  The electronic, magnetic and orbital structures of KCrF_3 are determined in
all its recently identified crystallographic phases (cubic, tetragonal, and
monoclinic) with a set of {\it ab initio} LSDA and LSDA+U calculations. The
high-temperature undistorted cubic phase is metallic within the LSDA, but at
the LSDA+U level it is a Mott insulator with a gap of 1.72 eV. The tetragonal
and monoclinic phases of KCrF_3 exhibit cooperative Jahn-Teller distortions
concomitant with staggered 3x^2-r^2/3y^2-r^2 orbital order. We find that the
energy gain due to the Jahn-Teller distortion is 82/104 meV per chromium ion in
the tetragonal/monoclinic phase, respectively. These phases show A-type
magnetic ordering and have a bandgap of 2.48 eV. In this Mott insulating state
KCrF_3 has a substantial conduction bandwidth of 2.1 eV, leading to the
possibility for the kinetic energy of charge carriers in electron- or
hole-doped derivatives of KCrF_3 to overcome the polaron localization at low
temperatures, in analogy with the situation encountered in the colossal
magnetoresistive manganites.
