Ligand field model

M. Gerloch, The Cellular Ligand-Field Model , in Understanding Molecular Properties, (Eds. J.S. Avery, J.P. Dahl, A.E. Hansen), Reidel, 1987, p.lll. 

Despite the title in reference (6), both references (6) and (7) describe the cellular ligand-field model. 

Quadrupole splittings are often interpreted from ligand field models with simple rules for the contributions from each occupied f-orbital (see discussion above). However, these models fail even qualitatively in the case of more covalent metal-ligand bonds. An example concerns the quadrupole spUttings of Fe(IV)-oxo sites in their 5 = 1 or 5 = 2 spin states. Here, ligand field considerations do not even provide the correct sign of the quadrupole splitting [60]. 

The determination of the electronic structure of lanthanide-doped materials and the prediction of the optical properties are not trivial tasks. The standard ligand field models lack predictive power and undergoes parametric uncertainty at low symmetry, while customary computation methods, such as DFT, cannot be used in a routine manner for ligand field on lanthanide accounts. The ligand field density functional theory (LFDFT) algorithm23-30 consists of a customized conduct of nonempirical DFT calculations, extracting reliable parameters that can be used in further numeric experiments, relevant for the prediction in luminescent materials science.31 These series of parameters, which have to be determined in order to analyze the problem of two-open-shell 4f and 5d electrons in lanthanide materials, are as follows. 

The above results justify a simple ligand field model for the bis(ligand) metal species which is based on the assumption of pseudoaxial symmetry (40). This model allowed a consistent reinterpretation of an early ESR study of Co(C5H5BPh)2 (13) (42) the reinterpretation was later confirmed by additional and more sophisticated ESR work on 13 (43,44). 

Nevertheless, despite the discouraging predictions of the early calculations, some attempts were made to apply the ligand field model to sandwich complexes. The first approach on these lines, due to Matsen (28), assumed a strong ligand field of D h symmetry, which was shown to split the d-orbital manifold into three levels characterised by the value of m. Unfortunately, the calculated energetic order for the metallocenes was found to be... 

In conclusion though, it may reasonably be maintained that the ligand field model has contributed significantly to the advances in knowledge concerning transition metal sandwich complexes over the last ten years, and that it offers a valid and convenient framework for further experimental and theoretical progress. 

As indicated in Section 1. (i) our approach to the interpretation of the electronic spectra of the hexafluorometallates of the Ad and 5d series closely follows that employed previously (7), and need not be recapitulated in detail. The ligand field model is adopted for the interpretation of the d—d transitions, and the qualitative molecular orbital approach for the treatment of both these and, more particularly, the charge-... 

Fig. 1. Ligand-field model for the electronic structure of substitutional hydrogen in silicon in terms of the interactions between the vacancy orbitals and the atomic-hydrogen orbitals [Although the a state is shown as being not entirely passivated (still below the bottom of the conduction-band edge), it could in fact be in the conduction band, but with a host-like state pushed down slightly into the band gap.] (Reprinted with permission from the American Physical Society, DeLeo, G.G., Fowler, W.B., Watkins, G.D. (1984). Phys. Rev. B 29, 1819.)...

K Schubert The Two-Correlations Model, a Valence Model for Metallic Phases CLimres, A.Louat, Mfl/anc/iard Rare-Earth Oxygen Bonding in the LnMQj Xenotime Stracture Spectroscopic Investigation and Comparative Study of Ligand Field Models... 

Jj,j-orbitals having the highest energy. In the ligand field model, the metal d-orbitals do not mix with the chalcogenide s- and p-orbitals and the metal d-... 

Van Vleck also pointed out that even in the case of very highly covalent bonding [as in, e.g., Ni(CO)4 or Fe(CN)J ], which is best treated by using MO theory, the symmetry properties and requirements remain exactly the same as for the crystal field model and the ligand field model. 

Turning from the more practical side of recent advances, let us consider the routine aspect of the calculation of molecular susceptibilities from the eigenvalues and eigenvectors produced by some ligand field model. The usual procedure, using Van Vleck s equation... 

A ligand field model has been used for the interpretation of the magnetic behavior of the Mo(R2Dtc)4 complexes (485). Extended Hiickel calculations compare the electron-donating characteristics of the dithiocarbamate ligand to other 1,1-dithio chelates. This calculation concluded that (1) there is more metal character in the lowest unoccupied MO in the dithiocarbamate complexes, and (2) there is more ligand character in the lowest unoccupied MO in the dithioacid complexes (485). This seems to be in agreement with the electronic spectra. 

Here, the factor A has been introduced to accommodate the fact that L is an effective operator in the ligand field model, and in the same sense A for use in these equations may not have a direct relationship to its use in the interpretation of spectra, say A is generally expected to be somewhat less than unity. There is no similar TIP contribution for AUg) ground terms as there is no higher-lying term of the same multiplicity. 

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