The bending vibrational levels of the acetylene cation: A case study of the Renner-Teller effect in a molecule with two degenerate bending vibrations

Forty three vibronic levels of $C2H2+$⁠, $X̃Πu2$⁠, with $υ4=0–6$⁠, $υ5=0–3$⁠, and $K=0–4$⁠, lying at energies of $0–3520cm−1$ above the zero-point level, have been recorded at rotational resolution. These levels were observed by double resonance, using $1+1′$ two-color pulsed-field ionization zero-kinetic-energy photoelectron spectroscopy. The intermediate states were single rovibrational levels chosen from the $ÃAu1$⁠, $4ν3$ $(K=1–2)$⁠, $5ν3$ $(K=1)$⁠, $ν2+4ν3$ $(K=0)$⁠, and $47206cm−1$ $(K=1)$ levels of $C2H2$⁠. Seven of the trans-bending levels of $C2H2+$ (⁠$υ4=0–3$⁠, $K=0–2$⁠) had been reported previously by Pratt et al. [J. Chem. Phys. 99, 6233 (1993)]; our results for these levels agree well with theirs. A full analysis has been carried out, including the Renner-Teller effect and the vibrational anharmonicity for both the trans- and cis-bending vibrations. The rotational structure of the lowest 16 vibronic levels (consisting of the complete set of levels with $υ4+υ5⩽2$⁠, except for the unobserved upper $Πu2$ component of the $2ν4$ overtone) could be fitted by least squares using 16 parameters to give an rms deviation of $0.21cm−1$⁠. The vibronic coupling parameter $ε5$ (about whose magnitude there has been controversy) was determined to be $−0.02737$⁠. For the higher vibronic levels, an additional parameter, $r45$⁠, was needed to allow for the Darling-Dennison resonance between the two bending manifolds. Almost all the observed levels of the $υ4+υ5=3$ and 4 polyads (about half of the predicted number) could then be assigned. In a final fit to 39 vibronic levels with $υ4+υ5⩽5$⁠, an rms deviation of $0.34cm−1$ was obtained using 20 parameters. An interesting finding is that Hund’s spin-coupling cases (a) and (b) both occur in the $Σu$ components of the $ν4+2ν5$ combination level. The ionization potential of $C2H2$ (from the lowest rotational level of the ground state to the lowest rotational level of the cation) is found to be $91953.77±0.09cm−1$ $(3σ)$⁠.