Franck-Condon weighted density of states FCWD

The Franck-Condon-weighted density of states (FCWD) reflects the influence of all of the nuclear modes of the system, often represented in terms of effective normal... 

The summed term in eq. 4.40 is often referred to as the Franck-Condon weighted density of states (FCWD), and the equation written in the compact form of eq. 4.5. This is the master equation for the calculation of rates of nonadiabatic ET where the reactants remain in thermal equilibration with their surroundings. 

Considering the charge injection as a non-adiabatic radiationless process [5], expressed by (5), depends on two factors (1) the squared electronic coupling matrix element between the donor and the acceptor (IHP in (5) and (2) the Franck-Condon weighted density of states (FCWD), which is a function of the reorganization energy k and of the driving force AG, see Fig. 2, and equation (6) [5] ... 

In this equation, FCWD is the Franck-Condon weighted density of states, and it contains information concerning overlap between the vibrational wavefunctions of the reactant and product states. 

Here, = < /, V /y> is the electronic coupling matrix element and (FCWD) denotes the Franck-Condon weighted density of states. In the high-temperature regime — that is, when assuming that all vibrational modes are classical (fico, kgT ), the FCWD obeys a standard Arrhenius type of equation ... 

In Eq. (1), FCWD is the Franck-Condon weighted density of states that describes the nuclear contribution to k, and //daW is the electronic coupling matrix element that defines the interaction strength occurring between the reactant and product wavefunctions at the transition state. In the classical limit, the Franck-... 

FCWDS is the Franck-Condon weighted density of states and V the electronic coupling matrix element. In a semiclas-sical treatment, this equation can be separated into a preexponential factor A and an exponential term that relates et to the driving force AG and nuclear reorganization energies of reactant A. and solvent... 

An alternative approach to polaron transport in organic solids is in terms of electron transfer (ET). The process can be viewed as a special case of the non-radiative decay of an electronic state. The derivation of the theory is developed in various books or review papers [13-15]. The parameter of importance here is the transition probability per unit time (or transition rate) kif between an initial and a final state. The rate is estimated within the Franck-Condon approximation. In the high-temperature regime ( cOif < kT) the Franck-Condon-weighted density (FCWD) reduces to a standard Arrhenius equation, so the rate takes its semiclassical Marcus theory expression [16] ... 

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