Excited States from State-Specific Orbital-Optimized Pair Coupled Cluster

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 a 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 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 1 or 2 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 Δoo-pCCD model, excitation energies are 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 CH+, BH, nitroxyl, nitrosomethane,
and formaldehyde, we found that Δoo-pCCD provides quite accurate
excitation energies, with root-mean-square deviations (with respect
to full configuration interaction results) lower than those of CC3
and comparable to those of EOM-CCSDT, two methods with a much higher
computational cost.