Fermi Golden Rule, electron-transfer

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

Electron transfer theories in mixed-valence and related systems have been summarized elsewhere ((5) and references therein). Conventionally, the electron transfer rate is calculated perturb tionally using the Fermi golden rule assuming that the electronic perturbation (e) is small. The most detailed... 

Finally, it may be useful to note that the Fermi golden rule and time correlation function expressions often used (see ref. 12, for example) to express the rates of electron transfer have been shown [13], for other classes of dynamical processes, to be equivalent to LZ estimates of these same rates. So, it should not be surprising that our approach, in which we focus on events with no reorganization energy requirement and we use LZ theory to evaluate the intrinsic rates, is closely related to the more common approach used to treat electron transfer in condensed media where the reorganization energy plays a central role in determining the rates but the z factor plays a second central role. 

The manifestation of the dipole-dipole approximation can be seen explicitly in Equation (3.134) as the R 6 dependence of the energy transfer rate. In Equation (3.134) the electronic and nuclear factors are entangled because the dipole-dipole electronic coupling is partitioned between k24>d/(td R6) and the Forster spectral overlap integral, which contains the acceptor dipole strength. Therefore, for the purposes of examining the theory it is useful to write the Fermi Golden Rule expression explicitly,... 

The nonadiabatic electron transfer between donor (D) and acceptor (A) centers is treated by the Fermi Golden Rule... 

The Fermi Golden rule describes the first-order rate constant for the electron transfer process, according to equation (11), where the summation is over all the vibrational substates of the initial state i, weighted according to their probability Pi, times the square of the electron transfer matrix element in brackets. The delta function ensures conservation of energy, in that only initial and final states of the same energy contribute to the observed rate. This treatment assumes a weak coupling between D and A, also known as the nonadiabatic limit. 

One of the basic mechanisms in multichromophoric systems, electronic excitation transfer has been in the past and still is in many studies largely described using Forster theory. As stated by Forster [20], this model is developed for the weak coupling limit as it is based on an equilibrium Fermi Golden Rule... 

Royea W. J., Fajardo A. M. and Lewis N. S. (1997), Fermi golden rule approach to evaluating outer-sphere electron-transfer rate constants at semiconductor/liquid interfaces , J. Phys. Chem. B 101, 11152-11159. 

In this section we derive expressions for the rates of electron transfer within the Fermi Golden Rule approximation. As we described for exciton transport in Section 9.2.4, these rates can be used to model charge transport using the density matrix formalism. There is a wide and thorough discussion of this topic in May and Kiihn (2000). 

The nonadiabatic electron transfer rate is then given by the Fermi Golden Rule expression,... 

Many texts give a comprehensive account of the current theories for electron and energy transfer (e.g. Balzani, 2000) and this section is therefore limited to provide the most crucial mathematical relations, in most cases without formal derivation. The Fermi Golden Rule, Eq. 1, describes the rate of transfer between two adiabatic potential surfaces provided the electronic coupling is not too large ... 

The classical model based on potential energy curves does not explain correctly the existence of nuclear tunneling at low temperature nor the difficulties in observing the inverted region (i.e. the region where the rate of reaction should decrease when the exothermicity increases). It is thus necessary to devise quantum models taking into account the existence of vibronic levels. The electron transfer is then a non radiative process between manifolds of vibronic levels and the rate can be calculated from the Fermi Golden Rule ... 

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