The dynamic Jahn-Teller effect

Another factor contributing to the asymmetry and breadth of absorption bands in crystal field spectra of transition metal ions is the dynamic Jahn-Teller effect, particularly for dissolved hexahydrated ions such as [Fe(H20)6]2+ and [Ti(H20)6]3+, which are not subjected to static distortions of a crystal structure. The degeneracies of the excited 5Eg and 2Eg crystal field states of Fe2+ and Ti3+, respectively, are resolved into two levels during the lifetime of the electronic transition. This is too short to induce static distortion of the ligand environment even when the cations occupy regular octahedral sites as in the periclase structure. A dual electronic transition to the resolved energy levels of the Eg excited states causes asymmetry and contributes to the broadened absorption bands in spectra of most Ti(m) and Fe(II) compounds and minerals (cf. figs 3.1,3.2 and 5.2). 

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In the limit of strong vibronic coupling, F4S = 0, c = 5 /3, s=, c2 - s2 =, and the dynamic Jahn-Teller effect thus renders nugatory the orbital contributions to the angular momentum, and reduces the splitting, A, by a factor of two. Note in addition that the c and s quantities used in the vibronic treatment do not correspond to those of the adiabatic case, although the expressions are formally similar, so that the static distortion, A, cannot accurately be calculated from the c and s values deduced from the and 4 data. 

To summarize, the dynamical Jahn-Teller effect is found to be more significant (about one order of magnitute larger) than the GP effect as far as the... 

A very similar situation is presented by the dynamic Jahn-Teller effect, in which a trapped electron that has distorted its surroundings hops between two configurations with a frequency given by (6) for a proof see Sturge (1967). 

An interesting aspect of this problem is that posed by the Jahn-Teller effect in the benzene anion. These ions, together with the cations and anions of coronene (Bolton and Carrington, 1961c de Boer and Weissman, 1958), have spectra consisting of unusually broad lines which are very hard to saturate. Theoretical studies (McConnell, 1961 McConnell and McLachlan, 1961) suggest that the broadening is a result of spin-orbit interaction but the relaxation is linked to the dynamic Jahn-Teller effect. 

H. Bill, in The Dynamical Jahn-Teller Effect in Localized Systems (eds Yu. E. Perlin and M. Wagner), Elsevier, Amsterdam, 1984. 

This is the condition of the attractive interaction between the flu electrons originated in the dynamic Jahn-Teller effect and, for this condition to be satisfied, S must overcome U as we can see from equations (4) and (7). 

We now study the characteristics of the order parameter of the superconductivity induced by the attractive interaction between the flu electrons originated in the dynamic Jahn-Teller effect. To this end, we estimate the energy gain per Cgo molecule due to the superconductivity by using a simple consideration of Hint. It is reasonable to expect that there can be three types of order parameter, i.e., those of the Ag, Hg, and TXg symmetries, because flu X qu is reduced to the sum of these three representations. We examine the three possibilities below. 

It is thus reasonable to conclude that the mechanism of the superconductivity in A3C6o is the dynamic Jahn-Teller effect when we consider it in the real space while it is the Moskalenko-Suhl-Kondo mechanism when we consider it in the wavenumber space, as schematically shown in Fig 11. That is, for A C o the superconductivity induced by the dynamic Jahn-Teller effect is equivalent to that induced by the Moskalenko-Suhl-Kondo mechanism. Soon after the discovery of the superconductivity in A3C6o, Rice et al. [23], Asai and Kawaguchi [24], and Kristoffel and Ord [25] pointed out the importance of the Moskalenko-Suhl-Kondo mechanism in the superconductivity of A3C60- This is a remarkable suggestion although, at that time, it was too early to understand a variety of behaviors of AVC60 in a unified way. 

Fig. 11. Schematic diagram for (a) the dynamic Jahn-Teller effect and (b) the Moskalenko-Suhl-Kondo mechanism. In the former, the distorted Cg molecule undergoes the tunneling motion between three equivalent configurations. This results in the formation of the orbital-singlet state. In the latter, as shown by the black arrows, the Cooper pairs are transferred from one Fermi sphere to another, which is the pair-transfer process, a remarkable feature of multiband superconductors, and stabilizes the superconductivity. Also, as shown by the white arrows, the Cooper pairs are scattered coherently within each Fermi sphere, which is the pair-scattering process in usual superconductors.

Shankland, T. J. (1968) Pressure shift of absorption bands in MgO Fe2+ the dynamic Jahn-Teller effect. J. Phys. Chem. Solids, 29,1907-9. 

The theoretical treatment of the dynamic Jahn-Teller effect in Li3 with the PNO-CEPA-CI ab initio method (25) has been refined in the groundstate and extended to the lowest four electronically excited states in the PNO-CI approximation(26,27). Two cross sections for the adiabatic hypersurfaces for the groundstate E and the lowest excited state, E",are shown in Figure 11. The flat groundstate surface exhibits a roughly triangular trough... 

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