Ligand field theory development

Whereas IR spectroscopy is often employed in coordination chemistry to identify functional groups or ligand types, and thus differs little from its application in organic chemistry, UV-Vis spectroscopy for coordination complexes relies heavily on the special theories (crystal and ligand field theory) developed for these complexes. Thus, it will be a target for particular attention here. Another physical method closely tied up with these theories is... 

The optical properties of transition-metal (TM) ions in crystals have generally analyzed by the ligand-field theory developed by Sugano et al. In the ligand-field theory, the multiplet energies of the TM ions in the octahedral (or tetrahedral) symmetry are expressed in terms of the Racah parameters B and C) and the crystal-field parameter (A). However, in the analysis based on this theory, the parameters axe determined from the experimental optical spectra under a certain trial assignment of the observed peaks. Therefore, correct parameters cannot be obtained unless the optical spectrum of the material is available and well understood. Even if the correct parameters are... 

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. 

Development of Coordination Chemistry Since 1930 Coordination Numbers and Geometries Nomenclature of Coordination Compounds Cages and Clusters Isomerism in Coordination Chemistry Ligand Field Theory Reaction Mechanisms... 

Although the ligand field theory can be used to rationalize the geometry of some transition metal molecules and complex ions, the study of the shapes of transition metal molecules in terms of the electron density distribution is still the subject of research and it has not reached a sufficient stage of development to enable us to discuss it in this book. 

At an early stage in the development of ligand field theory, it was found that A the splitting parameter for tetrahedral MX4, should be equal to (4/9) of A0, the splitting parameter for octahedral MX6, and experimental data are in good agreement with this prediction. However, this takes no account of the fact that the M—X distance in tetrahedral MX4 is usually some 8—10% shorter than in octahedral MX6. In the pointcharge crystal field model, A is proportional to R-5, so that if the difference in R between MX4 and MX6 is taken into account, we predict (At/A0) to be 0.6—0.7, compared with the experimental value of about 0.5. An AOM treatment (131) leads to better results, since here we find ... 

In the last decade, the advent of ligand-field theory has given a tremendous impetus to the study of transition metals, and of these, nickel has been among the most studied. This element can have a variety of stereochemical configurations under various conditions, and the aim of this chapter is to summarize the position of our knowledge up to the early part of 1961. It is necessary to give such a date because the field is very active at the time of writing, and new developments are to be anticipated. Palladium and platinum have not received quite so much attention as nickel from the structural point of view the trans-effect should be mentioned, however, and has been reviewed by Basolo in Volume 3 of this series. 

With the exception of these changes, the practical development of ligand field theory and crystal field theory are the same. 

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. 

The crystal and ligand field theories were developed to deal with only those properties of the complexes that are derived directly from the set of electrons originally occupying the d orbitals of the metal ion. Since these orbitals are the principal parents of the e and t2 MOs of the complex it is not unreasonable to treat the latter as though they were nothing more than split (crystal field theory) or split and somewhat diluted (ligand field theory) metal d orbitals. It is clear, however, that such a view can be only an approximation—indeed, a fairly ruthless one. Yet, with judicious empirical choice of one or more... 

Obviously, in a presentation such as this, there is not room to develop the basics of the various forms of ligand field theory in detail nor to describe applications to all the relevant physical properties. This chapter will set out to compare the major aspects of the different forms, will give an account of their use in the interpretation of spectra and magnetism of transition metal complexes, and will make some mention of other areas. 

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. 

In this chapter, we have developed the information content of different excited state spectroscopic methods in terms of ligand field theory and the covalency of L—M bonds. Combined with the ground-state methods presented in the following chapters, spectroscopy and magnetism experimentally define the electronic structure of transition metal sites. Calculations supported by these data can provide fundamental insight into the physical properties of inorganic materials and their reactivities in catalysis and electron transfer. The contribution of electronic structure to function has been developed in Ref. 61. 

It may hence be pertinent to draw the attention to two kinds of development of ligand field theory which have taken place since 1962. They are both related to the Wolfsberg-Helmholz model (27) where it is assumed that the non-diagonal elements between orbitals centered on afferent atoms are proportional to the product of their overlap integral and their average energy with a proportionality constant k usually assumed to have values between 1.6 and 2. Thus, the secular determinant for two interacting orbitals is ... 

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