  We derive the second-order approximation (PT2) to the ensemble correlation
energy functional by applying the G\"{o}rling-Levy perturbation theory on the
ensemble density-functional theory (EDFT). Its performance is checked by
calculating excitation energies with the direct ensemble correction method in
1D model systems and 3D atoms using numerically exact Kohn-Sham orbitals and
potentials. Comparing with the exchange-only approximation, the inclusion of
the ensemble PT2 correlation improves the excitation energies in 1D model
systems in most cases, including double excitations and charge-transfer
excitations. However, the excitation energies for atoms are generally worse
with PT2. We find that the failure of PT2 in atoms is due to the two
contributions of an orbital-dependent functional to excitation energies being
inconsistent in the calculations. We also analyze the convergence of PT2
excitation energies with respect to the number of unoccupied orbitals.
