We use the Second Moment Tight Binding with charge eQuilibration (SMTB-Q) advanced empirical potential to study clusters of oxygen interstitials in hyperstoichiometric UO2. This potential reproduces the trends obtained from density functional theory calculations. We exhibit a new form of cuboctahedron that proves to be the most stable oxygen cluster in UO2+x. Considering different types of random arrangements of these clusters, we reproduce the fact that UO2 and U4O9 are the only two stable phases at low temperature in their composition range. Focusing on U4O9 at low temperature, we obtain a model for the α-U4O9 phase, which exhibits the experimental R3c space group. We present the results of the original neutron diffraction experiments measured on U4O9 at 1.5 K and perform a Rietveld refinement of the calculated U4O9 structure, which enables us to propose a complete description of the α-U4O9 phase