  The ground-state structural and electronic properties of ferroelectric
BiFeO$_3$ are calculated using density functional theory within the local
spin-density approximation and the LSDA+U method. The crystal structure is
computed to be rhombohedral with space group $R3c$, and the electronic
structure is found to be insulating and antiferromagnetic, both in excellent
agreement with available experiments. A large ferroelectric polarization of
90-100 $\mu$C/cm$^2$ is predicted, consistent with the large atomic
displacements in the ferroelectric phase and with recent experimental reports,
but differing by an order of magnitude from early experiments. One possible
explanation is that the latter may have suffered from large leakage currents.
However both past and contemporary measurements are shown to be consistent with
the modern theory of polarization, suggesting that the range of reported
polarizations may instead correspond to distinct switching paths in structural
space. Modern measurements on well-characterized bulk samples are required to
confirm this interpretation.
