  The projection-based quantum embedding method is applied to electronically
excited states of valence, Rydberg, and charge-transfer character, valence- and
core-ionized states, as well as bound and temporary radical anions. We embed
different variants of equation-of-motion coupled-cluster singles and doubles
(EOM-CCSD) theory in density functional theory and investigate the performance
of the resulting methods using small organic molecules microsolvated by a
varying number of water molecules as test cases. States that are unstable
towards electron loss are treated by means of a complex-absorbing potential.
Besides transition energies, we also present Dyson orbitals and natural
transition orbitals for embedded EOM-CCSD. Our results illustrate that embedded
EOM-CCSD describes ionization and valence excitation very well and that these
transitions are quite insensitive towards technical details of the embedding
procedure. On the contrary, more care is required when dealing with Rydberg
excitations or electron attachment. For the latter type of transition in
particular, the use of long-range corrected density functionals is mandatory
and truncation of the virtual orbital space -- which is indispensable for the
application of projection-based embedding to large systems -- proves to be
difficult.
