Vibrational trapping intramolecular

In the classical limit where the condition << kgT is met for the trapping vibrations, the rate constant for electron transfer is given by eq. 6. In eq. 6, x/4 is the classical vibrational trapping energy which includes contributions from both intramolecular (X ) and solvent (XQ) vibrations (eq. 5). In eq. 6 AE is the internal energy difference in the reaction, vn is the frequen-... 

For the normal modes that contribute to vibrational trapping, AQe 0. If there is a series of such modes, X, is given by equation (22) where the summation is over all of the trapping vibrations. For the general case of unequal force constants, the contribution of the intramolecular vibrations to AG is not given by but rather by a more complex expression arising from the energy minimization procedure described in the derivation of equation (16a). 

In those cases when no sharp groups of slow electrons are observed, the unselective deformation of the distribution curve can be ascribed to the excitation of intramolecular and intermolecnlar vibrations in the lattice. The appearance of sharp groups of slow electrons is to be ascribed to the electronic excitation of the molecular ions formed, as was the case for the photoionization of similar compounds in the gas phase, dealt with in the previous sections. As recently found, energy losses of 0.3-0.4 e.v. may be due to the excitation of electrons from traps. 

The Fe111/11 case is particularly simple. For electron transfer reactions in general, several normal modes may contribute to the trapping of the exchanging electron at a particular site. In addition, intramolecular vibrational modes are of relatively high frequency, 200-4000 cm-1, and at room temperature the classical approximation is not valid since only the v = 0 level is appreciably populated. In order to treat the problem more generally, it is necessary to turn to the quantum mechanical results in a later section. 

Equation (36), which attempts to include both t and re, has been proposed as a more general expression for et.48 Note that in the limit, when Te -4 t , the expression for the electron transfer rate constant (equation 37) no longer depends on the extent of electronic coupling since vel > vn. In this limit the rate constant for electron transfer for a vibrational distribution near the intersection region is dictated by rates of repopulation of those intramolecular and/or solvent modes which cause the trapping of the exchanging electron. 

The most striking application of electron transfer theory has been to the direct calculation of electron transfer rate constants for a series of metal complex couples.36 37 46 The results of several such calculations taken from ref. 37b are summarized in Table 2. The calculations were made based on intemuclear separations appropriate to the reactants in close contact except for the second entry for Fe(H20)j3+/2+, where at r = 5.25 A there is significant interpenetratidn of the inner coordination spheres. The Ke values are based on ab initio calculations of the extent of electronic coupling. k includes the total contributions to electron transfer from solvent and the trapping vibrations using the dielectric continuum result for A0. the quantum mechanical result for intramolecular vibrations, and known bond distance changes from measurements in the solid state or in solution. 

Figure 7 Potential energy curves illustrating the contribution from an intramolecular trapping vibration j to the energy of an IT band for (a) AE = 0. (b) AE 0...

The absorption band shape is necessarily dictated by those same intramolecular trapping and solvent vibrations which determine the rate of thermal electron transfer since the change in electronic distribution is the same for the two processes. The band shape depends on the product of two terms. The first is the transition moment M = the square of which determines the... 

An intermediate epoxy ketene (39) from a-cleavage of 2,5-diphenyl-3(2H)-furanone (40) has been proposed by Padwa and co-workers to explain photoisomerization to 4,5-diphenyl-2(5H)-furanone (47)38. The epoxy ketene was not observed when the irradiation was monitored by infrared spectroscopy and was not trapped by methanol. The authors suggest that the intermediate may be formed with excess vibrational energy and as a result undergo very rapid intramolecular reaction. 

The processes of energy acquisition, storage and disposal in clusters are of considerable interest in their own right and also for the interpretation of similar processes in finite systems. Consider vibrational energy excitation of an intramolecular vibration of a molecule in a cluster, or of a cluster inter-molecular mode(s), which can be accomplished by collisional excitation, photoselective vibrational excitation, electronic excitation followed by intramolecular radiationless transitions or exciton trapping.178 In charged clusters... 

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