The Jahn-Teller effect in icosahedral symmetry

The resurgence of interest in properties of molecules of icosahedral symmetry follows the discovery of the C60 molecule. Due to the high symmetry of the icosahedron, almost all the electronic and vibrational levels are highly degenerate, so that in dealing with properties of these systems, the Jahn-Teller interaction must almost always be allowed for. This thesis primarily explores the properties of the icosahedral G ⊗ (g ⊕ h] interaction and related subsystems in the strong coupling régime. Mappings of the adiabatic potential energy surfaces facilitate an analysis of the geometrical phase or Berry phase acquired by the quantal system on transportation around adiabatic circuits in parameter space. The Berry phase information in conjunction with an analysis 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 definition of these Ham factors. In such cases the extended matrix elements between and within vibronic tunnelling sublevels cannot be ignored. A calculation of all the standard and extended matrix elements is presented. A further introduction of a matrix of Ham factors facilitates the description of H multiplicity within an H manifold. Finally, two problems are investigated numerically; aimed at making some allusion towards possible experimental manifestations of G ⊗(g(⊕)h). The first investigation considers the variations in the eigensystem and Ham factors of G ⊗ (g ⊕ h), as a function of the coupling to the two modes. The second investigation considers the structure in the optical absorption line shapes for the transitions from orbital singlet to quartet, G, states in an icosahedral environment. The quartet states are subject to both spin-orbit and linear Jahn-Teller interactions.</p

The Jahn-Teller effect in icosahedral symmetry

The resurgence of interest in properties of molecules of icosahedral symmetry follows the discovery of the C60 molecule. Due to the high symmetry of the icosahedron, almost all the electronic and vibrational levels are highly degenerate, so that in dealing with properties of these systems, the Jahn-Teller interaction must almost always be allowed for. This thesis primarily explores the properties of the icosahedral G ⊗ (g ⊕ h] interaction and related subsystems in the strong coupling régime. Mappings of the adiabatic potential energy surfaces facilitate an analysis of the geometrical phase or Berry phase acquired by the quantal system on transportation around adiabatic circuits in parameter space. The Berry phase information in conjunction with an analysis 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 definition of these Ham factors. In such cases the extended matrix elements between and within vibronic tunnelling sublevels cannot be ignored. A calculation of all the standard and extended matrix elements is presented. A further introduction of a matrix of Ham factors facilitates the description of H multiplicity within an H manifold. Finally, two problems are investigated numerically; aimed at making some allusion towards possible experimental manifestations of G ⊗(g(⊕)h). The first investigation considers the variations in the eigensystem and Ham factors of G ⊗ (g ⊕ h), as a function of the coupling to the two modes. The second investigation considers the structure in the optical absorption line shapes for the transitions from orbital singlet to quartet, G, states in an icosahedral environment. The quartet states are subject to both spin-orbit and linear Jahn-Teller interactions.</p

Leaf trait variation is similar among genotypes of Eucalyptus camaldulensis from differing climates and arises as plastic response to season rather than water availability

We used a widely-distributed tree Eucalyptus camaldulensis subsp. camaldulensis to partition intraspecific variation in leaf functional traits to genotypic variation and phenotypic plasticity. We examined if genotypic variation is related to the climate of genotype provenance and whether phenotypic plasticity maintains performance in a changing environment. Ten genotypes from different climates were grown in a common garden under watering treatments reproducing the wettest and driest edges of the subspecies’ distribution. We measured functional traits reflecting leaf metabolism and associated with growth (respiration rate, nitrogen and phosphorus concentrations, and leaf mass per area) and performance proxies (aboveground biomass and growth rate) each season over a year. Genotypic variation contributed substantially to the variation in aboveground biomass but much less in growth rate and leaf traits. Phenotypic plasticity was a large source of the variation in leaf traits and performance proxies, and was greater among sampling dates than between watering treatments. The variation in leaf traits was weakly correlated to performance proxies, and both were unrelated to the climate of genotype provenance. Intraspecific variation in leaf traits arises similarly among genotypes in response to seasonal environmental variation, instead of long-term water availability or climate of genotype provenance