Constructing, solving and applying the vibronic Hamiltonian

Tregenna-Piggott, Philip L. W. and Riley, Mark J. (2009). Constructing, solving and applying the vibronic Hamiltonian. In: Horst Koppel, David R. Yarkony and Heinz Barentzen, Jahn-Teller effect: Fundamentals and implications for physics and chemistry. 19th International Jahn-Teller Symposium, Heidelberg, Germany, (371-413). 25-29 August 2008. doi:10.1007/978-3-642-03432-9_13


Author Tregenna-Piggott, Philip L. W.
Riley, Mark J.
Title of paper Constructing, solving and applying the vibronic Hamiltonian
Conference name 19th International Jahn-Teller Symposium
Conference location Heidelberg, Germany
Conference dates 25-29 August 2008
Proceedings title Jahn-Teller effect: Fundamentals and implications for physics and chemistry   Check publisher's open access policy
Journal name Springer Series in Chemical Physics   Check publisher's open access policy
Place of Publication Berlin, Germany
Publisher Springer Verlag
Publication Year 2009
Sub-type Fully published paper
DOI 10.1007/978-3-642-03432-9_13
ISBN 9783642034312
9783642034329
ISSN 0172-6218
Editor Horst Koppel
David R. Yarkony
Heinz Barentzen
Volume 97
Start page 371
End page 413
Total pages 43
Language eng
Abstract/Summary The Jahn–Teller effect is shrouded in mysticism and cynicism. To paraphrase a remark that a colleague recently relayed, “For every anomalous spectrum, structural distortion or novel physical property, there is a vibronic Hamiltonian and ensuing explanation that few can appreciate or comprehend.” The aim of this article is to provide a basic introduction to the Jahn–Teller effect, pitched at a level that undergraduates in chemistry can understand, with an emphasis on how to calculate a given experimental quantity. We show that armed with just a little group theory and matrix mechanics, vibronic Hamiltonians can be readily constructed, solved, and the molecular property of interest extracted from the eigenvalues and eigenfunctions. The manifestation of the Jahn–Teller effect does indeed come in many shapes and forms, three signatures of which are briefly discussed. (1) The vibronic energy spectrum is best revealed by spectroscopy and two examples are taken from the literature that elucidate the intricate energy-level pattern of the E ⊗ e vibronic interaction. (2) ‘The Ham effect’, ‘Ham factors’ and ‘Ham quenching’ are now common parlance in spectroscopy and the phenomenon is aptly illustrated by the magnetic and spectroscopic data of the titanium(III) and vanadium(III) aqua ions. (3) The plasticity of the co-ordination sphere is the quintessential feature of transition metals exhibiting strong Jahn–Teller coupling. We show how a concomitant description of structural and spectroscopic data can be obtained employing a model in which the potential energy surface resulting from the cubic Jahn–Teller Hamiltonian is perturbed by anisotropic strain.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

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