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Abstract: 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 d q 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 T d 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 D 2d 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. [Copyright &y& Elsevier]

With tetragonal distortions of tetrahedral d² complexes as examples, nonadditive and additive ligand fields are compared computationally, using Kohn-Sham density functional theory (KS-DFT) and ligand-field theory to obtain 45 linear, parametrical equations. For each complex, a ‘data’ reduction from three nonadditive-field parameters to two parameters of the additive field occurs. The complexes VX4- and CrX4 (where X = F, Cl, Br, I) provide the two-dimensional spectrochemical series of the σ and π AOM parameters, which are known semiempirically for the halide ligands. The same parametrical results can be obtained from the Kohn-Sham orbital energies of the ‘average of configuration’ computation. [ABSTRACT FROM AUTHOR]

The Amsterdam Density Functional (ADF) package has been used to constrain Kohn-Sham DFT in such a fashion that a transition from KS-DFT to ligand-field theory in the form of the parametrical d[sup q] model is completely well-defined. A relationship is established between the strong-field approximation of the parametrical d² model for the tetrahedral complexes VCl[sup -, sub 4] and VBr[sup -, sub 4] and certain fixed-orbital ADF-computed energies. In this way values for all the parameters of the d² model may be computed, thus allowing the ADF results to be expressed in terms of a KS-DFT energy matrix that can be diagonalized. This means that the KS-DFT deficiency with regard to computation of nondiagonal elements has been overcome and the KS-DFT eigenenergies have become available through the KS-DFT mimicking of the ligand-field plus repulsion model. By using mutually orthogonal strong-field energy matrices, the mimicking has been further elucidated. The computed values for the empirical parameters of VCl[sup -, sub 4]- and VBr[sup -, sub 4] are in good agreement with experimental data. The spectrochemical and the nephelauxetic series have been computed by including the remaining halide complexes and the quantitatively special position of F[sup -] among the halides corroborated for both series. [ABSTRACT FROM AUTHOR]