Crystal-field theory

Thomas Wolfram; Şinasi Ellialtıoğlu

doi:10.1017/CBO9781139236294.005

4 - Crystal-field theory

Published online by Cambridge University Press: 18 December 2013

Thomas Wolfram and

Şinasi Ellialtıoğlu

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Thomas Wolfram: Affiliation:
University of Missouri, Columbia
Şinasi Ellialtıoğlu: Affiliation:
TED University, Ankara

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Summary

Splitting of d-orbital degeneracy by a crystal field

As we saw in the previous chapter the s- and p-orbital degeneracies are unaffected when an atom or ion is placed in a site of octahedral symmetry. On the other hand, the d-and f-orbital degeneracies are changed. Transition metal ions of Ti, Fe, Ni, and Co, for example, have 3d electrons in their outer unfilled shells and exist as positively charged ions in solids and molecular complexes. Most frequently, the transition metal ion is coordinated with six neighboring ligands at a site of octahedral symmetry. The second most common situation is tetrahedral coordination with four neighboring ligands. Many of these transition metal solids and molecular complexes are colored and many are magnetic. The colors are attributed to vibronic (electronic plus vibration) transitions between the d-orbital groups that are split in energy by the non-spherical potential of the ligands. When the ligand orbitals are included in determining the splitting, the procedure is called ligand-field theory. Splitting due to adjacent ligands is discussed in Chapter 6.

Crystal-field theory was developed by Bethe [4.1] and Van Vleck [4.2] to explain the optical spectra of transition metal complexes and to understand their magnetic properties. In its simplest form the crystal-field model represents the ligands surrounding a metal ion as point charges that interact with the transition metal ion only through an electrostatic potential.

Type: Chapter
Information: Applications of Group Theory to Atoms, Molecules, and Solids , pp. 90 - 122

DOI: https://doi.org/10.1017/CBO9781139236294.005 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2014

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References

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[4.5] T. M., Dunn, D. S., McClure, and R. G., Pearson, Some Aspects of Crystal Field Theory (New York: Harper & Row, 1965). (Note that there are errors in some of the formulas on pages 18 and 20. These have been corrected in our discussion.)

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