An all-electron study of the low-lying excited states and optical constants of Al₂O₃ in the range 5-80 eV

This paper reports calculated energies and electronic structures of O(2p), O(2s) and Al(2p) excited states in bulk [Formula: see text]-Al₂O₃, at the [Formula: see text] and [Formula: see text] surfaces and in the presence of O vacancy defects, obtained from all-electron HF, B3LYP, GGA and LDA calculations based on a recently described direct [Formula: see text]-SCF approach (Mackrodt et al 2018 J. Phys.: Condens. Matter 30 495901). The closely related frequency-dependent optical constants derived from B3LYP calculations within the CPHF/DF framework are also reported, where both sets of results are shown to compare favourably with the experimental spectra. The differences between the directly calculated excited state energies, which in [Formula: see text]-Al₂O₃ are equal to the leading excitation edges, based on the four functionals, are substantially less than the differences between the corresponding (ground state) band gaps, as reported previously for AFII NiO (Mackrodt et al 2018 J. Phys.: Condens. Matter 30 495901). For the B3LYP functional, these energies are 8.7 eV, 12.5 eV and 73.7 eV for the O(2p), O(2s) and Al(2p) excitations respectively. The O(2p) edge is predicted to be degenerate, with distinct excitations from O(2p) states that are parallel to and perpendicular to the c-axis, in agreement with the reported spectra (Tomiki et al 1993 J. Phys. Soc. Japan 62 573). Detailed analyses of the charge and spin distributions in the four bulk excited states indicate that these are essentially charge-transfer excitonic, with acceptor sites at the nearest neighbour positions. Despite the close proximity of the O([Formula: see text]) and O(2p[Formula: see text]) excited state energies, the charge and spin distributions are predicted to be quite different.