Within the application of the incremental scheme to cerium dioxide high-level quantum chemical calculations, using the coupled-cluster approach, have been performed for (Ce4 ) m(O2−) n clusters. Two different approaches were considered. In the first one all increments were obtained from the nearly neutral Ce4O7-cluster. In the second approach different clusters were used for the evaluation of increments. Several embeddings were tested: from purely point charges up to pseudopotential-surrounding of oxygens to imitate the Ce-ions. The advantages and disadvantages of applied embedding schemes were discussed.