  We present a theoretical investigation, based on ab initio calculations and
the quasi-harmonic approximation, on the stability properties of magnesium
(MgCO$_3$) and calcium (CaCO$_3$) carbonates at high temperatures and
pressures. The results indicate that those carbonates should be stable in
Earth's lower mantle, instead of dissociating into other minerals, in chemical
environments with excesses of SiO$_2$, MgO, or MgSiO$_3$. Therefore,
considering the lower mantle chemical composition, filled with major minerals
such as MgSiO$_3$ and MgO, calcium and magnesium carbonates are the primary
candidates as carbon hosts in that region. For the thermodynamic conditions of
the mantle, the results also indicate that carbon should be primarily hosted on
MgCO$_3$. Finally, the results indicate that carbon, in the form of free
CO$_2$, is unlikely in the lower mantle.
