Atomistic computer simulations, using classical potential models, have been used to model ceria nanoparticles (NPs) with diameters of approximately 1 and 2 nm. Lattice expansion is observed in the stoichiometric 1 nm NP, consistent with experiment, indicating that reduction is not the primary driver for such expansion. Furthermore, on reduction, the 1 nm NP is found to distort significantly, offering a possible explanation for its reduced oxygen storage capacity compared to the 2 nm NP. Point defect calculations on the 2 nm NP indicate that while doping with La is energetically favourable, Fe incorporation is not.