  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 has been successful in describing shake-up effects
but ignores atomic multiplets. More complete methods, such as dynamic
mean-field theory can be computationally problematic. Here we show that
separating the dynamic Coulomb interactions into local and longer-range parts
with ab initio parameters yields a combined multiplet plus cumulant approach
that accounts for both local atomic multiplets and satellite excitations. The
approach is illustrated in transition metal oxides and explains the multiplet
peaks, charge-transfer satellites and distributed background features observed
in XPS experiment.
