  We use the Quasiparticle Random Phase Approximation (QRPA) and the Skyrme
interactions SLy4 and SkM* to systematically calculate energies and transition
strengths for the lowest 2+ state in spherical even-even nuclei.The SkM*
functional, applied to 178 spherical nuclei between Z=10 and 90, produces
excitation energies that are on average 11% higher than experimental values,
with residuals that fluctuate about the average by -35%+55%. The predictions of
SkM* and SLy4 have significant differences, in part because of differences in
the calculated ground state deformations; SkM* performs better in both the
average and dispersion of energies. Comparing the QRPA results with those of
generator-coordinate-method (GCM) calculations, we find that the QRPA
reproduces trends near closed shells better than the GCM, and overpredicts the
energies less severely in general. We attribute part of the difference to a
deficiency in the way the GCM is implemented.
