Multiphonon electron transfer

In-situ tunneling through metalloproteins as a three-center multiphonon electron transfer process... 

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

The effect of temperature on the photoinduced electron transfer from [Ru(bpy)3]2+ to methyl viologen solubilized in cellophane has been investigated 98 K The first-order rate constant which depends exponentially on the distance between the reactants shows a non-Arrhenius type of behavior in the temperature interval from 77 to 294 K. This phenomenon, previously found to be of great importance in biological systems, is quantitatively interpreted in terms of a nonadiabatic multiphonon non-radiative process. 

As an illustration of these considerations, the Arrhenius plot of the electron transfer rate constant, observed by De Vault and Chance [1966], is shown in Figure 2.11. Note that only Er, which actually is the sum of reorganization energies for all degrees of freedom, enters into the high-temperature rate constant formula (2.66). At low temperature, however, to preserve Er, one has to fit an additional parameter a>, which has no direct physical significance for a real multiphonon problem. 

The quantum mechanical treatment of non-adiabatic electron transfers are normally considered in terms of the formalism developed for multiphonon radiationless transitions. This formalism starts from Fermi s golden rule for the probability of a transition from a vibronic state Ay of the reactant (electronic state A with vibrational level v) to a set of vibronic levels B of the product... 

Established views of the electrochemical electron transfer process as a multiphonon electronic transition composed of contributions from all the electronic levels of the metallic electrode carries over to chemical and bioelectrochemical nanoscale systems. Notions in focus are illuminated by the following cathodic electrochemical current density form, j(ri) at the overpotential t] (with an analogous form for the anodic process) 4-26... 

TABLE 2. Physical parameters pertinent to the multiphonon theory of electron transfer... 

II. NONADIABATIC ELECTRON TRANSFER THEORY The conventional multiphonon nonadiabatic ET theory rests on the following assumptions ... 

Fig. 13.2 The relaxation of different vibrational levels of the ground electronic state of 2 in a sohd Ar matrix. Analysis of these results indicates that the relaxation of the v < 9 levels is dominated by radiative decay and possible transfer to impurities. The relaxation ofthe upper levels probably takes place by the multiphonon mechanism discussed here. (From A. Salloum and H. Dubust, Chem. Phys. 189, 179 (1994).)...

The observation that the reaction requires an induction time of tens of picoseconds can be used to differentiate between proposed mechanisms of how shock wave energy localizes to cause chemical reaction. This induction time is expected for mechanisms that involve vibrational energy transfer, such as multiphonon up-pumping [107], where the shock wave excites low frequency phonons that multiply annihilate to excite the higher frequency modes involved in dissociation. It is also consistent with electronic excitation relaxing into highly excited vibrational states before dissociation, and experiments are underway to search for electronic excitations. On the other hand, prompt mechanisms, such as direct high frequency vibrational excitation by the shock wave, or direct electronic excitation and prompt excited state dissociation, should occur on sub-picosecond time scales, in contrast to the data presented here. 

W(0) is the asymptotic transfer probability for AE — 0 and ft a parameter determined by the strength of the electron-lattice coupling as well as by the nature of phonons involved. This expression is similar to that for multiphonon radiationless decay except for the fact that fi represents the coupling between the two species involved. 

Miyakawa and Dexter (1971) showed that it is still legitimate to write the probability of energy transfer in the form of eq. (142), where p(E) is taken as Ssa, the overlap of the lineshape functions for emission in ion S and absorption of ion A, including the phonon sidebands in the lineshape. It is necessary to consider each partial overlap between the m-phonon emission line shape of ion S and the n-phonon absorption lineshape of ion A. This mathematical assumption has gained experimental credibility through the existence of multiphonon sidebands for trivalent R ions which, in a case of very weak electron-phonon coupling (Auzel 1976) could not be observed directly by usual spectroscopy. 

In region (2), the excess electron can be viewed as being localized in preexisting traps (vacancies, holes) or in potential fluctuations which develop into deeper traps. The configurational fluctuations of the liquid are not affected by the excess electron and the trapping site represents an attractive potential for the electron. The state of the electron is described by a localized wave function. Transport occurs by multiphonon absorption of the electron and transfer to a new trapping site or by photodiffusion. An exception are the electron bubbles in IHe, INe, and IH2 which are discussed in Section 7.2. 

---