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

We study the Jahn-Teller effect of positive fullerene ions C-2(60)+ and C-1(60)2+. 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 C-1(60)2+, 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 (g(2)=g(4)), which is reduced to the motion of a particle on a five-dimensional sphere. In the icosahedraI molecule, the final outcome assesses the presence and/or absence of a Berry phase of pi for the h(u) hole coupled to G(g)/H-h vibrations. Some qualitative consequences on groundstate symmetry, low-lying excitations, and electron emission from C-60 are spelled out.