Theoretical models that reliably can predict off-stoichiometry in materials via accurate descriptions of underlying thermodynamics are crucial for energy applications. For example, transition-metal and rare-earth oxides that can tolerate a large number of oxygen vacancies, such as CeO<
sub>
2<
/sub>
and doped CeO<
sub>
2<
/sub>
, can split water and carbon dioxide via a two-step, oxide-based solar thermochemical (STC) cycle. The search for new STC materials with a performance superior to that of state-of-the-art CeO<
sub>
2<
/sub>
can benefit from predictions accurately describing the thermodynamics of oxygen vacancies. The sub-lattice formalism, a common tool used to fit experimental data and build temperature-composition phase diagrams, can be useful in this context. Here, sub-lattice models are derived solely from zero-temperature quantum mechanics calculations to estimate fairly accurate temperature- and oxygen-partial-pressure-dependent off-stoichiometries in CeO<
sub>
2<
/sub>
and Zr-doped CeO<
sub>
2<
/sub>
. Physical motivations for deriving some of the ?excess? sub-lattice model parameters directly from quantum mechanical calculations, instead of fitting to minimize deviations from experimental and/or theoretical data, are identified. As a result, important limitations and approximations of the approach used are specified and extensions to multi-cation oxides are also suggested to help identify novel candidates for water and carbon dioxide splitting and related applications.