  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.
