Symmetry-adapted excited states for the T1u⊗hg Jahn-Teller system -: art. no. 075102

Jahn-Teller (JT) systems typically contain a set of equivalent-energy wells in the lowest adiabatic potential-energy surface (APES). Quantum-mechanical tunneling between these wells (the dynamic JT effect) must be allowed for by taking appropriate symmetrized combinations of oscillator-type states associated with the wells. It is important to be able to describe the excited states of such systems for a number of reasons. One particular reason is that they are required for the calculation of second-order vibronic reduction factors, which in turn are useful for modeling experimental data using effective Hamiltonians. In this paper, projection-operator techniques are used to obtain general expressions for the symmetry-adapted excited states of the icosahedral T-1u circle timesh(g) JT system for the case of D-5d minima in the APES. Analytical expressions for the states and their energies for one-phonon excitation are given explicitly. The energies of a selection of states with two-phonon excitations are also obtained and plotted. The results obtained in this paper are applicable to the C-60(-) molecule.