Here we report the optical and x-ray absorption (XAS) spectra of the wide-band-gap oxide MgO using density functional theory (DFT) and many-body perturbation theory (MBPT). Our comprehensive study of the electronic structure shows that while the band gap is underestimated with the exchange-correlation functional PBEsol (4.58 eV) and the hybrid functional HSE06 (6.58 eV) compared to the experimental value (7.7 eV), it is significantly improved (7.52 eV) and even overcompensated (8.53 eV) when quasiparticle corrections are considered. Inclusion of excitonic effects by solving the Bethe-Salpeter equation (BSE) yields the optical spectrum in excellent agreement with experiment. Excellent agreement is observed also for the O and Mg K-edge absorption spectra, demonstrating the importance of the electron-hole interaction within MBPT. Projection of the electron-hole coupling coefficients from the BSE eigenvectors on the band structure allows us to determine the origin of prominent peaks and identify the orbital character of the relevant contributions. The real space projection of the lowest energy exciton wavefunction of the optical spectrum indicates a Wannier-Mott type, whereas the first exciton in the O K-edge is more localized.
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