Ligand field and density functional descriptions of the d-states and bonding in transition metal complexes

The d-orbital energy sequences for low symmetry transition metal complexes derived from Kohn-Sham density functional theory and ligand field theory are different due to each model's treatment of interelectron repulsion. The implications for providing a unified description of the underlying metal-ligand bonding are analysed and illustrated using conventional and time-dependent DFT. Previous detailed spectroscopic studies have established the d orbital sequence in planar coordination complexes containing pi-donor halide ligands as dx2-y2 >> dxy > dxz, dyz > dz2 while for a sigma-only system like [Pd(NH3)4]2+, ligand field approaches like the angular overlap model (AOM) or cellular ligand field (CLF) model predict dxz, dyz, and dxy, should be degenerate. However, the energies of the Kohn Sham (KS) 'd' orbitals of [PdCl4]2- and [Pd(NH3)4]2+ place dxy below the dxz/dyz pair. Direct use of the KS orbital eigenvalues in AOM or CLF analyses would imply both ligands are pi acceptors. This result is independent of the choice of functional or whether the calculation is carried out in vacuo or in a polarised continuum representing solvation by water. The origin of the difference between the KS and LFT d orbital sequences derives from their treatments of d-d interelectron repulsion. KS orbitals include interelectron repulsion contributions while LFT d orbitals do not. For a low-spin d8 complex, DFT gives less d-d interelectron repulsion in the xy plane leading to a lowering of dxy relative to dxy/dyz. This differential effect can be reversed qualitatively by progressively removing electron density from dz2 and placing it in dx2-y2. When about 0.6 electrons is rearranged, E(dxy) > E(dxz/dyz) for [PdCl4]2- and the dpi orbitals for [Pd(NH3)4]2+ are virtually degenerate. The wider ramifications of these interelectron repulsion effects are discussed for other symmetries. Excited d state energies for [PdCl4]2- are computed using both time dependent density functional theory (TDDFT) and determinant energies. The latter give the experimental sequence 1A2g < 1Eg < 1B1g while TDDFT gives 1Eg < 1A2g < 1B1g. Both give transition energies up to 30% lower than observed. A DFT analysis of the bonding energies in [PdCl4]2- indicates that the Pd-Cl pi bonding in the molecular plane is about 33% weaker than the out-of-plane pi interaction due to non-zero overlap between ligand orbitals. The normal LFT assumption of linear ligation may not always be valid.