  The energetics of point defects in oxide materials plays a major role in
determining their high-temperature properties, but experimental measurements
are difficult, and calculations based on density functional theory (DFT) are
not necessarily reliable. We report quantum Monte Carlo (QMC) calculations of
the formation energy $E_{\rm S}$ of Schottky defects in MgO, which demonstrate
the feasibility of using this approach to overcome the deficiencies of DFT. In
order to investigate system-size errors, we also report DFT calculations of
$E_{\rm S}$ on repeating cells of up to $\sim 1000$ atoms, which indicate that
QMC calculations on systems of only 54 atoms should yield high precision. The
DFT calculations also provide the relaxed structures used in the variational
and diffusion Monte Carlo calculations. For MgO, we find $E_{\rm S}$ to be in
close agreement with results from DFT and from model interaction potentials,
and consistent with the scattered experimental values. The prospects for
applying the same approach to transition metal oxides such as FeO are
indicated.
