Transition metal complexes crystal field theory

Scientists have long recognized that many of the magnetic properties and colors of transition-metal complexes are related to the presence of d electrons in the metal cation. In this section we consider a model for bonding in transition-metal complexes, crystal-field theory, that accounts for many of the observed properties of these substances. Because the predictions of crystal-field theory are essentially the same as those obtained with more advanced molecular-orbital theories, crystal-field theory is an excellent place to start in considering the electronic structure of coordination compounds. 

For transition metal complexes, techniques derived from a crystal-field theory or ligand-field theory description of the molecules have been created. These tend to be more often qualitative than quantitative. 

Transition metals readily form complexes, such as [Fe(CN)6], the ferrocyanide ion, Ni(CO)4, nickel tetracarbonyl, and [CuC ], the copper tetrachloride ion. MO theory applied to such species has tended to be developed independently. It is for this reason that the terms crystal field theory and ligand field theory have arisen which tend to disguise the fact that they are both aspects of MO theory. 

In all these discussions, we separate, as best we might, the effects of the d electrons upon the bonding electrons from the effects of the bonding electrons upon the d electrons. The latter takes us into crystal- and ligand-field theories, the former into the steric roles of d electrons and the geometries of transition-metal complexes. Both sides of the coin are relevant in the energetics of transition-metal chemistry, as is described in later chapters. 

Color is a spectacular property of coordination complexes. For example, the hexaaqua cations of 3 transition metals display colors ranging from orange through violet (see photo at right). The origin of these colors lies in the d orbital energy differences and can be understood using crystal field theory. 

Historically, crystal field theory was the first theoretical model (11, 86, 101, 123) used to explain d-d transition energies in metal complexes. Its usefulness is restricted to those complexes whose bonding is largely ionic, and its mqjor deficiency arises from its inability to account for charge transfer transitions. The iterative extended Hiickel and the ab initio, limited basis set, Hartree-Fock calculations are capable of de-... 

For conciseness, the title of this chapter is simply Ligand Field Theory. However, many of the principles which will be developed are as much a part of crystal field theory and the molecular orbital theory of transition metal complexes as they are of ligand field theory. Indeed the three theories are very closely related, and hence it seems advisable to begin this chapter with a brief, historically oriented discussion of the nature of these theories. 

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. 

Ligand field theory may be taken to be the subject which attempts to rationalize and account for the physical properties of transition metal complexes in fairly simple-minded ways. It ranges from the simplest approach, crystal field theory, where ligands are represented by point charges, through to elementary forms of molecular orbital theory, where at least some attempt at a quantum mechanical treatment is involved. The aims of ligand field theory can be treated as essentially empirical in nature ab initio and even approximate proper quantum mechanical treatments are not considered to be part of the subject, although the simpler empirical methods may be. 

Although the physical basis of the crystal field model is seen to be unsound, the fact remains that, in summarizing the importance of the symmetry of the ligand environment, it qualitatively reproduces many of the features of the magnetic and spectral properties of transition metal complexes. This early qualitative success established its nomenclature in the fields of these properties. While we shall have little more to say about crystal field theory as such, much of the rest of this article will be couched in the language of the crystal field model, and for that reason some little trouble has been taken to outline its development. 

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