The effects of anisotropy in Jahn–Teller systems: application to the icosahedral H ⊗ (h ⊕ g)system

Abstract

Jahn–Teller (JT) coupling between electronic motion and lattice or molecularvibrations results in an adiabatic potential energy surface that contains eitherwells or troughs of minimum-energy points. When wells are lowest in energy, thesystem will vibrate about the minimum-energy points. This vibration must betaken into account when describing the quantum mechanical states of the system.In general, the wells will be intrinsically anisotropic. This anisotropy alters thevibrational frequencies and hence the positions of the energy levels, and can beparticularly significant when the barriers between wells are shallow. Inthis paper, we will show how anisotropic states and their energies can becalculated using two unitary transformations. The first locates minimaon the adiabatic potential energy surface, and the second accounts foranisotropy in the shape of the minima. The method is developed in away general enough to allow it to be applied to any linear JT problem.The theory is then applied to the icosahedral H ⊗ (h ⊕ g) JTsystem. The results obtained will help the understanding of, for example,the effects of vibronic coupling in positively charged fullerene ions.