  We perform a comparative study of the free energies and the density
distributions in hard sphere crystals using Monte Carlo simulations and density
functional theory (employing Fundamental Measure functionals). Using a recently
introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009))
we obtain crystal free energies to a high precision. The free energies from
Fundamental Measure theory are in good agreement with the simulation results
and demonstrate the applicability of these functionals to the treatment of
other problems involving crystallization. The agreement between FMT and
simulations on the level of the free energies is also reflected in the density
distributions around single lattice sites. Overall, the peak widths and
anisotropy signs for different lattice directions agree, however, it is found
that Fundamental Measure theory gives slightly narrower peaks with more
anisotropy than seen in the simulations. Among the three types of Fundamental
Measure functionals studied, only the White Bear II functional (Hansen-Goos and
Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for
the equilibrium vacancy concentration and a physical behavior of the chemical
potential in crystals constrained by a fixed vacancy concentration.
