Excited States From State Specific Orbital Optimized Pair Coupled Cluster

TL;DR

This paper explores the use of state-specific orbital optimization in pair coupled cluster doubles (pCCD) to accurately describe excited states, showing that with proper orbitals, pCCD can match DOCI and provide reliable excitation energies efficiently.

Contribution

It demonstrates that optimizing orbitals for each excited state significantly improves pCCD's accuracy, enabling direct targeting of doubly-excited states without EOM formalism.

Findings

State-specific orbitals reduce pCCD-DOCI energy discrepancies by two orders of magnitude.

$ riangle$oo-pCCD yields excitation energies with RMS deviations lower than CC3.

pCCD with orbital optimization is computationally efficient and accurate for doubly-excited states.

Abstract

The pair coupled cluster doubles (pCCD) method (where the excitation manifold is restricted to electron pairs) has a series of interesting features. Among others, it provides ground-state energies very close to what is obtained with doubly-occupied configuration interaction (DOCI), but with polynomial cost (compared with the exponential cost of the latter). Here, we address whether this similarity holds for excited states, by exploring the symmetric dissociation of the linear \ce{H4} molecule. When ground-state Hartree-Fock (HF) orbitals are employed, pCCD and DOCI excited-state energies do not match, a feature that is assigned to the poor HF reference. In contrast, by optimizing the orbitals at the pCCD level (oo-pCCD) specifically for each excited state, the discrepancies between pCCD and DOCI decrease by one or two orders of magnitude. Therefore, the pCCD and DOCI methodologies still provide comparable energies for excited states, but only if suitable, state-specific orbitals are adopted. We also assessed whether a pCCD approach could be used to directly target doubly-excited states, without having to resort to the equation-of-motion (EOM) formalism. In our $\Delta$oo-pCCD model, excitation energies were extracted from the energy difference between separate oo-pCCD calculations for the ground state and the targeted excited state. For a set comprising the doubly-excited states of \ce{CH+}, \ce{BH}, nitroxyl, nitrosomethane, and formaldehyde, we found that $\Delta$oo-pCCD provides quite accurate excitation energies, with root mean square deviations (with respect to full configuration interaction results) lower than CC3 and comparable to EOM-CCSDT, two methods with much higher computational cost.