Problems with Crystal Field Theory

The main problem with CFT is that the 3d electrons are Uving their own life independent of the electrons of the ligands. More correctly, they are allowed to feel the fixed field of electrons and nuclei, but they are not allowed to mix with the ligand electrons and form molecular orbitals (MOs) and bonds. 

This is, in fact, the case. If the spatial distribution of the ligand electrons is taken into account, the nuclei become the main contributor to the field, and the ordering of the metal electrons should be opposite to what we know is correct from the experiments. CFT survives just because the A = lODq parameter can be assigned any value that fits the experimental results. In other words, it is not the electrostatic field that causes the crystal field splitting, but something else. 

CFT does not agree with the physics of the system. The conclusion is that 3d orbitals cannot be singled out. They take part in the ordinary formation of MOs. The crystal field splitting is due to the fact that the MOs becoming occupied in a metal complex are antibonding MOs. CFT has to be replaced by ligand field theory (LFT). 

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The obvious deficiency of crystal-field theory is that it does not properly take into account the effect of the ligand electrons. To do this a molecular-orbital (MO) model is used in which the individual electron orbitals become a linear combination of the atomic orbitals (LCAO) belonging to the various atoms. Before going into the general problem, it is instructive to consider the simple three-electron example in which a metal atom with one ligand atom whose orbital contains two electrons. Two MO s are formed from the two atomic orbitals... 

We may anticipate an eventual consensus on the amount and place of symmetry in the chemistry curriculum, but for now we have assumed no prior background in the subject- We have thus tried to illustrate a wide variety of uses of symmetry without delving deeply into the background theory. We hope that those new to the topic can find a useful introduction to the application of symmetry to problems in inorganic chemistry. On the other hand, those having previous experience with the subject may wish to use this chapter as a brief review. And, recognizing that things are in a state of flux, we have attempted to make it possible to study various topics such as orbital overlap, crystal field theory, and related material, as in the past, with minimal reference to symmetry if desired... 

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. 

The technical problem is of course to develop an adequate form of the intersubsystem junction for the case when the quantum system is represented by the d-shell. This is done using the EHCF(L) technique described above. In the EHCF(L), the effective crystal field in agreement with the general theory of Section 1.7.2 is given in terms of the /-system Green s function. The natural way to go further with this technique is to apply the perturbation theory to obtain estimates of the /-system Green s function entering eqs. (4.83) and/or (4.92). That is what we shall do now. 

The response of covalent crystals to magnetic fields is very weak and of less interest than the dielectric response. It may nevertheless prove useful as a probe of the electronic structure. An early discussion of the problem, with references to still earlier work, was given by KrumhansI (1959). Two recent treatments in terms of LCAO theory have been given by Sukhatmc and Wolff (1975) and by Chadi, White, and Harrison (1975). We shall follow the latter treatment but give a more complete formulation than given there. 

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