Huang-Rhys factors

The calculated values of the Huang—Rhys factor are also collected in Table 4, where it is seen that the contribution of... 

Table 4. Predicted Vibrational Energies tuo (in cm-1) Corresponding to the GC and EC Stationary Points, The Displacement Vector fc (in (amul/2-A)), the Energy Contribution Ek (in cm-1), and the Huang—Rhys Factor gk (dimensionless)...

Si is often called the Huang-Rhys factor or coupling constant. The plot of the Franck-Condon factor versus v[ is also shown in Fig. 7. 

Figure 7. (a) Schematic descriptions of the Huang-Rhys factor and the Franck-Condon factors... 

From Eq. (2.38) we can see that in order to analyze the absorption spectra it is necessary to know the vibrational modes involved and their Huang-Rhys factors. Fortunately for the B band, these data have been obtained by Mathies and Boxer (see Table I) by analyzing the resonance Raman spectra [42,46,47]. But they only analyzed the B band. The data shown in Table I for the P band are from the literature [42,46,47] and from our fitting of absorption spectra [68]. 

Selected Vibrational Frequencies, Huang-Rhys Factors, and Electronic Energy Levels of the Involved States of RCs of Rb. sphaeroides... 

Next we shall discuss how to theoretically construct the three-dimensional fs time-resolved spectra. For this purpose, recent fs time-resolved spectra reported by Scherer s group for Rb. sphaeroides R26 with A,cxcltatlon = 800 nm at room temperature are shown in Fig. 18 is considered [39]. They have used a laser pulse of 30 fs. To theoretically construct the fs time-resolved spectra, we need the potential surfaces for displaced surfaces we need the vibrational frequencies go, and their Huang-Rhys factors S,. For bacterial photosynthetic RCs, these physical constants are given in Table I. In addition to the potential surfaces, we need interactions between different electronic states which are shown in... 

Physically, S is the number of emitted phonons accompanying the optical transition. It is commonly used as a measure of electron-phonon interaction and is called the Huang-Rhys factor. At m = 0, the transition probabihty is given by the simple relation ... 

As a further point, we mention that the vibrational energy loss AE (Fig. 16) is also often expressed in terms of the strength of the electron-phonon coupling or of the Huang-Rhys factor S (see, for example, Stoneham, 1975,1977,1981), where... 

Fig. 17. A comparision of the temperature dependence of the line-shape function (G) of the transition probability for the multimode case (solid line) as against a single mode approximation (dashed line). Here the phonon frequency spectrum (A) is assumed to be of Gaussian form, A a>) = 2 2) 1,2exp [—(to — cu0)2/2

Here, S is the Huang-Rhys factor [63], which is related to the intensity of the 0-n vibronic transition, Io-n = e sSn/n, and reflects the time-dependent Stokes shift associated with a given type of vibrational mode (e.g., S 0.6 for the high-frequency C=C stretch modes [61,64,65]). For the class of systems studied here, two types of phonon modes are considered per monomer unit, i.e., high-frequency C=C stretch modes and low-frequency ring-torsional modes. 

It is convenient to introduce the dimensionless electron-vibron coupling constant, known as the Huang-Rhys factor,... 

It should be noted that due to er(Af)a a the Fourier transform of % (Lorentzian band-shape with the band-width determined by the dephasing constant of different Fourier transform bands are approximately proportional to the FCFs (0aij 0gg 2 (0ai/ 0go) 2- For the single displaced oscillator case, for example, I I2 = S e 2S, where S is the Huang-Rhys factor of this mode. 

Note The S value is the Huang-Rhys factor, or the (vibronic) coupling constant. Frequency (cm-1). 

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. 

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