THE JAHN-TELLER EFFECT IN ICOSAHEDRAL SYMMETRY - GROUND-STATE TOPOGRAPHY AND PHASES

The resurgence of interest in properties of molecules of icosahedral s ymmetry follows the discovery of the C-60 molecule. Because of the hig h symmetry almost all the electronic and vibrational states are highly degenerate, so in dealing with properties of these systems their Jahn -Teller interactions must almost always be allowed for. In this paper we explore the ground states of the G x (g + h) coupling scheme and th ose of the two subsystems, G x g and G x h. Using a mixture of analyti cal and numerical methods, we map the lowest adiabatic potential energ y surfaces of these systems. the mappings are map in such a way as to facilitate an analysis of the geometrical phase factor acquired by the quantal system on transportation round adiabatic circuits in paramete r space. These geometrical phase factors, or Berry phases, depend grea tly on the paths followed to complete these circuits. In this paper we introduce parametrizations that elucidate with ease such circuits and lead to simple and easily accessible graphical illustrations of the s ubsequently induced Berry phases. Finally, we use the information prov ided by the Berry phase analysis to obtain the correct ordering of the low-lying states at strong coupling, the energies of these states and the Ham factors of the Jahn-Teller-active operators within these stat es.