Jahn-Teller-type distortion

Cyclopentadienyl radicals are likely to experience Jahn-Teller-type distortion from planarity. The pentafluorocyclopentadienyl radical C5F 5214 was obtained by photolytic dissociation of the chlorine atom of C5F5C1. The fluorine hyperfine structure (A1S0 = 16 G)... 

The Jahn-Teller theorem indicates that when a degenerate shell is not completely filled, a distortion away from spherical symmetry occurs, leading to a loss of degeneracy. The splitting pattern produced by the Jahn-Teller type distortion is identical to that predicted by the crystal field approach used in the structural jellium model. 

Jahn-Teller type distortion, q must belong to one of the other irreducible representations. 

Apparently the detailed configuration of the atomic arrangement in simple metal clusters does not seem to play an important role in the study of their physical properties. The spherical jellium model is very successful in correlating the prominent features of the ionization potential and also the main features of the mass spectra. However, there is also evidence of some features that the spherical assumption is unable to explain. Whenever a top-shell is not completely filled (N 2, 8, 20, 40, 58, 92,...) the electronic density becomes non-spherical, which in turn leads to an ellipsoidal distortion of the ionic background. This Jahn-Teller-type distortion, similar to those observed for molecules and nuclei, leads to a splitting of all spherical shells into spheroidal sub-shells [41]. Ellipsoidal clusters are prevalent for open-shell configurations. 

An effective Hamiltonian for a static cooperative Jahn-Teller effect acting in the space of intra-site active vibronic modes is derived on a microscopic basis, including the interaction with phonon and uniform strains. The developed approach allows for simple treatment of cooperative Jahn-Teller distortions and orbital ordering in crystals, especially with strong vibronic interaction on sites. It also allows to describe quantitatively the induced distortions of non-Jahn-Teller type. 

Note that in fact cyclobutadiene does not have degenerate, singly-occupied molecular orbitals, as a Jahn-Teller type (actually a pseudo-Jahn-Teller) distortion lowers its symmetry from square to rectangular and leads to a closed-shell paired-electron molecule [4]. 

The cooperative Jahn-Teller type interaction is obtained by the orbital-lattice coupled model [12,13]. Let us consider the Hamiltonian with the Jahn-Teller coupling g, the kinetic energy and the lattice potential for the Jahn-Teller phonon mode, the orbital-strain interaction, and the elastic-strain energy. The Jahn-Teller distortion mode Qi around a metal site i is represented by the Jahn-Teller phonon coordinates k- By introduce the canonical transformation for k, the orbital and lattice degrees of freedom are separated. The final form of the interaction between the inter-site orbitals given by... 

It was shown by several workers that in this case the first-order Jahn-Teller distortion is due to an ej vibration, and that the second-order distortion vanishes. Therefore, in terms of simple Jahn-Teller theoi, the moat around the symmetric point should be a Mexican hat type, without secondary minima. This expectation was borne out by high-level quantum chemical calculations, which showed that the energy difference between the two expected C2v structures ( A2 and Bi) were indeed very small [73]. 

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