The Electronic Structures of Transition Metal Complexes

The basic difficulty with the CFT treatment is that it takes no account of the partly covalent nature of the metal-ligand bonds, and therefore whatever effects and phenomena stem directly from covalence are entirely inexplicable in simple CFT. On the other hand, CFT provides a very simple and easy way of treating numerically many aspects of the electronic structures of complexes. MO theory, in contrast, does not provide numerical results in such an easy way. Therefore, a kind of modified CFT has been devised in which certain parameters are empirically adjusted to allow for the effects of covalence without explicitly introducing covalence into the CFT formalism. This modified CFT is often called ligand field theory, LFT. However, LFT is sometimes also used as a general name for the whole gradation of theories from the electrostatic CFT to the MO formulation. We shall use LFT in the latter sense in this Chapter, and we introduce the name adjusted crystal field theory, ACFT, to specify the form of CFT in which some parameters are empirically altered to allow for covalence without explicitly introducing it. 

We shall begin by outlining the CFT formalism. It is extremely important for the reader to bear in mind while reading Section 20-2, however, that this is a sheer formalism, devoid of physical meaning because ligand atoms are not points. On the contrary, they are bodies with about the same size and structure as the metal atom itself. However, the CFT formalism is actually the historical origin of ligand field theory, it does provide useful results and it is absolutely necessary to be conversant with it in order to read the literature. 

Let us consider a metal ion, Mm+, lying at the center of an octahedral set of point charges, as shown in Fig. 20-1. Let us suppose that this metal ion has a single d electron outside of closed shells such an ion might be Ti111, Vlv, etc. In the free ion, this d electron would have had equal probability of being in any one of the five d orbitals, since all are equivalent. Now, however, 

In Fig. 20-4a it will be seen that we have designated the energy difference between the eg and the t2g orbitals as A , where the subscript o stands for octahedral. The additional feature of Fig. 20-4a—the indication that the eg levels lie A, above and the t2g levels lie A below the energy of the unsplit d orbitals—will now be explained. Let us suppose that a cation containing ten d electrons, two in each of the d orbitals, is first placed at the center of a hollow sphere whose radius is equal to the M—X internuclear distance, and 

By an analogous line of reasoning it can be shown that the electrostatic field of four charges surrounding an ion at the vertices of a tetrahedron causes the d shell to split up as shown in Fig. 20-4b. In this case the dxy, dyz and dzx orbitals are less stable than the dz2 and dxz yz orbitals. This may be appreciated qualitatively if the spatial properties of the d orbitals are considered with regard to the tetrahedral array of four negative charges as depicted in Fig. 20-5. If the cation, the anions and the cation-anion distance are the same in both the octahedral and tetrahedral cases, it can be shown that 

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Magnetic resonance methods in the study of the electronic structure of transition metal complexes. 

As noted in Section 9.1, there are three closely related theories of the electronic structures of transition metal complexes, all making quite explicit use of the symmetry aspects of the problem but employing different physical models of the interaction of the ion with its surroundings as a basis for computations. These three theories, it will be recalled, are the crystal field, ligand field, and MO theories. There is also the valence bond theory, which makes less explicit use of symmetry but is nevertheless in accord with the essential symmetry requirements of the problem. We shall now briefly outline the crystal field and ligand field treatments and comment on their relationship to the MO theory. 

Even though both Hohenberg-Kohn and Kohn-Sham papers have been subsequently recognized as extremely important for Chemistry, that recognition came late in the community of theoretical chemists. Meanwhile, the MS-Xa method received much more attention. Por example, in 1970, Johnson and Smith addressed polyatomic molecules such as perchlorate and sulphate ions for the first time [13]. A landmark application of MS-Xa was the first investigation by Johnson and Smith of the electronic structure of a coordination compound, namely the permanganate ion [22]. The interest in the MS-Xa method for calculating the electronic structure of transition metal complexes increased rapidly and realistic results were soon obtained [23-25]. 

Molecular symmetry and ways of specifying it with mathematical precision are important for several reasons. The most basic reason is that all molecular wave functions—those governing electron distribution as well as those for vibrations, nmr spectra, etc.—must conform, rigorously, to certain requirements based on the symmetry of the equilibrium nuclear framework of the molecule. When the symmetry is high these restrictions can be very severe. Thus, from a knowledge of symmetry alone it is often possible to reach useful qualitative conclusions about molecular electronic structure and to draw inferences from spectra as to molecular structures. The qualitative application of symmetry restrictions is most impressively illustrated by the crystal-field and ligand-field theories of the electronic structures of transition-metal complexes, as described in Chapter 20, and by numerous examples of the use of infrared and Raman spectra to deduce molecular symmetry. Illustrations of the latter occur throughout the book, but particularly with respect to some metal carbonyl compounds in Chapter 22. 

Magnetic resonance methods in the study of the electronic structure of transition metal complexes. D. R. Eaton and K. Zaw, Coord. Chem. Rev., 1971,7,197-227 (189). 

The d orbitals of these species resemble the orbitals of certain organic molecules or fragments, both in their shape and their electronic occupation. It is therefore important to be familiar with them if one wishes to establish a link between the electronic structures of transition metal complexes and of organic molecules (the tsolobal analogy, see Chapter 5). 

Valence-bond theory has been used to describe the electronic structure of transition-metal complex ions, with such concepts as d sp hybridization of the metal orbitals. However, the simple VB treatment of complex ions is not fully satisfactory and has been replaced by ligand-field theory, which is MO theory applied to species whose atoms have d (or /) electrons (see Murrell, Kettle, and Tedder, Chapter 13 Offenhartz, Chapter 9). 

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