Theoretical investigation of Jahn−Teller dynamics in the <SUP>2</SUP>E‘ electronic ground state of the cyclopropane radical cation

The static and dynamic aspects of (E × e)−Jahn−Teller (JT) interactions in the electronic ground state (X̃2E‘) of the cyclopropane radical cation are investigated with the aid of an ab initio based quantum dynamical approach. The valence photoelectron spectrum of cyclopropane pertinent to an ionization to the X̃2E‘ electronic manifold of its radical cation is calculated and compared with the most recent experimental recording of Holland and co-workers using He I and synchrotron radiation as excitation sources [J. Electron Spectrosc. Relat. Phenom. 2002, 57, 125]. A model diabatic Hamiltonian up to a quadratic vibronic coupling scheme and ab initio calculated coupling parameters are employed in the quantum dynamical simulations. Despite some minor details, the theoretical results are in good accord with the observed bimodal shape of the photoelectron band. The observed splitting of the maxima of ∼0.78 eV in the bimodal profile compares well with our theoretical value of ∼0.76 eV. A strong first-order JT activity of the degenerate vibrational modes is discovered, which results in the distinct twin structure of the photoelectron band, indicating transitions to both the sheets of the so-called Mexican hat potential energy surface of the X̃2E‘ electronic ground state of the radical cation. Two Condon active (A'1) and three JT active (E‘) vibrational modes are found to contribute mostly to the nuclear dynamics in this electronic manifold. The low-energy progression in the photoelectron band is found to be mainly caused by the degenerate CH2 wagging and ring deformation modes. While the linear vibronic coupling scheme overestimates the observed spacing in the low-energy progressions, it leads to a very good agreement with the overall shape of the observed band. The effect of quadratic coupling terms of the Hamiltonian on this low-energy progression is also discussed