Seniority and Hierarchy Configuration Interaction for Radicals and Excited States

Hierarchy configuration interaction (hCI) has recently
been introduced
as an alternative configuration interaction (CI) route combining excitation
degree and seniority number and has been shown to efficiently recover
both dynamic and static correlations for closed-shell molecular systems
[J. Phys. Chem. Lett. 2022, 13, 4342]. Here we generalize hCI for an arbitrary reference determinant,
allowing calculations for radicals and 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 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 the excitation energies of closed- and open-shell
systems. Our results underline that the choice of both the reference
determinant and the set of orbitals drives 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.