Product Jahn-Teller systems: The{T1⊗H}⊗(g+2h)icosahedral exciton

Abstract

The ${{T}_{1}\ensuremath{\bigotimes}H}\ensuremath{\bigotimes}(g+2h)$ product Jahn-Teller (JT) system offers a model Hamiltonian for the excited configuration of ${\mathrm{C}}_{60}.$ It describes the combined JT activity of two open shells transforming as the threefold and fivefold degenerate icosahedral representations ${T}_{1}$ and H. The two separate JT problems interfere via the interaction with common vibrational modes. In this paper we examine the structure of the resulting potential energy surface. The treatment first considers the simplified ${{T}_{1}\ensuremath{\bigotimes}H}\ensuremath{\bigotimes}(2h)$ problem. The coupling conditions for this problem can be represented in a two-dimensional phase diagram with a rich structure. The diagram is separated in four domains by four trough lines. These correspond to different embeddings of $\mathrm{SO}(3)$ in $\mathrm{SO}(5)$ and describe the possible spherical couplings between a three vector and a five tensor. Outside the trough lines symmetry is broken to ${D}_{5d},$ ${D}_{3d},$ ${D}_{2h},$ and even ${C}_{2h}.$ Several tables offer a description of the structural aspects of these low-symmetry solutions. In the second part the full multimode Hamiltonian is treated by the method of the isostationary function. It is shown that the interconfigurational coupling term of this Hamiltonian reduces to the same tensorial form as for the simplified single mode ${{T}_{1}\ensuremath{\bigotimes}H}\ensuremath{\bigotimes}(2h)$ case.