Crystal field theory scope

The spectrochemical series was established from experimental measurements. The ranking of ligands cannot be fully rationalized using crystal field theory, and more advanced bonding theories are beyond the scope of general chemistry. 

The above discussion has considered the stabilization of complexes in terms of the crystal field theory. It is desirable to consider the same topic in terms of modern molecular orbital theory. Although the development and sophisticated consideration of the MO treatment is far beyond the scope of this chapter, an abbreviated, qualitative picture will be presented, focusing again on the energy levels of the highest occupied and lowest empty orbitals and again using the square planar d case. 

The foregoing discussion of valence is. of course, a simplified one. From ihe development of the quantum theory and its application to the structure of the atom, there has ensued a quantum theory of valence and of the structure of the molecule, discussed in this hook under Molecule. Topics thal are basically important to modem views of molecular structure include, in addition to those already indicated the Schroedinger wave equation the molecular orbital method (introduced in the article on Molecule) as well as directed valence bonds bond energies, hybrid orbitals, the effect of Van der Waals forces and electron-dcticiem molecules. Some of these subjects are clearly beyond the space available in this book and its scope of treatment. Even more so is their use in interpretation of molecular structure. [However, sec Crystal Field Theory and Ligand.)... 

The simplest description of transition metal ions is given by crystal field theory [3], but any mathematical discussion is beyond the scope of this chapter. Consequently, only some qualitative results are given here. For more detail the reader is directed to any of the references in the bibliography listed under Inorganic Ions. 

Crystal-field theory will be briefly described here using a weak-field approach. Those interested in complete treatments beyond the scope of this article are referred to discussions in appropriate monographs. " Perturbation theory is used assuming free ion eigenfimctions and eigenvalues, and the Hamiltonian is... 

Modern ligand field theory is based on crystal field theory. It attributes partial covalent character and partial ionic character to bonds. It is a more sophisticated theory, beyond the scope of this text. 

Crystal-field theory can be used to explain many observations in addition to those we have discussed. The theory is based on electrostatic interactions between ions and atoms, which essentially means ionic bonds. Many hnes of evidence show, however, that the bonding in complexes must have some covalent character. Therefore, molecular-orbital theory c s > (Sections 9.7 and 9.8) can also be used to describe the bonding in complexes, although the application of molecular-orbital theory to coordination compounds is beyond the scope of our discussion. Crystal-field theory, although not entirely accurate in all details, provides an adequate and useful first description of the electronic structure of complexes. 

In the scope of the Judd-Ofelt theory three parameters .22, 24, and 2 are commonly used to describe the transitions between J multiplets. For this case, the contributions from individual crystal field split levels of a given multiplet are simply summed up. To account for individual transitions, effective transition operators can be used to derive a parametrization... 

A quantitative treatment of these effects on NQR is outside the scope of today s solid state theory. Therefore a qualitative estimation of the crystal field effect seems to be necessary. This justifies classifying the crystal field... 

These two approximations are what characterizes the kinematic approach to diffraction and make it possible to describe the effect in a relatively simple way. The dynamic theory [AUT 05] takes both of these effects into account. The implementation of this dynamic theory is necessary when studying diffraction by very high qtrality single crystals, or also in the field of homoepitxial thin film characterization. These two subjects are beyond the scope of this book and therefore from here on, we will apply the kinematic theory of X-ray diffraction. 

Clearly, the issues of first principles and transferability are more pertinent to an essentially academic book such as the present one, while production details are more aptly included in internal technical manuals (heaven knows how much vital information is secreted in confidential company reports and thus hidden from the scientific community). The matter can be reformulated as follows the value of a parametric theory is directly proportional to the extension of the factual landscape to which it applies, and inversely proportional to the effort made in its development. Atom-atom formulations cannot yet be beaten in this respect. They apply with success to a wide scope of different problems and can give reliable theoretical estimates of crystal sublimation enthalpies and liquid evaporation enthalpies. And yet they are limited by their intrinsically scarce adherence to first principles, with a lack of contact between parameters and the implied physics. For these reasons, the future is not in their direction, and different paths must be sought, presumably in the direction of closer relationships between empirical force field parameters and quantum chemical data, considering that many molecular properties are nowadays more cheaply... 

The above comments represent only some particularly chosen topics and events in the mathematical development of the continuum theory for liquid crystals, focusing especially on nematic and smectic C materials. In a book of this scope it is inevitable that some major topics have not been included, such as soliton-like behaviour in nematics or the flexoelectric effect, and many important contributions to the field have been omitted for the sake of brevity. Nevertheless, readers should have no difficulty in accessing these topics in the current literature if they have been armed with the material presented in subsequent Chapters. Interested readers can find more extensive details on the development of liquid crystals in the historical review by Kelker [143] or the forthcoming volume in this book series by Sluckin. Dunmur and Stegemeyer [253]. 

To describe interfacial forces caused by orientation correlations, Landau theory in combination with a mean field approach has been applied. In Landau theory, the free energy density of a system is expanded in a power series of the order parameters and their derivatives. A description of the theory is beyond the scope of this book and the reader is referred to textbooks on the statistical physics of liquids. It was first applied to describe hydration forces (see below) [1135,1136]. De Gennes applied it to liquid crystals [1137], and sometimes the theory is referred to as Landau-de Gennes theory. 

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