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Pérez-Torres JF. Relativistic Effects in Ligand Field Theory (I): Optical Properties of d 1 Atoms in Oh' Symmetry. Inorg Chem 2024; 63:15016-15023. [PMID: 39082274 DOI: 10.1021/acs.inorgchem.4c01771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/13/2024]
Abstract
Ligand field theory, which explains the splitting of degenerate nd atomic orbitals due to static electric fields from point-charge ligands, is rederived using Dirac orbitals instead of Schrödinger orbitals, specifically using the nd3/2 and nd5/2 spinors. This formalism is, to some extent, equivalent to incorporating the spin-orbit interaction either in the nd atomic orbitals or in the ligand field orbitals (e.g., the t2g and eg orbitals arising from Oh symmetry). The spin-orbit interaction is of fundamental importance in the description of the magnetic and optical properties of the 4d and 5d transition metal complexes. Algebraic equations for the relativistic energy levels of d1 octahedral complexes as functions of the spin-orbit coupling constant ξnd and the ligand field parameters Dq and Dp are derived. It is demonstrated that these parameters allow a direct link between the ligand field theory and ab initio relativistic calculations, consistent with the emerging ab initio ligand field theory. The spin-orbit coupling constant and ligand field parameters of ReF6 obtained from optical absorption spectra are carefuly in the light of the new theory.
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Affiliation(s)
- Jhon Fredy Pérez-Torres
- Escuela de Química, Universidad Industrial de Santander, Cra. 27-9, 620008 Bucaramanga, Colombia
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Caviezel M, Horká-Zelenková V, Seyfang G, Quack M. High resolution FTIR and diode laser spectroscopy of trifluoromethylacetylene and tetrafluoromethane in a supersonic jet expansion. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2093285] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
Affiliation(s)
- M. Caviezel
- Laboratorium für Physikalische Chemie, ETH Zürich, Zürich, Switzerland
| | | | - G. Seyfang
- Laboratorium für Physikalische Chemie, ETH Zürich, Zürich, Switzerland
| | - M. Quack
- Laboratorium für Physikalische Chemie, ETH Zürich, Zürich, Switzerland
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Coello L, Lemus R. Vibrational description of the stretching modes of octahedral molecules: a local-to-normal mode transition criterion. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1865582] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | - Renato Lemus
- Instituto de Ciencias Nucleares, UNAM, Mexico City, Mexico
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Ischenko AA. Effect of vibronic interactions on molecular structures determined by gas electron diffraction. Struct Chem 2015. [DOI: 10.1007/s11224-015-0667-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Affiliation(s)
- Konrad Seppelt
- Institut
fuer Chemie and
Biochemie, Freie Universitaet, Fabeckstr. 34-36, 14195 Berlin, Germany
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7
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Suhm MA, Kollipost F. Femtisecond single-mole infrared spectroscopy of molecular clusters. Phys Chem Chem Phys 2013; 15:10702-21. [DOI: 10.1039/c3cp51515j] [Citation(s) in RCA: 69] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Wang X, Andrews L, Knitter M, Malmqvist PÅ, Roos BO. Experimental and Theoretical Investigation of Simple Terminal Group 6 Arsenide As≡MF3 Molecules. J Phys Chem A 2009; 113:6064-9. [DOI: 10.1021/jp901308n] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Xuefeng Wang
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22904-4319, and Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124, 2-221 00 Lund, Sweden
| | - Lester Andrews
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22904-4319, and Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124, 2-221 00 Lund, Sweden
| | - Marta Knitter
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22904-4319, and Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124, 2-221 00 Lund, Sweden
| | - Per-Åke Malmqvist
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22904-4319, and Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124, 2-221 00 Lund, Sweden
| | - Björn O. Roos
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22904-4319, and Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124, 2-221 00 Lund, Sweden
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Wang X, Andrews L, Lindh R, Veryazov V, Roos BO. A Combined Theoretical and Experimental Study of Simple Terminal Group 6 Nitride and Phosphide N≡MX3 and P≡MX3 Molecules. J Phys Chem A 2008; 112:8030-7. [DOI: 10.1021/jp804469a] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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Quack M, Stohner J, Willeke M. High-Resolution Spectroscopic Studies and Theory of Parity Violation in Chiral Molecules. Annu Rev Phys Chem 2008; 59:741-69. [DOI: 10.1146/annurev.physchem.58.032806.104511] [Citation(s) in RCA: 198] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
We review the high-resolution spectroscopic approach toward the study of intramolecular dynamics, emphasizing molecular parity violation. Theoretical work in the past decade has shown that parity-violating potentials in chiral molecules are much larger (typically one to two orders of magnitude) than anticipated on the basis of older theories. This makes experimental approaches toward small molecular parity-violating effects promising. The concepts and results of intramolecular dynamics derived from spectroscopy are analyzed as a sequence of symmetry breakings. We summarize the concepts of symmetry breakings (de facto and de lege) in view of parity violation in chiral molecules. The experimental schemes and the current status of spectroscopic experiments on molecular parity violation are established. We discuss the promises of detecting and accurately measuring parity-violating energy differences Δpv E on the order of 10−11 J mol−1 (approximately 100 aeV) in enantiomers of chiral molecules with regard to their contribution to fundamental physics in the framework of the standard model of particle physics and more speculative future fundamental symmetry tests such as for the combined charge conjugation, parity, and time-reversal (CPT) symmetry violation.
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Affiliation(s)
- Martin Quack
- ETH Zürich Laboratorium für Physikalische Chemie, CH-8093 Zürich, Switzerland
| | - Jürgen Stohner
- Permanent address: Institute of Chemistry and Biology, Zürich University of Applied Sciences, CH-8400 Winterthur, Switzerland
| | - Martin Willeke
- Permanent address: Departement für Materialwissenschaften, ETH Zürich, 8093 Zürich, Switzerland
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Hippler M, Oeltjen L, Quack M. High-Resolution Continuous-Wave-Diode Laser Cavity Ring-Down Spectroscopy of the Hydrogen Fluoride Dimer in a Pulsed Slit Jet Expansion: Two Components of the N = 2 Triad near 1.3 μm. J Phys Chem A 2007; 111:12659-68. [DOI: 10.1021/jp076894s] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Michael Hippler
- Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland, and Department of Chemistry, University of Sheffield, Sheffield S3 7HF, England
| | - Lars Oeltjen
- Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland, and Department of Chemistry, University of Sheffield, Sheffield S3 7HF, England
| | - Martin Quack
- Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland, and Department of Chemistry, University of Sheffield, Sheffield S3 7HF, England
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