental Symmetries Laboratory, RIKEN, Saitama, Japan
| | | | - Zoltán Harman
- Max Planck Institute for Nuclear Physics, Heidelberg, Germany
| | | | - Andreas Mooser
- Max Planck Institute for Nuclear Physics, Heidelberg, Germany
| | - Klaus Blaum
- Max Planck Institute for Nuclear Physics, Heidelberg, Germany
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Gerothanassis IP, Kridvin LB. 33S NMR: Recent Advances and Applications. Molecules 2024; 29:3301. [PMID: 39064879 PMCID: PMC11280432 DOI: 10.3390/molecules29143301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2024] [Revised: 07/05/2024] [Accepted: 07/09/2024] [Indexed: 07/28/2024] Open
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.
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Affiliation(s)
- Ioannis P. Gerothanassis
- Section of Organic Chemistry and Biochemistry, Department of Chemistry, University of Ioannina, GR-45110 Ioannina, Greece
| | - Leonid B. Kridvin
- A.E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033 Irkutsk, Russia
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Jackowski K, Wilczek M. Measurements of Nuclear Magnetic Shielding in Molecules. Molecules 2024; 29:2617. [PMID: 38893492 PMCID: PMC11173999 DOI: 10.3390/molecules29112617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2024] [Revised: 05/24/2024] [Accepted: 05/30/2024] [Indexed: 06/21/2024] Open
Abstract
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.
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Affiliation(s)
- Karol Jackowski
- Laboratory of NMR Spectroscopy, Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland;
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Jeszenszki P, Mátyus E. Relativistic two-electron atomic and molecular energies using LS coupling and double groups: Role of the triplet contributions to singlet states. J Chem Phys 2023; 158:054104. [PMID: 36754818 DOI: 10.1063/5.0136360] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
The triplet contribution is computed to the 1 and 2 S0e1 states of the He atom, to the 1S0e1 state of the Li+ and Be2+ ions, and to the X1Σg + ground state of the H2 molecule by extensive use of double-group symmetry (equivalent to LS coupling for the atomic systems) during the course of the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) wave equation. The no-pair DCB energies are converged within sub-parts-per-billion relative precision, using an explicitly correlated Gaussian basis optimized to the non-relativistic energies. The α fine-structure constant dependence of the triplet sector contribution to the variational energy is α4Eh at leading order, in agreement with the formal perturbation theory result available from the literature.
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Affiliation(s)
- Péter Jeszenszki
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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Ferenc D, Jeszenszki P, Matyus E. Variational versus perturbative relativistic energies for small and light atomic and molecular systems. J Chem Phys 2022; 157:094113. [DOI: 10.1063/5.0105355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac--Coulomb--Breit (DCB) equation to all orders of the $\alpha$ fine-structure constant. The analysis of the polynomial $\alpha$ dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit--Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The $\alpha$ dependence of the no-pair DCB energy shows that the higher-order ($\alpha^4 E_\mathrm{h}$) non-radiative QED correction is 5~\% of the leading-order ($\alpha^3 E_\mathrm{h}$) non-radiative QED correction for $Z=2$ (He), but it is 40~\% already for $Z=4$ (Be$^{2+}$), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.
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Makulski W, Aucar JJ, Aucar GA. Ammonia: the molecule for establishing 14N and 15N absolute shielding scales and a source of information on nuclear magnetic moments. J Chem Phys 2022; 157:084306. [DOI: 10.1063/5.0096523] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Multinuclear 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 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 calculations allow 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 reevaluation 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.
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Affiliation(s)
| | - Juan J. Aucar
- Natural and Exact Science Faculty, Northeastern University of Argentina, Argentina
| | - Gustavo A. Aucar
- Natural and Exact Science Faculty, Northeastern University of Argentina, Argentina
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Sailer T, Debierre V, Harman Z, Heiße F, König C, Morgner J, Tu B, Volotka AV, Keitel CH, Blaum K, Sturm S. Measurement of the bound-electron g-factor difference in coupled ions. Nature 2022; 606:479-483. [PMID: 35705820 PMCID: PMC9200642 DOI: 10.1038/s41586-022-04807-w] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 04/26/2022] [Indexed: 11/09/2022]
Abstract
Quantum electrodynamics (QED) is one of the most fundamental theories of physics and has been shown to be in excellent agreement with experimental results1-5. In particular, measurements of the electron's magnetic moment (or g factor) of highly charged ions in Penning traps provide a stringent probe for QED, which allows testing of the standard model in the strongest electromagnetic fields6. When studying the differences between isotopes, many common QED contributions cancel owing to the identical electron configuration, making it possible to resolve the intricate effects stemming from the nuclear differences. Experimentally, however, this quickly becomes limited, particularly by the precision of the ion masses or the magnetic field stability7. Here we report on a measurement technique that overcomes these limitations by co-trapping two highly charged ions and measuring the difference in their g factors directly. We apply a dual Ramsey-type measurement scheme with the ions locked on a common magnetron orbit8, separated by only a few hundred micrometres, to coherently extract the spin precession frequency difference. We have measured the isotopic shift of the bound-electron g factor of the isotopes 20Ne9+ and 22Ne9+ to 0.56-parts-per-trillion (5.6 × 10-13) precision relative to their g factors, an improvement of about two orders of magnitude compared with state-of-the-art techniques7. This resolves the QED contribution to the nuclear recoil, accurately validates the corresponding theory and offers an alternative approach to set constraints on new physics.
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Affiliation(s)
- Tim Sailer
- Max-Planck-Institut für Kernphysik, Heidelberg, Germany.
| | | | - Zoltán Harman
- Max-Planck-Institut für Kernphysik, Heidelberg, Germany
| | - Fabian Heiße
- Max-Planck-Institut für Kernphysik, Heidelberg, Germany
| | | | | | - Bingsheng Tu
- Max-Planck-Institut für Kernphysik, Heidelberg, Germany
| | - Andrey V Volotka
- Department of Physics and Engineering, ITMO University, St Petersburg, Russia
- Helmholtz-Institut Jena, Jena, Germany
| | | | - Klaus Blaum
- Max-Planck-Institut für Kernphysik, Heidelberg, Germany
| | - Sven Sturm
- Max-Planck-Institut für Kernphysik, Heidelberg, Germany
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