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The Jahn—Teller Effect

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Cooperative Phenomena in Jahn—Teller Crystals

Part of the book series: Modern Inorganic Chemistry ((MICE))

Abstract

In solving the Schrödinger equation, when several wave functions ϕ i correspond to the same energy E, such a state is called degenerate. Degeneracy is always associated with the existence of some symmetry element. The three p functions of the hydrogen atom serve as an example. Their degeneracy is due to the fact that such a system has spherical symmetry: Rotation about any axis through the nucleus leaves the Hamiltonian invariant, while transforming the p functions into each other. Such threefold degeneracy persists even if the free atom is in an external field of cubic symmetry created, for example, by six point charges forming an octahedral pattern around the nucleus. In fact, it is readily verified that cubic group operations transform the surrounding charges into each other, i.e., they leave the Hamiltonian invariant while once again transforming the three p functions into each other. At the same time, the distortion of the octahedron along the z axis (extension or compression) decreases the symmetry from cubic to tetragonal, partially lifting the degeneracy: E(p z ) ≠ E(p x ) = E(p y ). In turn, the twofold degeneracy remaining in the tetragonal group can be lifted by orthorhombic perturbations.

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Authors and Affiliations

  1. Boston University, Boston, Massachusetts, USA

    Michael D. Kaplan

  2. Northwestern University, Evanston, Illinois, USA

    Benjamin G. Vekhter

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  1. Michael D. Kaplan
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  2. Benjamin G. Vekhter
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Kaplan, M.D., Vekhter, B.G. (1995). The Jahn—Teller Effect. In: Cooperative Phenomena in Jahn—Teller Crystals. Modern Inorganic Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1859-4_1

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  • DOI: https://doi.org/10.1007/978-1-4615-1859-4_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5755-1

  • Online ISBN: 978-1-4615-1859-4

  • eBook Packages: Springer Book Archive

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