Multistate vibronic coupling effects in the K-shell excitation spectrum of ethylene: Symmetry breaking and core-hole localization

Abstract

The vibrational fine structure of the prominent C1s-π* absorption band of ethylene and some of its isotopomers has been investigated theoretically with the aid of a specific (linear) vibronic coupling model. The presence of two equivalent C1s levels gives rise to two nearly degenerate electronic states of g and u symmetry, respectively, which can interact vibronically via the (planar) antisymmetric C–H stretching and bending modes (ν11 and ν12). In addition to these states of immediate interest, the present model comprises three more pairs of “effective” states at higher energy allowing one to describe the excitation of additional asymmetric (nonplanar) modes as a result of linear vibronic coupling. To a good approximation the intrapair vibronic coupling can be eliminated by using a representation in terms of localized C1s hole states. As a further result, the in-plane and out-of-plane modes become separable. The required vibronic coupling constants have been determined with the aid of ab initio calculations at various nuclear conformations using a second-order polarization propagator method. After slight readjustment of some of the parameters, the calculated spectral profiles are found to be in excellent agreement with the experimental findings. The theoretical spectra reflect strong excitation of nontotally symmetric modes (and the concomitant symmetry lowering), involving mainly the planar C–H stretching mode ν11 and the out-of-plane C–H bending mode ν8. While the planar distortion is a consequence of the equivalent core levels, the nonplanar symmetry lowering can be rationalized in chemical terms as a rehybridization effect in which the sp2 bonding scheme in the ethylene ground state is changed to sp3 in the excited state.