  We propose an ab initio method to evaluate the core-valence-valence (CVV)
Auger spectrum of systems with filled valence bands. The method is based on the
Cini-Sawatzky theory, and aims at estimating the parameters by first-principles
calculations in the framework of density-functional theory (DFT). Photoemission
energies and the interaction energy for the two holes in the final state are
evaluated by performing DFT simulations for the system with varied population
of electronic levels. Transition matrix elements are taken from atomic results.
The approach takes into account the non-sphericity of the density of states of
the emitting atom, spin-orbit interaction in core and valence, and non
quadratic terms in the total energy expansion with respect to fractional
occupation numbers. It is tested on two benchmark systems, Zn and Cu metals,
leading in both cases to L23M45M45 Auger peaks within 2 eV from the
experimental ones. Detailed analysis is presented on the relative weight of the
various contributions considered in our method, providing the basis for future
development. Especially problematic is the evaluation of the hole-hole
interaction for systems with broad valence bands: our method underestimates its
value in Cu, while we obtain excellent results for this quantity in Zn.
