  Electronic structure and magnetic properties for iron-selenide KFe$_2$Se$_2$
are studied by first-principles calculations. The ground state is stripe-like
antiferromagnetic with calculated 2.26 $\mu_B$ magnetic moment on Fe atoms; and
the $J_1$, $J_2$ coupling strengths are calculated to be 0.038 eV and 0.029 eV.
The states around $E_F$ are dominated by the Fe-3d orbitals which hybridize
noticeably to the Se-4p orbitals. While the band structure of KFe$_2$Se$_2$ is
similar to a heavily electron-doped BaFe$_2$As$_2$ or FeSe system, the Fermi
surface of KFe$_2$Se$_2$ is much closer to \fs11 system since the electron
sheets around $M$ is symmetric with respect to $x$-$y$ exchange. These
features, as well as the absence of Fermi surface nesting, suggest that the
parental KFe$_2$Se$_2$ could be regarded as an electron over-doped 11 system
with possible local moment magnetism.
