Overcoming the out-of-plane bending issue in an aromatic hydrocarbon: the anharmonic vibrational frequencies of c-(CH)C3H2+

Abstract

The challenges associated with the out-of-plane bending problem in multiply-bonded hydrocarbon molecules can be mitigated in quartic force field analyses by varying the step size in the out-of-plane coordinates. Carbon is a highly prevalent element in astronomical and terrestrial environments, but this major piece of its spectra has eluded theoretical examinations for decades. Earlier explanations for this problem focused on method and basis set issues, while this work seeks to corroborate the recent diagnosis as a numerical instability problem related to the generation of the potential energy surface. Explicit anharmonic frequencies for c-(CH)C₃H₂⁺ are computed using a quartic force field and the CCSD(T)-F12b method with cc-pVDZ-F12, cc-pVTZ-F12, and aug-cc-pVTZ basis sets. The first of these is shown to offer accuracy comparable to that of the latter two with a substantial reduction in computational time. Additionally, c-(CH)C₃H₂⁺ is shown to have two fundamental frequencies at the onset of the interstellar unidentified infrared bands, at 5.134 and 6.088 μm or 1947.9 and 1642.6 cm⁻¹, respectively. This suggests that the results in the present study should assist in the attribution of parts of these aromatic bands, as well as provide data in support of the laboratory or astronomical detection of c-(CH)C₃H₂⁺.