  In quantum chemistry, obtaining a system's mean-field solution and
incorporating electron correlation in a post Hartree-Fock (HF) manner comprise
one of the standard protocols for ground-state calculations. In principle, this
scheme can also describe excited states but is not widely used at present,
primarily due to the difficulty of locating the mean-field excited states. With
recent developments in excited-state orbital relaxation, self-consistent
excited-state solutions can now be located routinely at various levels of
theory. In this work, we explore the possibility of correcting HF excited
states using M{\o}ller-Plesset perturbation theory to the second order. Among
various PT2 variants, we find that the restricted open-shell MP2 (ROMP2) gives
excitation energies comparable to the best density functional theory results,
delivering $\sim 0.2$ eV mean unsigned error over a wide range of
single-configuration state function excitations, at only non-iterative $O(N^5)$
computational scaling.
