Excited states from range-separated density-functional perturbation theory

We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straight-forward perturbation theory, and an extension of the G{\"o}rling--Levy one that has the advantage of keeping the ground-state density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the dihydrogene molecule. The first-order correction within this perturbation theory improves significantly the total ground-and excited-state energies of the different systems. However, the excitation energies are mostly deterio-rated with respect to the zeroth-order ones, which may be explained by the fact that the ionization energy is no longer correct for all interaction strengths. The second variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.