Vibronic Interactions and the Jahn-Teller Theorem
In this chapter the first principles which form the basis of the concept of vibronic interactions, the concept of mixing electronic states by nuclear displacements, are discussed. After analysis of the traditional adiabatic approximation and its limitations (Sec. 2.1), the so-called vibronic Hamiltonian which takes into account the nonadiabatic interaction of electrons and nuclei is deduced (Sect. 2.2). The proof and discussion of the Jahn-Teller theorem are presented in Sect. 2.3 by considering the shape of the adiabatic potential surface in the neighborhood of the point of electronic degeneracy where the deviations from the adiabatic approximation are most marked. This theorem served as a starting point for the development of the field as a whole, and therefore the physical consequences of the nonadiabatic vibronic mixing of electronic states are often called the Jahn-Teller effects.
KeywordsIrreducible Representation Adiabatic Approximation Schrodinger Equation Adiabatic Potential Vibronic Interaction
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- 2.7J. von Neumann, E. Wigner: Phys. Z. 30, 467–470 (1929)Google Scholar
- 2.8L.D. Landau, E.M. Lifshitz: Quantum Mechanics: Non-Relativistic Theory, 3rd ed. (Pergamon, Oxford 1977)Google Scholar
- 2.11E.B. Wilson, Jr., J.C. Decius, P.C. Cross: Molecular Vibrations (McGraw-Hill, New York 1955)Google Scholar
- 2.12C.J. Bradley, A.P. Cracknell: The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups (Clarendon, Oxford 1972)Google Scholar
- 2.13J.S. Griffith: The Irreducible Tensor Method for Molecular Symmetry Groups (Prentice-Hall, Englewood Cliffs, NJ 1962)Google Scholar
- 2.17I.V.V. Raghavacharyulu: “Simple Proof of the Jahn-Teller Theorem”, in Proc. Nucl. Phys. and Solid State Phys. Symp., Bangelore 1973 (Dept. of Atomic Energy, New Delhi 1973) pp. 296–298Google Scholar
- 2.18I.V.V. Raghavacharyulu: “The Jahn-Teller Theorem for Space Groups”, in Proc. Nucl. Phys. and Solid State Phys. Symp., Bangelore 1973 (Dept. of Atomic Energy, New Delhi 1973) p. 299Google Scholar