Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy
H. A. Jahn,Edward Teller +1 more
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In this paper, it was shown that if the total electronic state of orbital and spin motion is degenerate, then a non-linear configuration of the molecule will be unstable unless the degeneracy is the special twofold one (discussed by Kramers 1930) which can occur only when the molecule contains an odd number of electrons.Abstract:
In a previous paper (Jahn and Teller 1937) the following theorem was established: A configuration of a polyatomic molecule for an electronic state having orbital degeneracy cannot be stable with respect to all displacements of the nuclei unless in the original configuration the nuclei all lie on a straight line. The proof given of this theorem took no account of the electronic spin, and in the present paper the justification of this is investigated. An extension of the theorem to cover additional degeneracy arising from the spin is established, which shows that if the total electronic state of orbital and spin motion is degenerate, then a non-linear configuration of the molecule will be unstable unless the degeneracy is the special twofold one (discussed by Kramers 1930) which can occur only when the molecule contains an odd number of electrons. The additional instability caused by the spin degeneracy alone, however, is shown to be very small and its effect for all practical purposes negligible. The possibility of spin forces stabilizing a non-linear configuration which is unstable owing to orbital degeneracy is also investigated, and it is shown that this is not possible except perhaps for molecules containing heavy atoms for which the spin forces are large. Thus whilst a symmetrical nuclear configuration in a degenerate orbital state might under exceptional circumstances be rendered stable by spin forces, it is not possible for the spin-orbit interaction to cause instability of an orbitally stable state. 1—General theorem for molecules with spin Just as before we must see how the symmetry of the molecular framework determines whether the energy of a degenerate electronic state with spin depends linearly upon nuclear displacements. This is again determined by the existence of non-vanishing perturbation matrix elements which are linear in the nuclear displacements. These matrix elements are integrals involving the electronic wave functions with spin and the nuclear displacements, and we deduce as before from their transformation properties whether for a given molecular symmetry they can be different from zero.read more
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References
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Electronic Structures of Polyatomic Molecules and Valence. IV. Electronic States, Quantum Theory of the Double Bond
TL;DR: In this article, the Franck-Condon principle has been applied to the analysis of the double-bond of polyatomic molecules, and the results of the analysis have been shown to be consistent with the result of Bethe and Wigner.
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Zur Deutung der Spektren mehratomiger Moleküle
TL;DR: In this article, the Symmetrieeigenschaften der Ober-and Kombinationsschwingungen mehratomiger Molekule mit Hilfe der Gruppentheorie untersucht und das theoretische Termschema des Schwingungsspektrums fur alle moglichen Symmetsrien, d. h. h., fur samtliche Untergruppen der dreidimensionalen Drehspiegelgruppe angegeben.
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The Degeneracy, Selection Rules, and Other Properties of the Normal Vibrations of Certain Polyatomic Molecules
TL;DR: In this article, the number, degeneracies, and symmetries of the normal modes of vibration for molecules in which several atoms are bonded to a central atom are given for all possible structures with three to seven atoms and the more important structures of eight and nine atoms.