In this paper we will show that the description of an Auger process in terms of a process confined to one atom is in general not adequate and the Mulliken population is only in very specific cases a good alternative in evaluating the strength of inter-atomic transitions. The ionicity of the chemical bond cannot be used as a direct measure of the contribution of inter-atomic Auger transitions, as will be demonstrated in the case of the oxygen KVV Auger transitions in gaseous molecular oxygen and oxygen chemisorbed on the Si(001) surface. A full evaluation of inter-atomic transition rates shows that their strength depends on the inter-atomic distance as well as on the screening of the initial core hole.
Wormeester, H., Borg, H. J., & van Silfhout, A. (1991). The influence of inter-atomic transitions in Auger valence band spectroscopy: oxygen on Si(001)2x1. Surface science, 0(258), 197-209. https://doi.org/10.1016/0039-6028(91)90914-E