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

Abstract

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.

Interpreting Effects of Structure Variations Induced by Temperature and Pressure on Luminescence Spectra of Platinum(II) Bis(dithiocarbamate) Compounds

“…This destabilizes the LUMO level of the title complexes, since the d x 2 −y 2 orbital is prominently involved in σ bonding. 42 It will also destabilize the HOMO, but in a less important way, since this orbital is not involved in σ bonding for square-planar complexes. 41 Therefore, the HOMO−LUMO energy difference increases with increasing pressure, in direct formal analogy with the temperature effect for Pt(dopDTC) 2 .…”

Impact of the ionic forms on the UV–Vis spectra 2‐hydroxybenzylamine. A TD‐DFT study

“…The time-dependent (TD) generalization of the density functional theory (TD-DFT) [16] is one other effective method for calculating the excitation energies of organic and inorganic compounds [17,18]. At present, TD-DFT calculations are an attractive alternative to ab initio calculations that they match in accuracy but surpass in computational economy [19][20][21].…”

Comparative studies of the spectroscopy of CuCl2: DFT versus standard ab initio approaches

“…As stressed in Ref. 18,22 Even though it is now well documented that relativistic effects must be included even for first row transition metals like Cu in order to reach spectroscopic accuracy, given our present purpose, we shall only deal here with the scalar relativistic effects through the use of effective core potentials. 20͔͒ compared to the experimentally obtained value of 7100 cm −1 through gas-phase photoemission spectroscopy ͑PES͒ of the anion.…”