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The electronic, magnetic and orbital structures of KCrF_3 are determined inall its recently identified crystallographic phases (cubic, tetragonal, andmonoclinic) with a set of {\it ab initio} LSDA and LSDA+U calculations. Thehigh-temperature undistorted cubic phase is metallic within the LSDA, but atthe LSDA+U level it is a Mott insulator with a gap of 1.72 eV. The tetragonaland monoclinic phases of KCrF_3 exhibit cooperative Jahn-Teller distortionsconcomitant with staggered 3x^2-r^2/3y^2-r^2 orbital order. We find that theenergy gain due to the Jahn-Teller distortion is 82/104 meV per chromium ion inthe tetragonal/monoclinic phase, respectively. These phases show A-typemagnetic ordering and have a bandgap of 2.48 eV. In this Mott insulating stateKCrF_3 has a substantial conduction bandwidth of 2.1 eV, leading to thepossibility for the kinetic energy of charge carriers in electron- orhole-doped derivatives of KCrF_3 to overcome the polaron localization at lowtemperatures, in analogy with the situation encountered in the colossalmagnetoresistive manganites.

KCrF_3: Electronic Structure, Magnetic and Orbital Ordering from First Principles