Intermediate coupling, vibronic

At strong coupling to the leads and the finite level width the master equation approach can no longer be used, and we apply alternatively the nonequilibrium Green function technique which have been recently developed to treat vibronic effects in a perturbative or self-consistent way in the cases of weak and intermediate electron-vibron interaction [113-130]. 

The case of intermediate and strong electron-vibron interaction at intermediate coupling to the leads is the most interesting, but also the most difficult. The existing approaches are mean-field [131-133], or start from the exact solution for the isolated system and then treat tunneling as a perturbation [134-140]. The fluctuations beyond mean-field approximations were considered in Refs. [141,142]... 

Correspondingly, vibronic pseudo spin space has to be extended to include all tunneling splitting components. In the case of quadratic E e coupling with three wells, it is expressed by the vibronic pseudo spin x = 1 matrices 3x3. Similar to the intermediate coupling case, the intersite vibronic exchange is dominated by the elastic intercell interaction (36). 

The values in parentheses correspond to a weak shoulder before the first maximum. Though its distance is too large to be due to first-order spin-orbit coupling in the selenium atom, it may be the spin-forbidden transition to Ti or a symmetry-forbidden transition i.e. the precursor band ) to Ti intensified by intermediate coupling and vibronic effects. 

The second term comes about mechanistically as follows the state couples spin-vibronically with an intermediate singlet state which in turn is coupled vibronically with the perturbing singlet state. The selection lules are given for D2 symmetry in Table 9.8. With special reference to aromatic molecules for which the x direction would be out-of-plane, it is clear that this mechanism can readily distinguish and spatial triplet symmetries. In the former case 6iu, btu, and bzu vibrations in the spectrum should he y polarized and in the latter case they are z polarized. 

However, often the minimum in Si or Ti which is reached at first is shallow and thermal energy will allow escape into other areas on the Si or Ti surface before return to So occurs (Fig. 3, path e). This is particularly true in the Ti state which has longer lifetimes due to the spin-forbidden nature of both its radiative and non-radiative modes of return to So-The rate of the escape should depend on temperature and is determined in the simplest case by the height and shape of the wall around the minimum, similarly as in ground state reactions (concepts such as activation energy and entropy should be applicable). In cases of intermediate complexity, non-unity transmission coefficients may become important, as discussed above. Finally, in unfavorable cases, vibronic coupling between two or more states has to be considered at all times and simple concepts familiar from ground-state chemistry are not applicable. Pres-... 

Alexandrite, the common name for Cr-doped chrysoberyl, is a laser material capable of continuously tunable laser output in the 700-800 nm region. It was established that alexandrite is an intermediate crystal field matrix, thus the non-phonon emitting state is coupled to the 72 relaxed state and behaves as a storage level for the latter. The laser-emitted light is strongly polarized due to its biaxial structure and is characterized by a decay time of 260 ps (Fabeni et al. 1991 Schepler 1984 Suchoki et al. 2002). Two pairs of sharp i -lines are detected connected with Cr " in two different structural positions the first near 680 nm with a decay time of approximately 330 ps is connected with mirror site fluorescence and the second at 690 nm with a much longer decay of approximately 44 ms is connected with inversion symmetry sites (Powell et al. 1985). The group of narrow lines between 640 and 660 nm was connected with an anti-Stokes vibronic sideband of the mirror site fluorescence. 

A much more interesting example of the intermediate case is encountered when the density of states is rather small but the vibronic coupling elements are large (due to favorable Franck-Condon vibrational overlap factors). The consequences of this type of intramolecular vibronic coupling are seen in the anomalously long radiative lifetimes of the first singlet states of N02, S02, and CS2 86-99 and in the many extra unexpected lines in the spectra of these molecules. 

It is well known from the Bom-Oppenheimer separation [1] that the pattern of energy levels for a typical diatomic molecule consists first of widely separated electronic states (A eiec 20000 cm-1). Each of these states then supports a set of more closely spaced vibrational levels (AEvib 1000 cm-1). Each of these vibrational levels in turn is spanned by closely spaced rotational levels ( A Emt 1 cm-1) and, in the case of open shell molecules, by fine and hyperfine states (A Efs 100 cm-1 and AEhts 0.01 cm-1). The objective is to construct an effective Hamiltonian which is capable of describing the detailed energy levels of the molecule in a single vibrational level of a particular electronic state. It is usual to derive this Hamiltonian in two stages because of the different nature of the electronic and nuclear coordinates. In the first step, which we describe in the present section, we derive a Hamiltonian which acts on all the vibrational states of a single electronic state. The operators thus remain explicitly dependent on the vibrational coordinate R (the intemuclear separation). In the second step, described in section 7.55, we remove the effects of terms in this intermediate Hamiltonian which couple different vibrational levels. The result is an effective Hamiltonian for each vibronic state. 

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