Theoretical investigation of òΣ_g ⁺-X² Π_u vibronic-coupling and ultrafast internal-conversion dynamics in the acetylene cation

The dynamics and spectroscopy of the X̃²Π_u and òΣ⁺ _g states of C₂H₂ ⁺ and C₂D₂ ⁺ have been investigated in the framework of a vibronic-coupling model. The model includes six of the seven vibrational degrees of freedom and has been constructed on the basis of CASSCF/CASPT2 ab initio electronic-structure calculations. The main feature of the model is a conical intersection of the ²Σ_g ⁺ state with the ²Π_u state. Time-dependent quantum wave-packet calculations have been performed for this model and photoelectron spectra have been obtained by Fourier transformation of the so-called autocorrelation functions. The calculations provide the explanation of the observed extremely short lifetime of the òΣ_g ⁺ state in terms of an ultrafast internal-conversion process caused by the ²Σ_g ⁺-²Π_u conical intersection. The calculated photoelectron spectra and autocorrelation functions are compared with experimental data of Reutt et al. [J. Chem. Phys. 84 (1986) 3022]. The comparison provides evidence that the ultrafast dynamics of the ²Σ_g ⁺ state is affected by an additional curve crossing involving the ²Π_g shake-up state.