Phonon-vibron coupling

Phonon—vibron coupling, 1517 Photoactivity of semiconductor electrodes, 1089 Photoelectrochemistry, 1089 Photoelectrodes, 1088 Photomultiplier tube, 805... 

Fig. 9.29. Schematic diagram of a phonon-vibron coupling model. (Reproduced form J. O M. Bockris and S. u. M. Khan, Surface Electrochemistry, Plenum, 1993, p. 448.)...

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]. 

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. 

In the following, we summarize the pertinent results of our analysis of Refs. [50-53] where we applied the LVC Hamiltonian Eq. (1) in conjunction with a 20-30 mode phonon distribution composed of a high-frequency branch corresponding to C=C stretch modes and a low-frequency branch corresponding to ring-torsional modes. In all cases, the parametrization of the vibronic coupling models is based on the lattice model of Sec. 3.1 and the complementary diabatic representation of Sec. 3.2. 

If the vibronic coupling is week (in comparison with the phonon energy) the second order perturbation theory for the local Exe problem will give... 

Parameters (18) include vibronic coupling constant, V, and phonon band-structure factors, (/, y K j, A). For a particular crystal, finding these factors is a laborious problem of crystal lattice dynamics. Instead, in the OOA, 7y are used as free parameters of the theory. Still consistent with the fundamental theory of the JT effect, in this form the OOA is not directly derived from the theory. In other words, in the theory of cooperative JT effect, the OOA is a phenomenological approach. 

The magnetic-dipole allowed A -> Ai transition may become electric-dipole vibronicaUy allowed by vibronic coupling with phonons having E or A2 symmetry (see e.g. Ref. 43). Vibrational structure in the luminescence spectra associated with the electric-dipole allowed E Ai transition may be due to vibronic coupling with phonons having E, Ai, A2, Bx or B2 symmetry. 

The model which has been most widely applied to the calculation of vibronic intensities of the Cs2NaLnCl6 systems is the vibronic coupling model of Faulkner and Richardson [67]. Prior to the introduction of this model, it was customary to analyse one-phonon vibronic transitions using Judd closure theory, Fig. 7d, [117] (see, for example, [156]) with the replacement of the Tfectromc (which is proportional to the above Q2) parameters by T bromc, which include the vibrational integral and the derivative of the CF with respect to the relevant normal coordinate. The selection rules for vibronic transitions under this scheme therefore parallel those for forced electric dipole transitions (e.g. A/ <6 and in particular when the initial or final state is /=0, then A/ =2, 4, 6). 

Compared to uniform compression, uniaxial strain along one of the lattice vectors is more likely to lead to detonation. Dick has proposed [43] that detonation initiation in nitromethane is favored by shock-wave propagation in specific directions related to the orientation-dependent sterie hindrance to the shear flow. This proposal is based on a model according to which the sterically hindered shear process causes preferential excitation of optical phonons strongly coupled with vibrons. 

From the above description, it should be evident that the electronic excitation-emission transition is a dynamic process which is perturbed by vibronic coupling of the phonon spectrum present in the host lattice. Thus, the host is just as important as the activator center. Another way to describe the overall process is to state that the electronic transition in the activator center involves the zero-phonon Une, broadened above absolute zero temperatures by quantized phonon interactions to form a band of permissible excitation and emission energies. 

In this diagram, we have shown the absorption band and the emission band as being completely separated from each other for clarity. Usually, they are not. The zero phonon line is the same as the electronic transitions shown in 5.5.4., i.e.- the vertical arrows. Thus, the Stokes shift arises because of a change in , as we have said, with the added ho)j phonon energy perturbations (vibronic coupling) which cause a broad... 

As we have said, the excitation process results in a density of states arising from a random process of phonon perturbation of the excited state, both before it relaxes and afterwards as well. It is this random formation of Gaussian energy states that give rise to a broad band in excitation, and to a broad band in emission. The zero-phonon line arises from the nature of the electronic transition taking place which is broadened by the vibronic coupling process. As the temperature rises, increased phonon branching results and the emission band is even further broadened, as follows ... 

In the above diagram, the emission intensities of the three bands remain constant. It is the peak Intensity which changes as the band broadens. To this point, we have aceepted the fact that vibronic coupling leads to broad band excitation and emission in a phosphor. Take note that the above diagram is the result of experimental measurements which prove that as the temperature increases, the phonon spectrum becomes broadened, thereby leading to broadening of the bands. Thus, at - 200 °C., the number of phonon vibrations is restricted and a rather sharp emission band is seen. As the temperature rises, the number of separate phonon branches increases (the empty phonon levels become occupied) and the emission (excitation) band is further broadened. Note that at some temperature above 300 °C. (in this example), the phonon vibrations increase to the... 

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