Fermi Golden Rule, electron-transfer electronic coupling

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 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... 

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 ... 

To first order in the coupling constants Vk, the rate of electron transfer from a state k on the metal to the reactant at a given configuration is given by Fermi s golden rule ... 

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