We briefly introduce the theoretical concepts of one of the currently most reliable ab-initio approaches to the computation of electronic band structures. We use the nonlocal hybrid HSE03 functional as an approximation to exchange and correlation in a generalized Kohn-Sham equation to compute the starting point for the solution of the quasiparticle equation. Using this starting electronic structure we compute quasiparticle energies within the GW approximation which involves screening from the fully frequency-dependent dielectric function. Spin-orbit coupling is included in our calculations.

We present highly accurate electronic band structures of MgO, ZnO, and CdO, which we use to derive fundamental gaps, effective electron and hole masses, crystal-field and spin-orbit splittings, optical transition matrix elements, and even exciton binding energies. Chemical trends are pointed out. Since we are not limited to the equilibrium lattice structures of these materials, we predict and compare to values for the wurtzite polymorphs of MgO and CdO. Both become important in alloys and heterostructures of MgO and CdO together with wz-ZnO, e.g., for band-gap tailoring. However, it is practically impossible to fabricate samples of sufficient quality for experimental studies.

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