Non-adiabatic crossing of energy levels

Zener, Clarence

doi:10.1098/rspa.1932.0165

Cited by 4,572Atomic and Molecular PhysicsAdvanced Physical and Chemical Molecular InteractionsAdvanced Chemical Physics Studies

Non-adiabatic crossing of energy levels

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Zener, Clarence·1932·Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character

DOI 10.1098/rspa.1932.0165

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Abstract

Abstract The crossing of energy levels has been a matter of considerable discussion. The essential features may be illustrated in the crossing of a polar and homopolar state of a molecule. Let ψ1 (x/R), ψ2 (x/R) be two electronic eigenfunctions of a molecule with stationary nuclei. Let these eigenfunctions have the property that for R≫R0, ψ1 has polar characteristics, ψ2 homopolar; while at R≪R0, ψ2 has polar characteristics, ψ1 homopolar. In the region R=R0 these two eigenfunctions may be said to exchange their characteristics.

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For the mode coupling stages of the process, the problem can be described by analogy with the Landau-Zener model.
“For the mode coupling stages of the process, the problem can be described by analogy with the Landau-Zener (LZ) model [48, 49].”
From Quantisation of the elliptical Penning trap (2021) · cites this paper as [49]

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Authors: Zener, C.
Affiliations: National Research Fellow of U. S. A.
Corresponding author: Zener, Clarence
Venue: Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character
Publisher: The Royal Society
Published: 1932-09-01
Volume: 137
Issue: 833
Pages: 696-702
ISSN: 0950-1207 (ISSN-L)
2053-9150
DOI: 10.1098/rspa.1932.0165
OpenAlex: W1981659415
Cited by: 4,572
References: 0
Citations by year: 2026: 92 · 2025: 129 · 2024: 121 · 2023: 141 · 2022: 147 · 2021: 137 · 2020: 138 · 2019: 158 · 2018: 173 · 2017: 156 · 2016: 156 · 2015: 145 · 2014: 160 · 2013: 164 · 2012: 116
FWCI: 1.52
Type: journal article
Language: en
Open access: diamond
doi.org
Licence: royalsociety.org/journals/ethics-policies/data-sharing-mining/ (tdm)
Locations: Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character (publishedVersion)
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Molecular Physics
Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Keywords: energy level crossing, molecular electronic states, diatomic molecules, adiabatic approximation

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Non-adiabatic crossing of energy levels

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