  The modification of the properties of CeO$_2$ through aliovalent doping are
investigated within the \emph{ab-initio} density functional theory framework.
Lattice parameters, dopant atomic radii, bulk moduli and thermal expansion
coefficients of fluorite type Ce$_{1-x}$M$_{x}$O$_{2-y}$ (with M$ = $ Mg, V,
Co, Cu, Zn, Nb, Ba, La, Sm, Gd, Yb, and Bi)are presented for dopant
concentrations in the range $0.00 \leq x \leq 0.25$. The stability of the
dopants is compared and discussed, and the influence of oxygen vacancies is
investigated. It is shown that oxygen vacancies tend to increase the lattice
parameter, and strongly decrease the bulk modulus. Defect formation energies
are correlated with calculated crystal radii and covalent radii of the dopants,
but are shown to present no simple trend. The previously observed inverse
relation between the thermal expansion coefficient and the bulk modulus is
shown to persist independent of the inclusion of charge compensating vacancies.
