The Effective Crystal Field Potential

1st Edition

Editors: J. Mulak Z. Gajek
Hardcover ISBN: 9780080436081
eBook ISBN: 9780080530710
Imprint: Elsevier Science
Published Date: 22nd June 2000
Page Count: 316
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As it results from the very nature of things, the spherical symmetry of the surrounding of a site in a crystal lattice or an atom in a molecule can never occur. Therefore, the eigenfunctions and eigenvalues of any bound ion or atom have to differ from those of spherically symmetric respective free ions. In this way, the most simplified concept of the crystal field effect or ligand field effect in the case of individual molecules can be introduced.

The conventional notion of the crystal field potential is narrowed to its non-spherical part only through ignoring the dominating spherical part which produces only a uniform energy shift of gravity centres of the free ion terms. It is well understood that the non-spherical part of the effective potential "seen" by open-shell electrons localized on a metal ion plays an essential role in most observed properties. Light adsorption, electron paramagnetic resonance, inelastic neutron scattering and basic characteristics derived from magnetic and thermal measurements, are only examples of a much wider class of experimental results dependent on it. The influence is discerned in all kinds of materials containing unpaired localized electrons: ionic crystals, semiconductors and metallic compounds including materials as intriguing as high-Tc superconductors, or heavy fermion systems. It is evident from the above that we deal with a widespread effect relative to all free ion terms except those which can stand the lowered symmetry, e.g. S-terms.

Despite the universality of the phenomenon, the available handbooks on solid state physics pay only marginal attention to it, merely making mention of its occurrence. Present understanding of the origins of the crystal field potential differs essentially from the pioneering electrostatic picture postulated in the twenties. The considerable development of the theory that has been put forward since then can be traced in many regular arti


For experimentalists, particularly spectroscopists, and researchers involved in inelastic neutron scattering, magnetic measurements and the thermodynamics of solids. Also of interest to researchers in the areas of solid state physics and quantum chemistry.

Table of Contents

Chapter headings and selected sub-headings: Introduction. Parameterization of Crystal Field Hamiltonian. Operators and parameters of the crystal field Hamiltonian. Basic parameterizations. Symmetry transformations of the operators. The number of independent crystal field parameters. Standardization of the crystal field Hamiltonian. The Effective Crystal Field Potential. Chronological Development of Crystal Field Models. Ionic Complex or Quasi-Molecular Cluster. Generalized Product Function. Concept of the generalized product function. The density functions and the transition density functions. Model of the generalized product functions. Crystal field effect in the product function model. Point Charge Model (PCM). PCM potential and its parameters. Simple partial PCM potentials. Extension of PCM - higher point multipole contribution. One-Configurational Model with Neglecting the Non-Orthogonality. The Charge Penetration and Exchange Effects. Classical electrostatic potential produced by the ligand charge distribution. The charge penetration effect and the exchange interaction in the generalized product function model. The weight of the penetration and exchange effects in the crystal field potential. Calculation of the two-centre integrals. The Exclusion Model. One-Configurational Approach with Regard to Non-Orthogonality of the Wave Functions. Three types of the non-orthogonality. The contact-covalency - the main component of the crystal 84 field potential. The contact-shielding. The contact-polarization. Mechanisms of the contact-shielding and contact-polarization in terms of the exchange charge notion. Covalency Contribution, i.e. The Charge Transfer Effect. The one-electron excitations. Group product function for the excited state. The renormalization of the open-shell Hamiltonian due to the covalency effect. Basic approximations. Remarks on the covalency mechanism


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© Elsevier Science 2000
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About the Editor

J. Mulak

Z. Gajek

Affiliations and Expertise

Institute of Low Temperature and Structure Research, Polish Academy of Sciences, ul. Okolna 2, 50-422 Wroclaw, Poland.