Jahn-Teller effect vibronic coupling

Non-adiabatic coupling is also termed vibronic coupling as the resulting breakdown of the adiabatic picture is due to coupling between the nuclear and electi onic motion. A well-known special case of vibronic coupling is the Jahn-Teller effect [14,164-168], in which a symmetrical molecule in a doubly degenerate electronic state will spontaneously distort so as to break the symmetry and remove the degeneracy. 

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. 

II electronic states, 638-640 vibronic coupling, 628-631 triatomic molecules, 594-598 Hamiltonian equations, 612-615 pragmatic models, 620-621 Kramers doublets, geometric phase theory linear Jahn-Teller effect, 20-22 spin-orbit coupling, 20-22 Kramers-Kronig reciprocity, wave function analycity, 201 -205 Kramers theorem ... 

A quantitative treatment of the Jahn-Teller effect is more challenging (46). A major issue is that many theoretical models explicitly or implicitly assume the Bom—Oppenheimer approximation which, for octahedral Cu(II) systems in the vibronic coupling regime, cannot be correct (46,51). Hitchman and co-workers solved the vibronic Hamiltonian in order to model the temperature dependence of the molecular structure and the attendant spectroscopic properties, notably EPR spectra (52). Others, including us, take a more simphstic approach (53,54) but, in either case, a similar Mexican hat potential energy description of the principal features of the Jahn-Teller effect in homoleptic Cu(II) complexes emerges (Fig. 13). 

VIBRONIC COUPLING IN INORGANIC SYSTEMS PHOTOCHEMISTRY, CONICAL INTERSECTIONS, AND THE JAHN-TELLER AND PSEUDO-JAHN-TELLER EFFECTS... 

Because the kinetic energy dissipation of an excess electron by surrounding water molecules plays an essential role during the formation of electron-radical pairs, the influence of the quantum polarization of water molecules and OH radical must be investigated in detail. Further experimental studies on the short-time dependence of vibronic couplings in aqueous environment would permit to understand the contribution of Jahn-Teller effects on the crossing of an elementary redox reaction with OH radical. 

There is good reason to believe that the pseudo Jahn-Teller effect commonly assumes an important role in a number of molecular processes including electronic relaxation. Large classes of heterocyclic molecules whose zero-order BO electronic states may be very close to one another are ideal candidates for these types of vibronic interaction.127 Should the lowest state 0X of a given multiplicity be strongly coupled to a nearby electronic state 02 the following spectral effects can be expected ... 

Figure 69 Vibronic coupling for octahedral copper(II) (a) dynamic Jahn-Teller effect (alg and blg) (b) pseudo...

In the present paper we assume that the molecule has the icosahedral symmetry. If one wants to consider a distortion of C 0+ or Cb0. the energy levels and their eigenvectors obtained here can be used as a starting point for the description of the Jahn-Teller effect in these systems. Indeed, the electron-phonon (or vibronic) coupling occurs if [.Tei]2 contains Fvib [19]. (Here Fd is the symmetry of an electronic molecular term, while J b is the symmetry of a vibrational normal mode.) Calculations using the terms in scheme of Ref. [4] have been performed in Ref. [20]. 

Jahn-Teller effect for the ground T5 state of U4+ ions calculations of vibronic coupling constants for the eg, f2g(l) and r2g(2)... 

JAHN-TELLER EFFECT FOR THE GROUND r5 STATE OF U4+ IONS CALCULATIONS OF VIBRONIC COUPLING... 

Microscopic Approach to Cooperative Jahn-Teller Effect in Crystals with Strong Intra-Site Vibronic Coupling... 

The Jahn-Teller community has lost one of our illustrious members with the death of Frank Ham on December 12, 2002. Phrases such as The Ham effect , Ham factors and Ham quenching are terms that frequently appear in any article in which the Jahn-Teller effect or vibronic coupling is involved. I would like to record my own personal thoughts about Frank and on behalf of the whole Jahn-Teller community. 

The Hamiltonian Eq. (7) provides the basis for the quantum dynamical treatment to be detailed in the following sections, typically involving a parametrization for 20-30 phonon modes. Eq. (7) is formally equivalent to a class of linear vibronic coupling (LVC) Hamiltonians which have been used for the description of excited-state dynamics in molecular systems [66] as well as the Jahn-Teller effect in solid-state physics. In the following, we will elaborate on the general properties of the Hamiltonian Eq. (7) and on quantum dynamical calculations based on this Hamiltonian. 

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