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Reference: Cullerne, John Paul., (1995). The Jahn-Teller effect in icosahedral symmetry. DPhil. University of Oxford.Citable link to this page:


The Jahn-Teller effect in icosahedral symmetry

Abstract: The resurgence of interest in properties of molecules of icosahedral symmetry follows thediscovery of the C60 molecule. Due to the high symmetry of the icosahedron, almost all theelectronic and vibrational levels are highly degenerate, so that in dealing with properties of thesesystems, the Jahn-Teller interaction must almost always be allowed for. This thesis primarilyexplores the properties of the icosahedral G ⊗ (g ⊕ h] interaction and related subsystems in thestrong coupling régime. Mappings of the adiabatic potential energy surfaces facilitate an analysisof the geometrical phase or Berry phase acquired by the quantal system on transportation aroundadiabatic circuits in parameter space. The Berry phase information in conjunction with ananalysis of tunnelling, determines the properties of the ground state.The use of Ham factors achieves a characterization of the various coupling régimes. However,characterization of G and H Jahn-Teller systems, requires an extension of the standard definitionof these Ham factors. In such cases the extended matrix elements between and within vibronictunnelling sublevels cannot be ignored. A calculation of all the standard and extended matrixelements is presented. A further introduction of a matrix of Ham factors facilitates the descriptionof H multiplicity within an H manifold.Finally, two problems are investigated numerically; aimed at making some allusion towardspossible experimental manifestations of G ⊗(g(⊕)h). The first investigation considers the variationsin the eigensystem and Ham factors of G ⊗ (g ⊕ h), as a function of the coupling to the twomodes. The second investigation considers the structure in the optical absorption line shapesfor the transitions from orbital singlet to quartet, G, states in an icosahedral environment. Thequartet states are subject to both spin-orbit and linear Jahn-Teller interactions.

Type of Award:DPhil Level of Award:Doctoral Awarding Institution: University of Oxford Notes:This thesis was digitised thanks to the generosity of Dr Leonard Polonsky


O'Brien, M. C. M.More by this contributor



M.C.M. O'BrienMore by this contributor


 Bibliographic Details

Issue Date: 1995Identifiers

Urn: uuid:cc2b3605-f7dc-488d-820d-3a830a0119b3

Source identifier: 603826285 Item Description

Type: Thesis;

Language: eng Subjects: Jahn-Teller effect Icosahedra Symmetry (Physics) Buckminsterfullerene Tiny URL: td:603826285


Author: Cullerne, John Paul. - institutionUniversity of Oxford facultyFaculty of Physical Sciences - - - - Contributors O'Brien, M. C



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