The method of tight binding has been applied to determine the energy-band structure of the calcium-oxide crystal. The initial potential was constructed using the overlapping-atomic-potential model in terms of the charge densities of the neutral calcium and oxygen atoms. A reduced basis set was constructed using Bloch sums of contracted Gaussians. This basis set yielded accuracy equal to that obtained using Bloch sums of single Gaussians and resulted in a reduced size of the secular equation. The calculation was iterated to selfconsistency and the resulting band structure compared with experiment. The self-consistent band structure gives an energy for the $\Gamma$-point valence-band-to-conduction-band transition of 5.93 eV which compares with the experimental value of 7.03 eV. Comparison with experiment indicates that the strong influence of the unfilled calcium $3d$ electronic states upon the conduction band must be accounted for in interpreting some of the experimental data.

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