The Crystal-Field Premise

During the first twenty years or so of this century, an incredibly detailed understanding of atomic line spectra was built up with the application of the, then new, quantum theory. Indeed, the development of quantum theory came about in part by the need to understand these spectral properties. We shall have to review some basic features of the theory of atomic spectra for our present purposes, but we shall leave it for the moment. 

In the later 1920 s, physicists, rightly flushed with their successes with interpreting the rich, sharp spectra of atoms and gas phase ions, sought to extend their reach to the broader (and fewer) absorption bands that eharacterize the spectra of ions in crystalline matrices. These bands occur at utterly different frequencies to those of the corresponding free ions so that there is no similarity at all between the spectra of free ions and of those in ionic or covalent lattices. 

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. 

Those electrons must not only avoid each other but also the negatively charged anionic environment. In its simplest form, the crystal field is viewed as composed of an array of negative point charges. This simplification is not essential but perfectly adequate for our introduction. We comment upon it later. 

Transition MetalChemistry.M. Gerloch, E. C. Constable Copyright 1994 VCH Verlagsgesellschaft mbH, Weinheim ISBN 3-527-29218-7 

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