  We investigate the inhomogeneous unitary Fermi gas and use the
long-wavelength properties to predict the energies of small clusters of unitary
fermions trapped in harmonic potentials. The large pairing gap and scale
invariance place severe restrictions on the form of the density functional. We
determine the relevant universal constants needed to constrain the functional
from calculations of the bulk in oscillating external potentials. Comparing
with exact Quantum Monte Carlo calculations, we find that the same functional
correctly predicts the lack of shell closures for small clusters of fermions
trapped in harmonic wells as well as their absolute energies. A rapid
convergence to the bulk limit in three dimensions, where the surface to volume
ratio is quite large, is demonstrated. The resulting functional can be tested
experimentally, and is a key ingredient in predicting possible polarized
superfluid phases and the properties of the unitary Fermi gas in optical
lattices.
