  We revisit the problem of the spectra of two holes in a CuO$_{2}$ layer,
modeled as a Cu-d$^{8}$ impurity with full multiplet structure coupled to a
full O-2p band as an approximation to the local electronic structure of a hole
doped cuprate. Unlike previous studies that treated the O band as a featureless
bath, we describe it with a realistic tight binding model. While our results
are in qualitative agreement with previous work, we find considerable
quantitative changes when using the proper O-2p band structure. We also find
(i) that only the ligand O-2p orbitals play an essential role, within this
impurity model; (ii) that the three-orbital Emery model provides an accurate
description for the subspace with $^{1}\!A_1$ symmetry, which includes the
ground-state in the relevant region of the phase diagram; (iii) that this
ground-state has only $\sim 50\%$ overlap with a Zhang-Rice singlet; (iv) that
there are other low-energy states, in subspaces with different symmetries, that
are absent from the three-orbital Emery model and its one-band descendants.
These states play an important role in describing the elementary excitations of
doped cuprates.
