Electronic-vibrational coupling constants

Here V is the matrix element which describes the coupling of the electronic states of reactants and products, S is known as the electron-vibration coupling constant which is equal to the inner-shell reorganization energy X- expressed in units of vibrational quanta,... 

It was quantitatively interpreted (Rice et al., 1977) as originating from bond alternation phase oscillations (in contrast to the bond alternation amplitude oscillations mentioned in subsection 4.8.2D). The vibrational absorption lines labeled 2 to 10 are directly related to the Ag Raman lines of TCNQ. The broad peak above 1600 cm originates from the single electron transition across the gap, and the indented line shape of mode 2 is a consequence of Fano interference between the single electron continuum and the phonon mode. The line intensities are determined by the respective electron - vibration coupling constants. 

The reorganization free energy /.R represents the electronic-vibrational coupling, ( and y are fractions of the overpotential r] and of the bias voltage bias at the site of the redox center, e is the elementary charge, kB the Boltzmann constant, and coeff a characteristic nuclear vibration frequency, k and p represent, respectively, the microscopic transmission coefficient and the density of electronic levels in the metal leads, which are assumed to be identical for both the reduction and the oxidation of the intermediate redox group. Tmax and r max are the current and the overvoltage at the maximum. 

The shift of the emission maximum relative to the absorption maximum, the so-called Stokes shift, is determined by the value of Qq-Qo (see Fig. 1). For the equal force constant case this Stokes shift is equal to 2Shv [2], This indicates that the Stokes shift is small for the weak-coupling case and large for the strongcoupling case. It is also clear that the value of the Stokes shift, the shape of the optical bands involved, and the strength of the (electron-vibrational) coupling are related. For a more detailed account of these models the reader is referred to the literature mentioned above [1-4]. 

The first two terms describe, respectively, the radical electrons and the molecular vibrations in the absence of vibronic coupling. Linear electron-molecular vibration (e-mv) coupling is described explicitly by the third term in Eq. (2). The set of G constants gj denotes linear monomer TT-electron - molecular vibration coupling constants. In the following sections, the indicatrix measurements, electronic and molecular spectroscopies, and other techniques are analyzed as methods of characterizing the organic conductors. 

Table 1 Electron-Molecular Vibration Coupling Constants for TCNQ Salts...

The additional electron-phonon coupling constants could be calculated again with the help of quantum mechanically computed electronic wave functions of the stack (band structures) using again a potential hypersurface to determine the wave functions of these coupled vibrations. Presently, however, to obtain an orientation one can treat these coupling constants as parameters substituting different values for them. 

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