  A comprehensive investigation on point defects and their clustering behavior
in nonstoichiometric uranium dioxide UO2+x is carried out using LSDA+U method
based on density functional theory. Accurate energetic information and charge
transfers available so far are obtained. With these energies that have improved
more than 50% over that of pure GGA and LDA, we show the density functional
theory predicts the predominance of oxygen defects over uranium ones at any
compositions, which is possible only after treated the localized 5f electrons
properly. Calculations also suggest an upper bound of x~0.03 for oxygen
clusters to start off. The volume change induced by point uranium defects is
monotonic but nonlinear, whereas for oxygen defects, increase x always reduces
the system volume linearly, except dimers that require extra space for
accommodation, which has been identified as meta-stable ionic molecule. Though
oxygen dimers usually occupy Willis O'' sites and mimic a single oxygen in
energetics and charge state, they are rare at ambient conditions. Its
decomposition process and vibrational properties have been studied carefully.
To obtain a general clustering mechanism in anion-excess fluorites
systematically, we also analyze the local stabilities of possible basic
clustering modes of oxygen defects. The result shows an unified way to
understand the structure of Willis type and cuboctahedral clusters in UO2+x and
beta-U4O9. Finally we generalize the point defect model to the independent
clusters approximation to include clustering effects, the impact on defect
populations is discussed.
