Studies of the Jahn-Teller Effect. II. The Dynamical Problem

This paper examines the vibronic energy levels of a symmetrical non-linear molecule in a spatially doubly degenerate electronic state which is split in first order by a doubly degenerate vibrational mode. The vibronic levels are classified by a quantum number, which in certain cases is formally related to the combined angular momentum of electronic and vibrational motion, and numerical values are obtained for the energies of these levels as functions of this quantum number and a dimensionless parameter measuring the magnitude of the electronic-vibrational coupling. It is shown that the selection rules for transitions from these vibronic levels to those of a non-degenerate electronic state allow changes in vibrational energy of any integral number of quanta, as though the Jahn-Teller effect were equivalent to a distortion which makes allowed vibrational transitions which would otherwise be forbidden. Numerical values are given for the oscillator strengths of vibronic absorption or emission bands involving transitions between a Jahn-Teller distorted state and an electronically non-degenerate state. It is found that in transitions from the latter to the former the vibrational structure of the electronic band exhibits two intensity maxima if the distortion is large.