Seniority and Hierarchy Configuration Interaction for Radicals and Excited States

TL;DR

This paper extends hierarchy configuration interaction (hCI) to radicals and excited states, demonstrating its efficiency and accuracy in capturing electron correlation compared to other CI methods, especially when combined with perturbation corrections.

Contribution

The authors generalize hCI for arbitrary references, enabling accurate calculations for radicals and excited states, and compare its performance with eCI and sCI methods.

Findings

hCI outperforms or matches eCI in accuracy

sCI is less accurate than hCI and eCI

EN2 correction accelerates convergence of hCI and eCI

Abstract

Hierarchy configuration interaction (hCI) has been recently introduced as an alternative configuration interaction (CI) route combining excitation degree and seniority number, which showed to efficiently recover both dynamic and static 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 reference determinant, allowing calculations for radicals and for excited states in a state-specific way. We gauge this route against excitation-based CI (eCI) and seniority-based CI (sCI) by evaluating how different ground-state properties of radicals converge to the full CI limit. We find that hCI outperforms or matches eCI, whereas sCI is far less accurate, in line with previous observations for closed-shell molecules. Employing the second-order Epstein-Nesbet (EN2) perturbation theory as a correction significantly accelerates the convergence of hCI and eCI. We further explore various hCI and sCI models to calculate excitation energies of closed- and open-shell systems. Our results underline that both the choice of the reference determinant and the set of orbitals drive the fine balance between correlation of ground and excited states. State-specific hCI2 and higher order models perform similarly to their eCI counterparts, whereas lower orders of hCI deliver poor results, unless supplemented by the EN2 correction, which substantially improves their accuracy. In turn, sCI1 produces decent excitation energies for radicals, encouraging the development of related seniority-based coupled-cluster methods.