The ground and excited state properties of the Cr3+ ion doped into the cubic host lattices Cs2NaYCl6 and Cs2NaYBr6 have been studied using density functional theory. A new symmetry based technique was employed to calculate the energies of the multiplets 4A2g, 4T2g, 2Eg, and 4T1g. The geometry of the CrX^{3 -} ₆ cluster was optimized in the ground and excited states. A Madelung correction was introduced to take account of the electrostatic effects of the lattice. The experimental Cr–X distance in the ground state can be reproduced to within 0.01 Å for both chloride and bromide systems. The calculated d–d excitation energies are typically 2000–3000 cm–1 too low. An energy lowering is obtained in the first 4T2g excited state when the octahedral symmetry of CrX^{3 -} ₆ is relaxed along the eg Jahn–Teller coordinate. The geometry corresponding to the energy minimum is in excellent agreement with the 4T2g geometry derived from high-resolution optical spectroscopy of Cs2NaYCl6:Cr3+. It corresponds to an axially compressed and equatorially elongated CrX^{3 -} ₆ octahedron.