Vibrational coupling limit

The fonn of the classical (equation C3.2.11) or semiclassical (equation C3.2.11) rate equations are energy gap laws . That is, the equations reflect a free energy dependent rate. In contrast with many physical organic reactivity indices, these rates are predicted to increase as -AG grows, and then to drop when -AG exceeds a critical value. In the classical limit, log(/cg.j.) has a parabolic dependence on -AG. Wlren high-frequency chemical bond vibrations couple to the ET process, the dependence on -AG becomes asymmetrical, as mentioned above. 

C—F 1400-870 Correlations of limited applicability because of vibrational coupling with stretching... 

Equation 1 describes the radiationless decay rate for a single-frequency model with weak electron-vibration coupling in the low temperature limit as derived by Englman and Jortner. 

The process has been treated theoretically in terms of simplified models.14 58 The quantum mechanics is one of formulating the probability of crossing from an excited to a ground state, summed over all vibrational levels. For coordination compounds, the weak coupling limit is presumably the important approximation. Here, the transition is from low lying vibrational levels of the excited state to very high vibrational levels of the ground state. 

Define or describe the following terms or phenomena island of isomerism, spin-orbit coupling, (3 vibration, Schmidt limits, and Nilsson states. 

From the above data it is becoming clear that collective electronic and vibrational coupling effects exist between M4X and M4Y QD s in the p = 0.05-1.95 loading range. However, more sensitive spectroscopic and/or electrical transport techniques will be required in order to explore the interesting defect regime above and below these limits. These kinds of investigations are currently underway in our laboratory. 

In the previous section we have dealt with a simple, but nevertheless physically rich, model describing the interaction of an electronic level with some specific vibrational mode confined to the quantum dot. We have seen how to apply in this case the Keldysh non-equilibrium techniques described in Section III within the self-consistent Born and Migdal approximations. The latter are however appropriate for the weak coupling limit to the vibrational degrees of freedom. In the opposite case of strong coupling, different techniques must be applied. For equilibrium problems, unitary transformations combined with variational approaches can be used, in non-equilibrium only recently some attempts were made to deal with the problem. [139]... 

The picture of almost harmonic excitonically coupled states is particularly appropriate in the localization or weak coupling limit. This limit will be valid in smaller peptides that do not have the rather strict symmetries of helices or sheets. It is very likely that the vibrational frequencies of each amide unit will be different even in the absence of any coupling. An example of this limit is found in the pentapeptide discussed below. If the frequency separations between the uncoupled modes are large compared with the individual coupling terms, IAj/( i — ej)l < E the coupled states... 

While coupling in the triatomic species discussed here is relatively easy to estimate, since it is limited to the interaction of two vibrations, coupling in larger molecules can only be understood with the help of normal coordinate analysis (c.f. Sec. 4.2.2.3.2). 

Based on Eq. (44), Spalburg, Los and Gislason have derived the following analytical expression for vibrationally state-resolved change transfer cross sections in the weak-coupling limit ... 

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