  First, we briefly outline some aspects of the starting project to design
non-empirical energy functionals based on low-momentum vacuum interactions and
many-body perturbation theory. Second, we present results obtained within an
approximation of such a scheme where the pairing part of the energy density
functional is constructed at first order in the nuclear plus Coulomb two-body
interaction. We discuss in detail the physics of the odd-even mass staggering
and the necessity to compute actual odd-even mass differences to analyze it
meaningfully.
