Doping CeO$_2$ with {\it e.g.} Ca gives an enhanced reactivity towards reduction of SO$_2$ by CO, and total combustion of methane. Theoretical modelling using static minimizations and molecular dynamics (MD) simulations of the doped (110) face in combination with {\it ab initio} quantum chemical cluster models show large effects on the Ce(IV)/Ce(III) balance due to the doping. Computed oxygen to cerium charge transfer energies are strongly reduced as a result of the introduction of defects and oxygen vacancies, but not sufficiently to explain the observed reactivities. The structures resulting from the MD simulations for both the doped and undoped material are in good agreement with recent experimental pulsed neutron scattering results.