We have used an expansion in Gaussian orbitals to make the first self-consistent calculation of the energy bands of ${\mathrm{Cu}}_2$O. Although the ordering of the bands at $\Gamma$ is identical to that calculated by Dahl and Switendick, there is considerable difference in the two sets of bands due to a much larger O $2p$-Cu $3d$ hybridization in the self-consistent bands. Unlike Dahl and Switendick and in agreement with Elliott's interpretation of the excitonic data, we find that the spin-orbit splitting of the top of the valence band puts the ${\Gamma }_7^{+}(j=\frac{1}{2})$ level above the ${\Gamma }_8^{+}(j=\frac{3}{2})$.

• Received 3 August 1979

DOI:https://doi.org/10.1103/PhysRevB.21.1549