  We present a comprehensive theoretical study of the physical phenomena that
determine the relative energies of the three of the lowest electronic states of
each of the square-planar copper complexes $\cucl$, $\cunh$ and $\cuwater$, and
present a detailed analysis of the extent to which truncated configuration
interaction (CI) and coupled cluster (CC) theories succeed in predicing the
excitation energies. We find that ligand-metal charge transfer (CT) single
excitations play a crucial role in the correct determination of the properties
of these systems, even though the CT processes first occur at fourth order in
perturbation theory, and propose a suitable choice of minimal active space for
describing these systems with multi-reference theories. CCSD energy differences
agree very well with near full CI values even though the $T_1$ diagnostics are
large, which casts doubt on the usefulness of singles-amplitude based
multi-reference diagnostics. CISD severely underestimates the excitation
energies and the failure is a direct consequence of the size-inconsisency
errors in CISD. Finally, we present reference values for the energy differences
computed using explicitly correlated CCSD(T) and BCCD(T) theory.
