Electron-vibrational interaction

I have predicted that the very unusual low-frequency IR behavior for the Creutz-Taube ion calculated by Piepho, Schatz and Krausz [Piepho, S. B. Krausz, E. R. Schatz, P. N. J. Am. Chem. Soc. 1978, 100, 2996] on the assumption of only antisymmetric mode involvement in electron-vibrational interaction would not be found, and that it was an artifact of the method. The failure of experiments designed to locate such IR bands has subsequently been reported by Krausz, et al. 

There are several nonadiabatic interactions (see the appendix), for example, electron-vibration coupling and spin-orbit interaction. The electron-vibration interaction is described by the operator ... 

Owing to the electron-vibrational interaction in molecules, there is one more possible decay channel for SES. This is the nonradiative relaxation (internal conversion), in which the electron energy is transferred into vibrational energy of molecules (in the condensed phase, into thermal energy of the medium). If the molecule fluoresces, there may also occur fluorescence from the lowest excited state. (According to the empirical rule of Kasha,64 the molecular fluorescence occurs from the lowest excitation level irrespective of the wavelength of the exciting radiation.)... 

Abstract Theory of non-adiabatic electron-vibration interactions has been applied to the... 

Electronic-vibrational interaction vibronic selection rules... 

Electronic-vibrational interaction in degenerate states the Jahn-Tetler and Renner effects... 

Since the excess electron is localized on nondegenerate orbital the excess electron vibronic interaction is limited to the totally symmetric distortions of the first coordination sphere. This interaction reflects the difference of metal-ligand distances in different oxidation states. The matrix of the electron-vibrational interaction is diagonal on the basis of localized states with the matrix elements... 

Here He is the electronic Hamiltonian determining the wave functions and the eigenvalues of the Fe-(NO) fragment in the fixed nuclear configuration. Reading off the coordinate qA of the full symmetric vibration from its equilibrium position in the state 1Ai(Fe2+(d6)), one can write down the operator of the linear electron-vibrational interaction in the following form ... 

Yu. E. Perlin and B. S. Tsukerblat, Effects of Electron-Vibrational Interaction in the Optical Spectra... 

Figure 6 A scheme of the three possible resonances in OOTF. i) Global resonance (A). Very weak electron-vibration interaction is expected ii) Localized resonances or traps (B).Usually the LEPS experiments are not detecting electrons trapped in these resonances and they appear as a reduction in the transmission probability, iii) Quantum well structure (C). Here the electron is localized in one dimension, while it is delocalized in the other two dimensions. There is a significant electron-vibration coupling.

Another type of structure may result from localized resonance states formed by either traps or impurities in the film39 (see Fig. 6B). In this case, the electrons are localized at the trap and due to the high charge concentration strong electron-vibration interactions exist that result in inelastic processes in the film. While these traps are observed clearly in LEET,39 in the LEPS experiments they are manifest by reduction in the transmission probability and sometimes by charging effects, but cannot be observed as modulation on the amplitude of the spectra. 

Key words excited state relaxation, electron-vibrational interaction, vibrational coherence... 

In this section, we introduce the working principle of vibrational spectroscopy. It will be compared with a parent technique called Inelastic Electron Tunneling Spectroscopy, which was developed in the 60 s. Although the working principle is similar in each of them, the specific nature of electron-vibration interaction differs. We shall conclude this section by reviewing the most important achievements of single-molecule vibrational spectroscopy. 

This parametrization can be very demanding, hence one goes a step further and only calculates the electronic structure at equilibrium and the leading term in a Taylor expansion on the nuclear coordinates the electron-vibration interaction is linearized. 

This is nothing but the electron-vibration interaction in the chosen notation. The quantity h is the three index supervector acting on the vector of nuclear shifts they form the scalar product (.... ..) giving a 10 x 10 matrix, next forming a Liouville scalar product with matrix V. On the other hand, acting on the variations V of the density matrix by forming the Liouville scalar product h produces a vector to be convoluted with that of nuclear shifts 5q. With use of this set of variables the energy in the vicinity of the symmetric equilibrium point becomes ... 

As the size of the systems increases, when going from tricycle 45 to pentacycle 112, the Huang-Rhys factors (the electron- and hole-vibration constants) for high-frequency vibrations decrease as expected. In contrast, the vibronic interaction with low-energy vibrational modes shows an opposite trend for both electrons and holes. The electron-vibrational interaction with low-energy vibrations is much larger than the hole-vibrational interaction a similar pattern is also characteristic for oligoacenes. 

Here we show how the same problem can be analyzed by using the second approach described above. Using (20)-(22) and the experimental crystal field strength value Dq= 1,450 cm it is possible to estimate the constants of the electron-vibrational interaction in Hamiltonian (19). Using the ratio e- jea = 0.31 for the [CrFe] " cluster [29], we got for these constants the following numerical values ... 

The physics of CITE looks very simple and clear. Because of the vibronic (electron-vibrational) interaction each Jahn-Teller (JT) molecule (center) is characterized with several energetically equivalent minima corresponding to a possible distortion of the initial (at the absence of the vibronic interaction) symmetry. In case of many JT centers in a crystal matrix an effective interaction caused by lattice strains around the centers takes place. This interaction breaks the equivalence of the minima. The preference of the specific distortions around each of the JT centers leads to the ordering of the local distortions - structural phase transitions. As each distortion is related to a specific electronic state (orbital) the JT structural transition is at the same time an ordering of orbitals. The last is a central question of the modern orbital physics. 

Viljas, J.K., Cuevas, J.C., Pauly, F. and Hafner, M. (2005) Electron-vibration interaction in transport through atomic gold wires. Phys. Rev. B, 72, 245415-1-245415-18. 

Nimzi et al. [53] showed the two-level model was well adapted for the 4-(N-(2-hydroxyethyl-J -ethyl)-amino-4 -nitrobenzene (DRl) dye, while a three-level model had to be considered for the 4-dibutylamino-4 -nitrobenzene (DEANS) system, due to electron-vibration interactions values of /zoi. and A/zoi could be deduced for both molecules. 

Significant advances have occurred of late in the computation of electron-vibration interactions in molecules. These are based on more or less sophisticated versions of the LCAO-method. A brief review of these works up to about 1978 is now available5 0c) (Chap. 8). 

To provide a consistent formulation of the impurity electron-vibration interaction we exclude the purely vibrational part in 5V, which formed the subject of Sect. 2.3. We thus define the electron-vibration interaction by... 

Let ru and T) be the representations of the two (upper and lower) electronic states participating in the optical transition. Then the modes which will participate in the electron-vibration interaction will have representations that are included in the symmetric square of Tu + T). Thus, for the transitions - Tlu (the C band) in KC1 T1+ type phosphors, modes of representations... 

In writing out explicitly the electron-vibration interaction term appropriate to mAlg - Tlu optical transition, we first of all neglect Tiu -type vibrations. These are non-diagonal in the initial and final states, whose separation is large compared to the vibronic interaction strength. The electronic matrices oFl operating on the 4-vector (AIg, Tlux, Tluy, Tluz) are as follows... 

The choice in (4.13) is convenient for discussing optical transitions due to light having a definite polarisation, say along z, since with the matrix as in (4.13) the equilibrium positions of the coordinate in the initial (Alg) and final (the z-com-ponent of 7 lu)-states are displaced to the left and right by equal amounts. This will be apparent in the next but one equation giving the electron-vibration interaction. The relevant total Hamiltonian contains also an electronic term Hei... 

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