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Hierarchy configuration interaction (hCI) has been recently introduced as analternative configuration interaction (CI) route combining excitation degreeand seniority number, which showed to efficiently recover both dynamic andstatic correlations for closed-shell molecular systems[\href{https://doi.org/10.1021/acs.jpclett.2c00730}{\textit{J.~Phys.~Chem.~Lett.}~\textbf{2022},\textit{13}, 4342}]. Here, we generalize hCI for an arbitrary referencedeterminant, allowing calculations for radicals and for excited states in astate-specific way. We gauge this route against excitation-based CI (eCI) andseniority-based CI (sCI) by evaluating how different ground-state properties ofradicals converge to the full CI limit. We find that hCI outperforms or matcheseCI, whereas sCI is far less accurate, in line with previous observations forclosed-shell molecules. Employing the second-order Epstein-Nesbet (EN2)perturbation theory as a correction significantly accelerates the convergenceof hCI and eCI. We further explore various hCI and sCI models to calculateexcitation energies of closed- and open-shell systems. Our results underlinethat both the choice of the reference determinant and the set of orbitals drivethe fine balance between correlation of ground and excited states.State-specific hCI2 and higher order models perform similarly to their eCIcounterparts, whereas lower orders of hCI deliver poor results, unlesssupplemented by the EN2 correction, which substantially improves theiraccuracy. In turn, sCI1 produces decent excitation energies for radicals,encouraging the development of related seniority-based coupled-cluster methods.

Seniority and Hierarchy Configuration Interaction for Radicals and Excited States