Effective vibronic modes

The pertinent parameter values for the X — B vibronic interaction and the B state JT system are included in Table 1. To facilitate the numerical computations, an effective b2g mode has been introduced which is obtained from the two actual b2g modes v7 and v% through the relations [41,42]... 

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. 

The vibronic envelope ECWD (v) in Eq. [129] can be an arbitrary gas-phase spectral profile. In condensed-phase spectral modeling, one often simplifies the analysis by adopting the approximation of a single effective vibrational mode (Einstein model) with the frequency Vv and the vibrational reorganization energy Xy. The vibronic envelope is then a Poisson distribution of... 

Because the energy state of a Jahn-Teller complex depends on the local lattice distortions, the macroscopic long-distant strain that produces an ultrasonic wave should influence it as well. The cross effect is initiated by the Jahn-Teller complexes (1) the dispersion (i.e., frequency-dependent variation of phase velocity) and (2) attenuation of the wave. In terms of the elastic moduli it sounds as appearance (or account) of the Jahn-Teller contribution to the real and imaginary parts of the elastic moduli. For a small-amplitude wave it is a summand Ac. Obviously, interaction between the Jahn-Teller system and the ultrasonic wave takes place only if the wave, while its propagation in a crystal, produces the lattice distortions corresponding to one of the vibronic modes. 

To account for the low-energy vibronic structure of multi-mode E e systems, a cluster model has been introduced by O Brien et al. " This is an effective one-mode description which correctly reproduces the multi-mode stabilization energy, Eq. (16). For the description of multi-mode JT band shapes, on the other hand, another effective one-mode model is more appropriate, which may be called effective single-mode Hamiltonian. The idea consists in performing a rotation in normal-coordinate space such that the coupling terms, Eq. (15), are represented by a single mode in... 

As we ll discuss in Chap. 6, a nonlinear molecule with N atoms has 3N 6 vibrational modes, each involving movements of at least two, and sometimes many atoms. The overall vibrational wavefunction can be written as a product of wavefunctions for these individual modes, and the overall Franck-Condon factor for a given vibronic transition is the product of the Franck-Condon factors for all the modes. When the molecule is raised to an excited electronic state some of its vibrational modes will be affected but others may not be. The coupling factor (S) provides a measure of these effects. Vibrational modes for which S is large are strongly coupled to the excitation, and ladders of lines corresponding to vibronic transitions of each of these modes will feature most prominently in the absorption spectrum. 

Abstract We present an approach based on the quadratic vibronic coupling (QVC) Hamiltonian [NewJ Chem 17 7-29,1993] and the effective-mode formalism [Phys Rev Lett 94 113003, 2005] for the short-time dynamics through conical intersections in complex molecular systems. Within this scheme the nuclear degrees of freedom of the whole system are split as system modes and as environment modes. To describe the short-time dynamics in the macrosystem precisely, only three effective environmental modes together with the system s modes are needed. 

A more general description of the effects of vibronic coupling can be made using the model Hamiltonian developed by Koppel, Domcke and Cederbaum [65], The basic idea is the same as that used in Section III.C, that is to assume a quasidiabatic representation, and to develop a Hamiltonian in this picture. It is a useful model, providing a simple yet accurate analytical expression for the coupled PES manifold, and identifying the modes essential for the non-adiabatic effects. As a result it can be used for comparing how well different dynamics methods perform for non-adiabatic systems. It has, for example, been used to perform benchmark full-dimensional (24-mode) quantum dynamics calculations... 

A vibronic coupling model for mixed-valence systems has been developed over the last few years (1-5). The model, which is exactly soluble, has been used to calculate intervalence band contours (1, 3, 4, 5), electron transfer rates (4, 5, 6) and Raman spectra (5, 7, 8), and the relation of the model to earlier theoretical work has been discussed in detail (3-5). As formulated to date, the model is "one dimensional (or one-mode). That is, effectively only a single vibrational coordinate is used in discussing the complete ground vibronic manifold of the system. This is a severe limitation which, among other things, prevents an explicit treatment of solvent effects which are... 

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