Kohn-Sham DFT results projected on ligand-field models: Using DFT to supplement ligand-field descriptions and to supply ligand-field parameters

The use of density functional theory (DFT) as a means of providing otherwise inaccessible parameters of ligand-field theory (LFT) is discussed. This application of DFT strengthens both models: it revitalizes ligand-field theory by helping it relieving its permanent burden of over-parameterization, especially when applied to low-symmetry chemical systems, while LFT simultaneously provides a conceptual framework on which the plentiful numerical data from DFT computations can be reduced to familiar values of familiar parameters. The revived LFT contains information that cannot be extracted from DFT, but which, in principle, can be projected back on to DFT, thus providing the complete energy matrix of the partially filled dq configuration.Application to two kinds of chemical systems will be described: electronically strongly anisotropic nitride complexes and tetrahedral d2 systems. In the former applications, focus is on the ligand field, its symmetry partition, and its additivity. In the d2 systems, the focus is on extracting repulsion parameters, but also parameters of the angular overlap model will be discussed.Structural and spectroscopic studies corroborated by DFT computations demonstrate that complexes containing the {Cr(N)}2+ moiety coordinated to weak auxiliary ligands are better considered as perturbed linear systems than axially compressed octahedral systems. Average-of-configuration (AOC) computations on the tetrahedral systems, analysed by using two electronic interaction models, the Slater–Condon–Shortley model and the Parametrical Multiplet Term model, both formulated in terms of mutually orthogonal, barycentered coefficient operators, illuminate two-electron interactions. Thereby the quantitative influence of the individual parameters associated with these operators becomes the novelty of the analysis. The SCS model has D terms and E terms, where D is Jørgensen's spin-pairing energy parameter and E is proportional to the Racah parameter B. The PMT model has four terms, two D terms and two E terms, and can be used to free the SCS model, which is the superior model for comparing with experiments, from small unwanted parts of the DFT-computational results. For CrIVX4 in Td symmetry, the results were as a new illustration deprived of their ligand-field contribution and the remaining “molecular atom” analysed in the PMT model, whereas for the VIIIX4− complexes, distorted to D2d symmetry, the results were described with four PMT parameters, all following the nephelauxetic series, and three AOM parameters, whose computed values provide support to the concept of linear ligation.