Octahedral complexes molecular orbital model

The molecular orbital model can also be applied to complexes of the d-block elements. In octahedral complexes the d-orbitals of the metal are not degenerate, as they are in the free metal, because of the interaction between the ligand and metal orbitals. The five d-orbitals are split into three t2g (nonbonding) and two e (antibonding) MOs that is ... 

The molecular orbital model as a linear combination of atomic orbitals introduced in Chapter 4 was extended in Chapter 6 to diatomic molecules and in Chapter 7 to small polyatomic molecules where advantage was taken of symmetry considerations. At the end of Chapter 7, a brief outline was presented of how to proceed quantitatively to apply the theory to any molecule, based on the variational principle and the solution of a secular determinant. In Chapter 9, this basic procedure was applied to molecules whose geometries allow their classification as conjugated tt systems. We now proceed to three additional types of systems, briefly developing firm qualitative or semiquantitative conclusions, once more strongly related to geometric considerations. They are the recently discovered spheroidal carbon cluster molecule, Cgo (ref. 137), the octahedral complexes of transition metals, and the broad class of metals and semi-metals. 

Whether a complex is high- or low-spin depends upon the energy separation of the t2g and eg levels. Nationally, in a fj-bonded octahedral complex, the 12 electrons supplied by the ligands are considered to occupy the aig, and eg orbitals. Occupancy of the and eg levels corresponds to the number of valence electrons of the metal ion, just as in crystal field theory. The molecular orbital model of bonding in octahedral complexes gives much the same results as crystal field theory. It is when we move to complexes with M—L TT-bonding that distinctions between the models emerge. 

We outline the application to an octahedral id transition metal complex, as the relations derived in this case are used to interpret the results of spin density measurements (see Sections VI. A and VI. B). A similar approach may be used for other coordinations and for other metals. Some general consequences relating the symmetry properties of complexes and a molecular orbital model of bonding have been combined in the angular overlap 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-... 

When describing a complex in terms of molecular orbitals, we need to establish a model by which we can identify the orbitals utilized by both the metal and the ligands. We will first consider an octahedral complex with the positions of the ligands identified on the coordinate system shown in Figure 17.14, and the orbitals will be designated by the numbers assigned to the ligands in the positions indicated. 

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. 

Figure 5 The molecular orbital or ligand field picture of metal-ligand bonding in an MLe complex. Compare this picture with Figure 1 to see how the octahedral crystal field splitting pattern (in the box) is still present in the MO model...

Table 10.12 provides values of A for eight octahedral complexes of chromium(III). Select three of the hgands listed, draw the structures of their octahedral complexes of Cr(III), and calculate and view the molecular orbitals. Identify the t2g and eg orbitals, record the energy of each, and determine the A values. Is your trend consistent with the values in the table (Note The results are likely to vary significantly with the level of sophistication of the software used. If you have several molecular modeling programs available, you may want to try different ones to compare their results.)... 

Of the various models in their simplest forms, the molecular orbital (MO) model gives the most realistic view of the bonding in complex ions. Recall from our discussions in Chapter 14 that the MO model postulates that a new set of orbitals characteristic of the molecule is formed from the atomic orbitals of the component atoms. To illustrate how this model can be applied to complex ions, we will describe the MOs in an octahedral complex of general formula MLg ". To keep things as simple as possible, we will focus only on those ligand orbitals having lone pairs that interact with the metal ion valence orbitals (3d, 4s, and 4p). There are two important considerations in predicting how atomic orbitals will interact to form MOs ... 

As mentioned in the Introduction (Sect. 1), an approach commonly used in recent years to handle transition metal complexes is the molecular orbital approach. To set the scene for development of a localized model, we will begin our discussion by first giving a general account of this molecular orbital approach (which represents the delocalized model ) based on the octahedral complexes. 

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