  Electronic structure and magnetic properties for iron deficient
TlFe$_{2-x}$Se$_2$ compounds are studied by first-principles calculations. We
find that for the case of $x=0.5$ with a Fe-vacancy ordered orthorhombic
superstructure, the ground state exhibits a stripe-like antiferromagnetic
ordering and opens a sizable band gap if the short-ranged Coulomb interaction
of Fe-3d electrons is moderately strong, manifesting a possible Mott insulating
state. While increasing Fe-vacancies from the $x=0$ side, where the band
structure is similar to that of a heavily electron-doped FeSe system, the Mott
localization can be driven by kinetic energy reduction as evidenced by the band
narrowing effect. Implications of this scenario in the recent experiments on
TlFe$_{2-x}$Se$_2$ are discussed.
