Effect of Vibronic Interaction on the Singlet-Triplet Separation in Cyclopentadienyl Cations

Abstract

Vibronic wavefunctions and energies are obtained for the IAI', IE.', and 3A.' states of the cyclopentadienyl cation (C5H6+) and the pentadeuterio and pentachloro derivatives. Strong pseudo Jahn-Teller coupling occurs between the IE.' and the 3048 cm-l higher IAI' electronic states and has the effect of reducing the triplet-singlet excitation energy from 2613 cml to 275 cml in C 5 H6+. Thus, it is probable that vibrational-electronic interaction is an important factor in determining the relative stabilities of the singlet and the triplet states of these and related systems. Because coupling with the I A t' state is much stronger than interaction between the two degenerate lEI' components, the lowest singlet vibronic state of C6H6+ is totally symmetric, in contrast to the benzene anion. Comparison of the results for C6H6+, C6D6+' and C6Cl6+ shows that the extent of vibrational-electronic interaction and vibronic energy lowering are not very sensitive to moderate alterations in force constants and vibrational frequencies. The energy lowering in C 6 Cl 6 +, however, may be about 200 cml smaller than in C 5 H6+ if strong C-Cl, C-C vibration interactions are present. If the pentaphenyl derivative (Co<I>6+) is treated by the point-mass approximation, the vibronic wavefunctions are expected to resemble closely those obtained for C.Ch+. The major factors determining the relative energies of the singlet and the triplet vibronic states in the C.X.+ cations are the IAI'_IE.' and the IE.'-3A.' electronic energy separations. While the latter is smaller in C.ci>.+ than in C5H6+, the two singlets are more widely spaced, so that a smaller vibronic energy lowering results. The energies of the IE.' and the IAI' vibronic states are obtained as a function of the IAI'_IE.' electronic separation.