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We report density functional calculations of electronic structure andmagnetic properties of ternary iron chalcogenide TlFe$_{2}$Se$_{2}$, whichoccurs in the ThCr$_{2}$Si$_{2}$ structure and discuss the results in relationto the iron-based superconductors. The ground state is antiferromagnetic withcheckerboard order and Fe moment $\sim$ 1.90 $\mu$B. There is strongmagnetoelastic coupling similar to the Fe-based superconductors, reflected in asensitivity of the Se position to magnetism. Tl is monovalent in this compound,providing heavy electron-doping of 0.5 additional carriers per Fe relative tothe parent compounds of the Fe-based superconductors. Other than the change inelectron count, the electronic structure is rather similar to those materials.In particular, the Fermi surface is closely related to those of the Fe-basedsuperconductors, except that the electron cylinders are larger, and the holesections are suppressed. This removes the tendency towards a spin density wave.

Density Functional Study of the Over-Doped Iron Chalcogenide: TlFe$_{2}$Se$_{2}$ with ThCr$_{2}$Si$_{2}$ structure