  We study the bulk deformation properties of the Skyrme nuclear energy density
functionals. Following simple arguments based on the leptodermous expansion and
liquid drop model, we apply the nuclear density functional theory to assess the
role of the surface symmetry energy in nuclei. To this end, we validate the
commonly used functional parametrizations against the data on excitation
energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers
in actinide nuclei. After subtracting shell effects, the results of our
self-consistent calculations are consistent with macroscopic arguments and
indicate that experimental data on strongly deformed configurations in
neutron-rich nuclei are essential for optimizing future nuclear energy density
functionals. The resulting survey provides a useful benchmark for further
theoretical improvements. Unlike in nuclei close to the stability valley, whose
macroscopic deformability hangs on the balance of surface and Coulomb terms,
the deformability of neutron-rich nuclei strongly depends on the
surface-symmetry energy; hence, its proper determination is crucial for the
stability of deformed phases of the neutron- rich matter and description of
fission rates for r-process nucleosynthesis.
