Interplay between electronic correlation and metal-ligand delocalization in the spectroscopy of transition metal compounds: case study on a series of planar Cu${}^{2+}$ complexes

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 $\text{cucl}$, $\text{cunh}$ and $\text{cuwater}$, 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.