  Recent results of the Fayans energy density functional (EDF) for spherical
nuclei are reviewed. A comparison is made with predictions of several Skyrme
EDFs. The charge radii and characteristics of the first 2^+ excitations in
semi-magic nuclei are briefly discussed. The single-particle spectra of doubly
magic nuclei are considered in more detail. The phonon-particle coupling
effects are analyzed including the so-called tadpole term.
