Multistate and multimode vibronic dynamics: The Jahn–Teller and pseudo-Jahn–Teller effects in the ethane radical cation

Abstract

Multimode Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) coupling effects in the photoelectron spectrum of ethane are theoretically investigated. In this article, we focus on the vibronic structure of the second excited B ∼ 2 E u electronic manifold of the ethane radical cation which reveals an asymmetric band in the 14.5–16.5 eV ionization energy range in the experimental recordings. Ionization of an electron from the third occupied 1 e u molecular orbital of ethane produces the radical cation in the degenerate B ∼ 2 E u electronic manifold, which is prone to the JT instability when distorted along the degenerate e g vibrational modes. The theoretical formalism employed here is based on a model diabatic Hamiltonian and a quadratic vibronic coupling scheme with the parameters derived from ab initio electronic structure calculations. The photoelectron band is calculated by carrying out quantum dynamical simulations in the coupled manifold of electronic states. The B ∼ 2 E u electronic manifold of the radical cation is estimated to be ∼2.75 eV and ∼2.40 eV above its X ∼ 2 E g and the A ∼ 2 A 1 g electronic states, respectively. The symmetry selection rule suggests PJT coupling of these electronic states along the vibrational modes of e g/ e u symmetry. The quadratic JT spectrum simulated within the B ∼ 2 E u electronic manifold shows two maxima at ∼ 14.96 eV and ∼15.76 eV which are attributed to the two JT split adiabatic sheets of this electronic manifold. This is in good accord with their position observed at ∼15.0 eV and ∼15.8 eV, respectively, in the experimental recording. The diffuse structure of the overall band can be accounted to a large extent by considering the A ∼ 2 A 1 g - B ∼ 2 E u PJT interactions. The overall shape of the theoretical band agrees very well with the experimental results. Further refinement of the theoretical results may be accomplished by including X ∼ 2 E g - A ∼ 2 A 1 g - B ∼ 2 E u PJT interactions in the theoretical model. Importance of the latter vibronic interactions is also discussed in the text.