A benchmark study of the vertical electronic spectra of the linear chain radicals C2H and C4H

The ability of coupled-cluster models to predict vertical excitation energies is tested on the electronic states of carbon-chain radicals of particular relevance to interstellar chemistry. Using spin-unrestricted and -restricted reference wave functions, the coupled-cluster singles and doubles (CCSD) model and a triples-including model (CC3) are tested on the sigma radicals C2H and C4H. Both molecules exhibit low-lying excited states with significant double-excitation character (as well as states of quartet multiplicity) and are thus challenging cases for excited-state approaches. In addition, we employ two diagnostics for the reliability of the CC results: the approximate excitation level (AEL) relative to the ground state and the difference between excitation energies obtained with spin-unrestricted and spin-restricted reference wave functions (the U-R difference). We find that CCSD yields poor excitation energies for states with AEL significantly larger than ca. 1.1 and/or large U-R differences, as well as for certain states exhibiting large spin contamination or other inadequacies in the reference determinant. In such cases, connected triple excitations can be included in the model and generally provide improved results. Furthermore, we find that large discrepancies exist between CC and multireference (MR) results for certain states. These disagreements are not related to basis-set effects, but likely arise from the lack of spin adaptation in conventional spin-orbital CC implementations and active space selection in the MR models.