  Surface oxidation processes are crucial for the functionality of Cu-based
catalytic systems used for methanol synthesis, partial oxidation of methanol or
the water-gas shift reaction. We assess the stability and population of the
"8"-structure, a $|\begin{smallmatrix} 3&2\\ -1&2 \end{smallmatrix}|$ oxide
phase, on the Cu(111) surface. This structure has been observed in x-ray
photoelectron spectroscopy and low-energy electron diffraction experiments as a
Cu(111) surface reconstruction that can be induced by a hyperthermal oxygen
molecular beam. Using density-functional theory calculations in combination
with \textit{ab initio} atomistic thermodynamics and Boltzmann statistical
mechanics, we find that the proposed oxide superstructure is indeed metastable
and that the population of the "8"-structure is competitive with the known "29"
and "44" oxide film structures on Cu(111). We show that the configuration of O
and Cu atoms in the first and second layers of the "8"-structure closely
resembles the arrangement of atoms in the first two layers of Cu$_2$O(110),
where the atoms in the "8"-structure are more constricted. Cu$_2$O(110) has
been suggested in the literature as the most active low index facet for
reactions such as water splitting under light illumination. If the
"8"-structure were to form during a catalytic process, it is therefore likely
to be one of the reactive phases.
