Variational Rovibrational Calculation For Linear Tetraatomic Molecules: Ii. The B11244 Story Retold

The linear propynylidynium $l$-C$_3$H$^+$ ($\text{X}^1\Sigma^+$) is part of the select group of interstellar cations. Its discovery was accompanied by a controversy in the astrophysical community.\footnote{\ Pety~\textit{et al.}, \textit{Astron. Astrophys.} \textbf{548}, 68 (2012); \ Huang~\textit{et al.}, \textit{Astrophys. J. Lett.} \textbf{768}, 25 (2013).} Following its initial detection, theoretical calculations questioned the assignment based on 2\textsuperscript{nd} order vibrational perturbation theory (VPT2) calculations. The matter was ultimately resolved by laboratory rotational spectra.\footnote{\ Br\"{u}nken~\textit{et al.}, \textit{Astrophys. J. Lett.} \textbf{783}, 36 (2014).} The failure of VPT2 was subsequently attributed to a shallow CCC bending potential.\footnote{\ Botschwina \textit{et al.}, \textit{Astrophys. J.} \textbf{787}, 72 (2014).} Discrete Variable Representation (DVR) calculations\footnote{\ Mladenovi\'{c} \textit{J. Chem. Phys.} \textbf{141}, 224304 (2014).} later confirmed the $D_0/D_\text{e}$ ratio but resulted in a large sextic centrifugal distortion constant $H_0$ exceeding the astronomical value by an order of magnitude. Using a new variational method for tetraatomic linear molecules (C8v4; see also P5277), based on Watsons isomorphic Hamiltonian for linear molecules, theory and experiment are reconciled. The C8v4 calculations confirm the small size of $H_0$ obtained in previous experimental studies. A high-level composite \textit{ab initio} potential energy function (PEF) has been developed, combining explicitly correlated coupled-cluster results with corrections for core-valence correlation, scalar relativistic effects and higher-order correlation as well as the diagonal Born-Oppenheimer correction. Large scale C8v4 calculations using this PEF show excellent agreement with the available experimental rotational\textsuperscript{\emph{a,c}} and vibrational parameters.\footnote{\ Br\"{u}nken~\textit{et al.}, \textit{J. Phys. Chem. A} \textbf{123}, 8053 (2019).} The presented rotational spectroscopic parameters of excited vibrational states should facilitate forthcoming experimental spectroscopic studies on $l$-C$_3$H$^+$