  We report the understanding of the electronic band structure of
$Cs_4CuSb_2Cl_{12}$ perovskite through first-principles density-functional
theory calculations. We find that the most stable state has the
antiferromagnetic configuration where each $[CuCl_6]$ octahedral chain along
the [010] direction is antiferromagnetic. The reasonable band structure of the
compound can be obtained only if both the correct magnetic order and the
improved exchange interaction of the Cu $\it{d}$ electrons are taken into
account.
