The treatment of electronic correlations in open-shell systems is among the most challenging problems of condensed matter theory. Current approximations are only partly successful. Ligand field multiplet theory (LFMT) has been widely successful in describing intra-atomic correlation effects in x-ray spectra, but typically ignores itinerant states. The cumulant expansion for the one electron Greens function successfully describes shake-up effects but ignores atomic multiplets. More complete methods are computationally problematic. Here we show that separating the dynamic Coulomb interactions into local and longer-range parts yields an efficient, nearly ab initio multiplet + cumulant approach that accounts for both local atomic multiplet-splittings and charge-transfer shake-up satellites. An application to {alpha}-Fe 2 O 3 (hematite) yields very good agreement with XPS experiment, including the broad 9 eV satellites and distributed background features missing from previous approaches.
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