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Additional unpaired electrons have been introduced into colloidal ZnO quantum dots (QDs) photochemically and investigated by experimental and theoretical methods to test various possible descriptions of their wave functions. For n-type ZnO QDs with diameters between 3.0 and 7.0 nm, electron paramagnetic resonance (EPR) spectroscopy reveals size-dependent g* values in the range 1.960 < g* < 1.968 that are temperature independent and that rule out highly localized wave function descriptions. The size dependence of g* is described well using a k · p perturbation expression, indicating similarity between these quantum confined electrons and free carriers in bulk ZnO. Model calculations confirm that significant electron density can reside on the QD surfaces only for surface well depths that can be experimentally excluded. Together, these results allow a firm experimental description of the photogenerated electrons as delocalized within the conduction bands of the colloidal ZnO QDs, making them excellent candidates for investigation of spin effects in semiconductor nanostructures.

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We have investigated the T⊗t2 Jahn–Teller problem with linear and quadratic vibronic coupling including a fourth-order term. First, numerical calculations of the lowest vibronic states were carried out by direct diagonalization of the Hamiltonian. The results show that the energy level of the ground vibronic state, which is triply degenerate T for small quadratic coupling g values, intersects the next A level with increasing g, thus realizing the nondegenerate ground state at sufficiently large g values. This result reverses the long-standing belief that the ground vibronic state for the T⊗t2 system has the same degeneracy and symmetry T as the initial electronic state. To explain these results in terms of Berry phase requirements and conical intersections, the adiabatic potential energy surface of the system is analyzed, and the relationships among the type and number of minima, conical intersections, and relevant tunneling paths are revealed. Depending on the vibronic coupling parameter values, there are four trigonal minima and six orthorhombic saddle points, which become minima at large g values, plus ten lines of conical intersections on the lowest potential energy surface. The barriers between the minima are significantly increased near the lines of conical intersections where the Born–Huang terms diverge. For small enough quadratic coupling, only four lines of conical intersections that originate from the highest symmetry point and proceed along the four trigonal directions are significant in determining the Berry phase, and the triply degenerate ground T state is obtained. By increasing the quadratic coupling parameter, the remaining six lines of conical intersections approach the point of highest symmetry, thus allowing for alternative tunneling paths and Berry phases which lead to the nondegenerate A ground state. This explanation of the origin of the nondegenerate ground state for some range of values of the vibronic coupling parameters is strengthened by model calculations of tunneling splitting.

The adiabatic potential surface for icosahedral systems having three-, four-and five-fold degenerate orbital states interacting with five-fold degenerate vibrations (T-v, U-v and V-v problems) is investigated. It is shown that for the T-v and V-v Jahn-Teller cases the potential surface possesses respectively a twoor three-dimensional equipotential continuum of minima. For the U-v problem the potential surface contains 15 equivalent minima. The nature of the extremum points on 1;he adiabatic potential surfaces is elucidated. In the linear approximation to the V-v problem in the minima points the lowest potential surface is double degenerate due to the accidental occurrence of axial symmetry.