Ligand field theory calculations

So, ligand-field theory is the name given to crystal-field theory that is freely parameterized. The centrally important point is that ligand-field calculations, whether numerical or merely qualitative, explicitly or implicitly employ a ligand-field Hamiltonian, very much like the crystal-field Hamiltonian, operating upon a basis set of pure d orbitals. Instead of the crystal-field Hamiltonian (Eq. 6.15),... 

Warren KD (1984) Calculations of the Jahn-Teller Coupling Constants for d Systems in Octahedral Symmetry via the Angular Overlap Model. 57 119-145 Warren KD (1977) Ligand Field Theory off-Orbital Sandwich Complexes. 33 97-137 Warren KD (1976) Ligand Field Theory of Metal Sandwich Complexes. 27 45-159 Watson RE, Perlman ML (1975) X-Ray Photoelectron Spectroscopy. Application to Metals and Alloys. 24 83-132... 

In contrast to the EFG analyzed before, aU of these expectations from ligand field theory are largely confirmed by the DFT calculations. Despite the fact that the S = 2 state has a smaller prefactor for the isotropic Fermi contact term, the core polarization in the presence of four unpaired electrons is much larger and, consequently, the isotropic Fe-HFC is predicted to be roughly a factor of two larger in magnitude for as compared to 2g. Similarly, the dipolar MFCs are comparable for both spin states, which must be due to a considerable contribution from anisotropic covalency in the 5 = 2 species which partially compensates for the smaller prefactor. 

Since Mossbauer spectroscopy is sensitive to all terms in the SH, it is also sensitive to the ZFS and the g-tensor. The theory of both interactions can be approached along the same lines as explained in some detail in Appendix 1 (Part III, 3 of CD-ROM) [89, 90]. This becomes somewhat elaborate for the ZFS while the g-tensor is more readily approached. Both quantities have been previously treated in some detail and a protracted discussion would be inappropriate here [9, 79, 89-93]. In general, the accuracy with which both quantities can be calculated from DFT is rather moderate and a combination of ligand field theory and DFT or some... 

The extension to non-octahedral complexes is possible, but must be carried out with great care The orbitals chosen can be expressed as a linear combination of the usual orbitals for an octahedron, and electron-electron repulsions can then be calculated from those for the octahedral case. It is not necessarily adequate for tetrahedral complexes of the first row transition elements, to use ligand field theory in the strong field limit, even for powerful ligands in V(mesityl)4 the ligand field splitting is only 9250 cm ... 

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... 

One way to calculate the ZFS parameters is through ligand field theory (52,53) but for quantitative calculations it is nowadays possible to use accurate correlated ab initio methods. It is known that the direct spin—spin contribution (SSC) is dominant for organic molecules, and for a long time it was assumed that for inorganic complexes exclusively the SOC dominates. Nevertheless, exceptions to this rule have been identified (54,55). 

As a conclusion, Hartree-Fock calculations are seen to be qualitatively compatible with the simple models (ligand field theory for dd-transitions, and the weak coupling model for CT-transitions). However, the ab initio work strongly suggests that the results be situated in a different conceptual framework. 

In this chapter, we have developed the information content of different excited state spectroscopic methods in terms of ligand field theory and the covalency of L—M bonds. Combined with the ground-state methods presented in the following chapters, spectroscopy and magnetism experimentally define the electronic structure of transition metal sites. Calculations supported by these data can provide fundamental insight into the physical properties of inorganic materials and their reactivities in catalysis and electron transfer. The contribution of electronic structure to function has been developed in Ref. 61. 

Historically the first non-empirical calculation of entire multiplet structures of transition metal (TM) ions in crystals was performed by Watanabe and Kamimura based on the combination of a local density approximation (LDA) calculation and the ligand field theory (Watanabe and... 

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