Jahn-Teller effect in the cyclopentadienyl radical: an example of three mode coupling

The cyclopentadienyl radical C₅H₅· vibronic wavefunctions and energy levels are calculated and used to discuss the vibrational structure of the allowed ²A″₂ ←²E″₁ electronic transition in C₅H₅ and allowed A←E transitions in similar systems in which Jahn-Teller coupling occurs through two or three vibrational modes. As has been pointed out by Alpert and Silbey, the vibrational pattern predicted for single mode coupling is markedly distorted. With larger coupling parameters than those used by Alpert and Silbey, in an E ← A transition (e.g., the benzene Rydberg states) progressions in the individual coupling vibrations cannot be distinguished. In an A ← E transition (e.g., C₅H₅·), the higher progression members lose intensity and combination levels in the coupling vibrations appear. In both cases, a complex pattern of 1-1 hot band splittings results. Comparison is made with the experimental C₅H₅· spectrum, and assignments are suggested for three of the observed A″₂ state frequencies.