  We have employed first-principles electronic structure calculations to
examine the hypothetical (but plausible) oxide spinel, LiCr2O4 with the d^{2.5}
electronic configuration. The cell (cubic) and internal (oxygen position)
structural parameters have been obtained for this compound through structural
relaxation in the first-principles framework. Within the one-electron band
picture, we find that LiCr2O4 is magnetic, and a candidate half-metal. The
electronic structure is substantially different from the closely related and
well known rutile half-metal CrO2. In particular, we find a smaller conduction
band width in the spinel compound, perhaps as a result of the distinct topology
of the spinel crystal structure, and the reduced oxidation state. The magnetism
and half-metallicity of LiCr2O4 has been mapped in the parameter space of its
cubic crystal structure. Comparisons with superconducting LiTi2O4 (d^{0.5}),
heavy-fermion LiV2O4 (d^{1.5}) and charge-ordering LiMn2O4 (d^{3.5}) suggest
the effectiveness of a nearly-rigid band picture involving simple shifts of the
position of E_F in these very different materials. Comparisons are also made
with the electronic structure of ZnV2O4 (d^{2}), a correlated insulator that
undergoes a structural and antiferromagnetic phase transition.
