  The electronic and atomic structure of several $(1\times 1)$ terminations of
the (110) polar orientation of SrTiO$_3$ surface are systematically studied by
first-principles calculations. The electronic structure of the two
stoichiometric SrTiO- and O$_2$-terminations are characterized by marked
differences with respect to the bulk, as a consequence of the polarity
compensation. In the former, the Fermi level is located at the bottom of the
conduction band, while in the latter the formation of a peroxo bond between the
two surface oxygens results in a small-gap insulating surface with states in
the gap of the bulk projected band structure. We also consider three non
stoichiometric terminations with TiO, Sr and O compositions, respectively, in
the outermost atomic layer, which automatically allows the surface to be free
from any macroscopic polarization. They are all insulating. The cleavage and
surface energies of the five terminations are computed and compared, taking
into account the influence of the chemical environment as a function of the
relative richness in O and Sr. From our calculations it appears that some (110)
faces can even compete with the TiO$_2$ and SrO terminations of the (100)
cleavage surface: in particular, the (110)-TiO termination is stable in Sr-poor
conditions, the (110)-Sr one in simultaneously O- and Sr-rich environments. The
available experimental data are compared to the outcomes of our calculations
and discussed.
