  We perform ab initio simulations of the total and partial Auger decay widths
of 1s^-1, 2s^-1, and 2p^-1 ionized hydrogen sulfide and 2s^-1 ionized argon
with non-Hermitian quantum chemistry. We use coupled cluster theory with single
and double substitutions (CCSD) and equation of motion CCSD (EOM-CCSD) and
discuss the novel application of (equation of motion-) second order
M{\o}ller-Plesset perturbation theory (MP2). We find good agreement between the
methods for the 1s^-1 hole of H2S, whereas for the other holes we can only use
the EOM methods. We obtain very large decay widths of the 2s^-1-vacant states
due to intense Coster-Kronig transitions with excellent agreement to
experiments. The three 2p^-1 holes show completely different spectra because a
decay channel is only significant when one of the final holes is spatially
aligned with the initial hole. Lastly, we observe that triplet channels are
much more important for the 2s^-1 and 2p^-1 holes than for the 1s^-1 hole, for
which it is well known that triplet channels only contribute weakly to the
total Auger intensity.
