Berry phase of adiabatic electronic configurations in fullerene anions

TL;DR

This paper investigates the Berry phase in adiabatic electronic configurations of fullerene anions, revealing its dependence on spin multiplicity and electron count, and clarifying vibronic state symmetries.

Contribution

It provides a new analysis of the Berry phase in Jahn-Teller systems, showing only two adiabatic orbitals have nonzero Berry phase and establishing a relation with angular momentum.

Findings

Only two adiabatic orbitals have nonzero Berry phase

Berry phase depends on spin multiplicity and electron number

Clarifies the symmetry and nature of vibronic states in high spin configurations

Abstract

The selection rule on vibronic angular momentum of $t_{1u}^n \otimes h_g$ Jahn-Teller problem ($n = $ 1-5) is reinvestigated. It is shown that among three adiabatic orbitals only two have nonzero Berry phase. Thus, the Berry phase of adiabatic electronic configurations depends on the spin multiplicity as well as the number of electrons. On this basis, the general relation between the Berry phase and the angular momentum is described. It allows, in particular, to clarify the nature of vibronic states arising from high spin configurations. In comparison with the previous solution for the low-lying vibronic states for bimodal systems, the present solutions correctly fulfill all the symmetry requirement.