Core electrons Crystal field theory

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

A common assumption is that C = 4B. In crystal field theory, the d orbital energies are effectively core energies the electron repulsions within the d-shell are not included. They thus differ significantly from S.C.F. orbital energies, which take into account all electron-electron repulsions. 

In the theory of electronic structure of crystals, we also use the molecrdar-cluster model being based on physical reasons we choose a molecular fragment of a crystal and somehow try to model the influence of the rest of a crystal on the cluster chosen (for example, by means of the potential of point charges or a field of atomic cores). Prom the point of view of symmetry such a model possesses only the symmetry of point group due to which it becomes impossible to estabhsh a connection of molecular-cluster electronic states with those of a boundless crystal. At the same time, with a reasonable molecular-cluster choice it is possible to describe well enough the local properties of a crystal (for example, the electronic structure of impurity or crystal imperfections). As an advantage of this model it may also be mentioned an opportunity of application to crystals of those methods of the account of electronic correlation that are developed for molecules (see Chap. 5). 

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