  The structural stability of CeFe$_{12}$ is investigated by using
first-principles calculation. The formation energies of CeFe$_{12}$ relative to
the Ce$_{2}$Fe$_{17}$ + bcc-Fe phase and to the CeFe$_{2}$ + bcc-Fe phase are
calculated with the assumptions of trivalency and tetravalency for Ce. Those
values are compared with corresponding results in $R$Fe$_{12}$ for $R=$ Nd, Sm,
and Zr. Our results suggest that the tetravalent Ce is a promising stabilizer
of the ThMn$_{12}$ structure. We also show that the stabilizing effect of an
element depends as much on the valency as on the size of the $R$ element by
investigating $R$Fe$_{12}$ where $R$ is assumed to have a hypothetical valency
on the basis of first-principles calculation.
