Octahedral complex crystal field model

A quantitative consideration on the origin of the EFG should be based on reliable results from molecular orbital or DPT calculations, as pointed out in detail in Chap. 5. For a qualitative discussion, however, it will suffice to use the easy-to-handle one-electron approximation of the crystal field model. In this framework, it is easy to realize that in nickel(II) complexes of Oh and symmetry and in tetragonally distorted octahedral nickel(II) complexes, no valence electron contribution to the EFG should be expected (cf. Fig. 7.7 and Table 4.2). A temperature-dependent valence electron contribution is to be expected in distorted tetrahedral nickel(n) complexes for tetragonal distortion, e.g., Fzz = (4/7)e(r )3 for com-... 

Foyt et al. [137] interpreted the quadrupole-splitting parameters of low-spin ruthenium(II) complexes in terms of a crystal field model in the strong-field approximation with the configuration treated as an equivalent one-electron problem. They have shown that, starting from pure octahedral symmetry with zero quadrupole splitting, A q increases as the ratio of the axial distortion to the spin-orbit coupling increases. 

The sequence of energy levels obtained from a simple molecular orbital analysis of an octahedral complex is presented in Fig. 1-12. The central portion of this diagram, with the t2g and e levels, closely resembles that derived from the crystal field model, although some differences are now apparent. The t2g level is now seen to be non-bonding, whilst the antibonding nature of the e levels (with respect to the metal-ligand interaction) is stressed. If the calculations can be performed to a sufficiently high level that the numerical results can be believed, they provide a complete description of the molecule. Such a description does not possess the benefit of the simplicity of the valence bond model. 

The crystal field model also applies to square planar and linear complexes. The crystal field diagrams for these cases are shown in Fig. 20.29. The ranking of orbitals in these diagrams can be explained by considering the relative orientations of the point charges and the orbitals. The diagram in Fig. 20.28 for the octahedral arrangement can be used to obtain these orienta-... 

What is the major focus of the crystal field model Why are the d orbitals split into two sets for an octahedral complex What are the two sets of orbitals ... 

Thus far we have considered the crystal-field model only for complexes having an octahedral geometry. When fliere are only four ligands about the metal, the geometry is generally tetrahedral, except for the special case of metal ions with a d electron configuration, which we will discuss in a moment The crystal-field splitting of the metal d orbitals in tetrahedral complexes differs from that in octa-... 

The crystal-field model also applies to tetrahedral and square-planar complexes, which leads to different d-orbital splitting patterns. In a tetrahedral crystal field, the splitting of the d orbitals is exactly opposite that of the octahedral case. The splitting by a tetrahedral crystal field is much smaller tlaan that of an octahedral crystal field, so tetrahedral complexes are always high-spin complexes. 

We will discuss the crystal field model here. It assumes that the bonding between metal ions and ligands is essentially ionic. More specifically, it considers the effect of approaching Ugands upon the energies of electronic levels in transition metal cations. We will apply this model to octahedral complexes. Before doing so, it maybe helpful to review the electronic structure of uncomplexed trcuisition metal cations, originally covered in Chapter 6. 

Mallinson et al. (1988) have performed an analysis of a set of static theoretical structure factors based on a wave function of the octahedral, high-spin hexa-aquairon(II) ion by Newton and coworkers (Jafri et al. 1980, Logan et al. 1984). To simulate the crystal field, the occupancy of the orbitals was modified to represent a low-spin complex with preferential occupancy of the t2g orbitals, rather than the more even distribution found in the high-spin complex. The complex ion (Fig. 10.14) was centered at the corners of a cubic unit cell with a = 10.000 A and space group Pm3. Refinement of the 1375 static structure factors (sin 8/X < 1.2 A 1) gave an agreement factor of R = 4.35% for the spherical-atom model with variable positional parameters (Table 10.12). Addition of three anharmonic thermal... 

However, since CFT is a rather crude model, such an exact relationship is seldom of use. Instead, it is instructive and convenient to realize that, with all conditions being equal, the crystal field splitting for a tetrahedral complex is about half of that for an octahedral complex. 

The Angular Overlap Model is a ligand field model which uses parameters20 (A = a, n, 6...) for expressing the orbital energies. For d orbitals X can be only a, n and <5, but it is customary to use as parameters e = e a - ej and e = e - ej. In octahedral complexes a simple correlation exists between these parameters and the usual crystal field parameters21 ... 

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