Jahn-Teller effect, linear vibronic

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 ... 

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. 

Cyclohexane Two-photon absorption spectrum of lowest excited singlet state (I A,) of cyclohexane in a supersonic jet. Sharp bands in the region 55 000—58 000 cm assigned to transitions to vibronic levels of 3s, E, Rydberg state. Non-linear Jahn-Teller effects 383... 

To illustrate the gauge invariant reference section for MAB, let us revisit the linear + quadratic E< e Jahn-Teller effect, which is known to exhibit a nontrivial MAB structure. There, the symmetry induced degeneracy of two electronic states (E) is lifted by their interaction with a doubly degenerate vibrational mode (e). In the vicinity of the degeneracy point at the symmetric nuclear configuration, this may be modeled by the vibronic Hamiltonian [39]... 

The general principles for the construction of the vibronic Hamiltonian and the symmetry selection rules are the same as indicated above and discussed in more detail in Chapter 7. The previous distinction between trigonal and tetragonal point groups does not play a role, and the first-order coupling is always accomplished by doubly degenerate (e) vibrational modes. In an analogous notation as in Eq. (3), the Hamiltonian for the linear (E + A) (g) e pseudo-Jahn-Teller effect is found to... 

The effective-mode transformation described here is closely related to earlier works which led to the construction of so-called interaction modes [75, 76] or cluster modes [77, 78] in Jahn-Teller systems. The approach of Refs. [54,55,72] generalizes these earlier analyses to the generic form - independent of particular symmetries - of the linear vibronic coupling Hamiltonian Eq. (8). 

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