Theory of vibronic coupling in linear molecules

Abstract

Vibronic coupling between different electronic states of linear molecules is investigated by an expansion of the molecular Hamiltonian in powers of the bending amplitude ρ. A matrix Hamiltonian is derived which describes the simultaneous interaction between Σ+, Σ−, Π, and Δ electronic states and represents a generalization of the well-known Hamiltonian of the Renner–Teller effect in an isolated Π electronic state. We discuss the influence of the vibronic coupling on the adiabatic potential energy surfaces as well as on the spectral intensity distribution for the transition from a well separated initial (linear) state into the manifold of interacting states. In contrast to the Renner–Teller effect even the linear (in ρ) vibronic coupling between Σ and Π or Π and Δ electronic states can lead to nonlinearity of the lower electronic state if the coupling is sufficiently strong. To facilitate the interpretation of the spectrum it is also calculated in the adiabatic and Franck–Condon approximations and compared to the exact result. Model spectra are presented for a wide range of parameters where perturbation theory breaks down and numerical methods have to be applied. Two main regimes can be distinguished. When the energy difference between the interacting states is much larger than the bending frequency (’’off-resonant case’’) the bands of the different electronic states do not overlap and can be considered separately. In this case Σ electronic states are well understood adiabatically and Π electronic states as exhibiting an induced Renner–Teller effect. When the above energy difference is smaller than or equal to the bending frequency (’’resonant case’’) additional interstate nonadiabatic interactions occur and the separation of the different electronic states is no longer possible. The nature of the nonadiabatic interactions is discussed in detail.