State-Specific Coupled-Cluster Methods for Excited States

We reexamine $\Delta$CCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain where the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here is to evaluate the effectiveness of $\Delta$CCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the $\Delta$CCSD and EOM-CCSD methods, for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly-excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our dataset, consisting of 276 excited states stemming from the \textsc{quest} database [\href{https://doi.org/10.1002/wcms.1517}{V\'eril \textit{et al.}, \textit{WIREs Comput. Mol. Sci.} \textbf{2021}, 11, e1517}], provides a significant base to draw general conclusions concerning the accuracy of $\Delta$CCSD. Except for the doubly-excited states, we found that $\Delta$CCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of \SI{0.10}{\eV} and \SI{0.07}{\eV}) is less pronounced than that obtained for singly-excited states of closed-shell systems (MAEs of \SI{0.15}{\eV} and \SI{0.08}{\eV}). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for $\Delta$CCSD.