Dynamical Jahn-Teller effect and Berry phase in positively charged fullerenes: Basic considerations.

We study the Jahn-Teller effect of positive fullerene ions C60 and 1C 60 . The aim is to discover if this case, in analogy with the negative ion, possesses a Berry phase or not, and what are the consequences on dynamical Jahn-Teller quantization. Working in the linear and spherical approximation, we find no Berry phase in 1C 60 , and presence/absence of Berry phase for coupling of one L = 2 hole to an L = 4/L = 2 vibration. We study in particular the special equal-coupling case (g2 = g4), which is reduced to the motion of a particle on a 5-dimensional sphere. In the icosahedral molecule, the final outcome assesses the presence/absence of a Berry phase of π for the hu hole coupled to Gg/Hh vibrations. Some qualitative consequences on ground-state symmetry, ∗Email: [email protected] †Email: [email protected] ‡Email: [email protected]