Density-functional modelling of core-hole effects in electron energy-loss near-edge spectra.

A series of (MgO)n supercells (n = 1, 4, 8, 16, 32) with three-dimensional periodic boundary conditions is investigated by density-functional band-structure calculations. The influence of supercell size and shape on calculated electron energy-loss near-edge spectra is assessed quantitatively, employing the Z + 1 approximation for the representation of final-state effects. Relevant convergence criteria are the length scale set by the spatial extension of the valence-electron screening cloud around the core hole and the interaction energy of neighbouring core-hole centres. A sufficient supercell size provided, the Z + 1 approximation yields a highly satisfactory description of excitations from the 1s shell of light elements, such as Mg and O, compared to experimental data. For comparison, pseudopotentials for excited states were generated for Mg, both with a large core (1s, 2s, 2p orbitals) and a small core (1s orbital only) included into the pseudopotential. The corresponding calculations with frozen core holes lead to very good agreement with the results from the Z + 1 calculation for the 1s excitations. The explicit treatment of the subvalence shell (2s, 2p), however, is mandatory for the proper modelling of excitations from orbitals higher than 1s. This indicates that the core polarisability plays an important role in excitations from more extended shells.