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 mostly deteriorate 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 (Grling Levy) variant of the perturbation theory should improve these results but has not been tested yet along the range separated adiabatic connection..
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