Ligand field theory procedures

Our discussion here of computational procedures will be very superficial and aimed at bringing out the physical features of the models. For a full treatment of this subject with references to the original literature, and for further discussion of the interpretation of the chemical behavior of transition metal compounds in terms of ligand field theory, the reader is referred to the publications cited in Appendix IX. 

Although essentially within the spirit of ligand field theory as enunciated in introductory remarks, there is an approach to dealing with the metal-ligand bonding which has developed into a field of its own, and deserves separate treatment. It is the so-called Angular Overlap Model (AOM). The choice of name arose from the early ways iif which its procedures were applied, and is no longer particularly apt. Nevertheless the name persists and is likely to do so, and will be employed here. Some of the reasons for the initial choice of the name will become obvious as the subject is outlined. 

Principles of symmetry and group theory find applications in several areas of quantum chemistry like chemical bonding, molecular spectroscopy, ligand field theory, crystal field theory etc. The procedure in all these cases involves—... 

The main features of the optical absorption and emission spectra of transition metal complexes can be interpreted on the basis of crystal-field or ligand-field theory. Generally, the energies of the absorption and the emission bands correspond to energetic differences between electronic states. Therefore, an interpretation of the optical spectra will start with a comparison between the experimental spectra and the term diagram of the complex ion, according to the crystal-field theory. This procedure will be demonstrated by two informative examples. 

The (n—l)d and (n—2)f orbitals occupy a small volume, as discussed before, and thus especially the overlap of the (n—2)f orbital with ligand orbitals would be rather small. Consequently, the potential energy curves of states belonging to a specific electronic configuration with metal df orbitals and a and it MOs derived from and p with ligand orbitals are similar. This is the underlying philosophy of the implementation of ligand-field theory to interpret complex spectra of lanthanide oxides. We will illustrate this procedure further in section 6. 

Why then bother about much more expensive QM-based models One reason is that MM may only lead to accurate results for molecules of the same type used for the optimization and validation of the force field, i.e. extrapolation is seen to be dangerous if not impossible [9], This also extends to transition states and shortlived, unstable intermediates and therefore to chemical reactivity. Since electrons are not considered explicitly in MM, electronic effects related to structural distortions, specific stabilities and spectroscopy cannot be modeled by MM. However, in all other areas, there is no good reason for not using a well-optimized and validated MM model. Also, there are MM-based approaches to deal with most of the deficiencies listed above [9,20-28]. In the last decade, there have been a number of approaches, which have, based on simple rules [29], valence bond theory [30-33] and ligand-field theory [20-23], allowed the simplification of the force-field optimization and validation procedures and/or inclusion of electronic effects in MM models. 

The zero-order product functions, IMq Lq) for the ground state and IM, Lq) for the excited d-d or f—f electronic state of the metal ion in the complex, require an augmentation with additional functions of the set for correction to first-order. The latter are either other metal ion functions, e.g. IM Lq), which is the course adopted in crystal field theory, or other ligand functions, e.g. Mq Lj) and IMg L ), as is assumed in the ligand polarization treatment. The two procedures are mutually exclusive to first-order, on account of the one-electron character of the transition moment operators, although the results of the two treatments are additive in a general independent-systems representation. 

An outline of the calculational procedures related to the application of Eq. (1) may be found in the books by Griffith [67] and Low [14]. Concerning the theory of the free ion, the text by Condon and Shortley [63] should be consulted. A basic introduction into the theory of the ligand field and spin-orbit coupling is contained in the treatment by Ballhausen [57]. 

There are two connected approaches to the cfp the ab initio and the parametric approach. We shall examine in sect. 4 the theories which have been worked out to evaluate the contributions to the ligand field ex nihilo. None of these can be considered faultless. What they can do at most is to give starting values for a fitting procedure the second (parametric) approach with which we are going to deal now. 

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