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

Abstract

Vibronic wavefunctions and energies are obtained for the A1'1, E2'1, and A2'3 states of the cyclopentadienyl cation (C5H5+) and the pentadeuterio and pentachloro derivatives. Strong pseudo Jahn-Teller coupling occurs between the E2'1 and the 3048 cm−1 higher A1'1 electronic states and has the effect of reducing the triplet-singlet excitation energy from 2613 cm−1 to 275 cm−1 in C5H5+. 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 A1'1 state is much stronger than interaction between the two degenerate E1'1 components, the lowest singlet vibronic state of C5H5+ is totally symmetric, in contrast to the benzene anion. Comparison of the results for C5H5+, C5D5+, and C5Cl5+ 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 C5Cl5+, however, may be about 200 cm−1 smaller than in C5H5+ if strong C–Cl, C–C vibration interactions are present. If the pentaphenyl derivative (C5 φ5+) is treated by the point-mass approximation, the vibronic wavefunctions are expected to resemble closely those obtained for C5Cl5+. The major factors determining the relative energies of the singlet and the triplet vibronic states in the C5X5+ cations are the A1'1-E2'1 and the E2'1-A2'3 electronic energy separations. While the latter is smaller in C5 φ5+ than in C5H5+, the two singlets are more widely spaced, so that a smaller vibronic energy lowering results. The energies of the E2'1 and the A1'1 vibronic states are obtained as a function of the A1'1-E2'1 electronic separation.