Relativistic theory of nuclear shielding in one-electron atoms 1. Theoretical foundations and first-order terms.
Saved in:
| Title: | Relativistic theory of nuclear shielding in one-electron atoms 1. Theoretical foundations and first-order terms. |
|---|---|
| Authors: | Pyper, N. C. |
| Source: | Molecular Physics. 08/10/99, Vol. 97 Issue 3, p381-390. 10p. |
| Subjects: | Relativistic particles, Radiation shielding, Atomic orbitals |
| Abstract: | The nuclear shielding in NMR spectroscopy is given in relativistic theory (Pyper, N. C., 1983, Chem. Phys. Lett ., 96, 204) as the sum of the exact relativistic analogues of the non-relativistic diamagnetic and paramagnetic terms augmented by a further purely relativistic term. In this paper this theory, based on the Gordon decomposition of the Dirac current, is extended to encompass the point charge-point dipole model of the nucleus, the previous formulation (Pyper, 1983) being restricted to spatially extended descriptions of the nuclear charge and magnetization. For the point nucleus case, analytical expressions for both the purely relativistic shielding contribution and diamagnetic term are derived for all orbitals. The result for the diamagnetic shielding is derived by invoking the relativistic virial theorem, and thus depends only on the orbital energy and magnetic quantum number m . Therefore it shows, for given m , the same 'accidential' degeneracy between orbitals differing in the sign of the quantum number kappa as the energy. The purely relativistic contribution to the shielding is shown to differ from the electronic contribution to the hyperfine energy by a factor of only m multiplied by fundamental constants. The present purely relativistic term is shown to equal the previous result (Pyper, 1983) even though appearing in a different form. For the interaction with a uniform magnetic field the relativistically exact Hamiltonian obtained from the Gordon decomposition is used with the virial theorem to derive a new expression for the g factor for all orbitals. The resulting simple expression depends only on the orbital energy in addition to the quantum numbers kappa and m . [ABSTRACT FROM AUTHOR] |
| Copyright of Molecular Physics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 3844585 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Relativistic theory of nuclear shielding in one-electron atoms 1. Theoretical foundations and first-order terms. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pyper%2C+N%2E+C%2E%22">Pyper, N. C.</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Molecular+Physics%22">Molecular Physics</searchLink>. 08/10/99, Vol. 97 Issue 3, p381-390. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Relativistic+particles%22">Relativistic particles</searchLink><br /><searchLink fieldCode="DE" term="%22Radiation+shielding%22">Radiation shielding</searchLink><br /><searchLink fieldCode="DE" term="%22Atomic+orbitals%22">Atomic orbitals</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The nuclear shielding in NMR spectroscopy is given in relativistic theory (Pyper, N. C., 1983, Chem. Phys. Lett ., 96, 204) as the sum of the exact relativistic analogues of the non-relativistic diamagnetic and paramagnetic terms augmented by a further purely relativistic term. In this paper this theory, based on the Gordon decomposition of the Dirac current, is extended to encompass the point charge-point dipole model of the nucleus, the previous formulation (Pyper, 1983) being restricted to spatially extended descriptions of the nuclear charge and magnetization. For the point nucleus case, analytical expressions for both the purely relativistic shielding contribution and diamagnetic term are derived for all orbitals. The result for the diamagnetic shielding is derived by invoking the relativistic virial theorem, and thus depends only on the orbital energy and magnetic quantum number m . Therefore it shows, for given m , the same 'accidential' degeneracy between orbitals differing in the sign of the quantum number kappa as the energy. The purely relativistic contribution to the shielding is shown to differ from the electronic contribution to the hyperfine energy by a factor of only m multiplied by fundamental constants. The present purely relativistic term is shown to equal the previous result (Pyper, 1983) even though appearing in a different form. For the interaction with a uniform magnetic field the relativistically exact Hamiltonian obtained from the Gordon decomposition is used with the virial theorem to derive a new expression for the g factor for all orbitals. The resulting simple expression depends only on the orbital energy in addition to the quantum numbers kappa and m . [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Molecular Physics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=3844585 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/00268979909482839 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 381 Subjects: – SubjectFull: Relativistic particles Type: general – SubjectFull: Radiation shielding Type: general – SubjectFull: Atomic orbitals Type: general Titles: – TitleFull: Relativistic theory of nuclear shielding in one-electron atoms 1. Theoretical foundations and first-order terms. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pyper, N. C. IsPartOfRelationships: – BibEntity: Dates: – D: 10 M: 08 Text: 08/10/99 Type: published Y: 1999 Identifiers: – Type: issn-print Value: 00268976 Numbering: – Type: volume Value: 97 – Type: issue Value: 3 Titles: – TitleFull: Molecular Physics Type: main |
| ResultId | 1 |
