Nonadiabatic regime

In the nonadiabatic regime A is proportional to the adiabatic splitting 2 Fd. The instanton trajectory crosses the barrier twice, each time bringing the factor A/A a associated with the probability to cross the nonadiabaticity region remaining on the same adiabatic term (and thus... 

An interesting question then arises as to why the dynamics of proton transfer for the benzophenone-i V, /V-dimethylaniline contact radical IP falls within the nonadiabatic regime while that for the napthol photoacids-carboxylic base pairs in water falls in the adiabatic regime given that both systems are intermolecular. For the benzophenone-A, A-dimethylaniline contact radical IP, the presumed structure of the complex is that of a 7t-stacked system that constrains the distance between the two heavy atoms involved in the proton transfer, C and O, to a distance of 3.3A (Scheme 2.10) [20]. Conversely, for the napthol photoacids-carboxylic base pairs no such constraints are imposed so that there can be close approach of the two heavy atoms. The distance associated with the crossover between nonadiabatic and adiabatic proton transfer has yet to be clearly defined and will be system specific. However, from model calculations, distances in excess of 2.5 A appear to lead to the realm of nonadiabatic proton transfer. Thus, a factor determining whether a bimolecular proton-transfer process falls within the adiabatic or nonadiabatic regimes lies in the rate expression Eq. (6) where 4>(R), the distribution function for molecular species with distance, and k(R), the rate constant as a function of distance, determine the mode of transfer. 

In summary, although the BH model predicts an inverted region for the kinetics of proton in the nonadiabatic regime, the BH model is only in qualitative accord with the data derived from the proton transfer within the benzophenone-N, A -dimethylaniline contact radical ion pairs. The failure of the model lies in its ID nature as it does not take into account the degrees of freedom for the vibrations associated with the proton-transfer mode. By incorporating these vibrations into the BH model, the LH model provides an excellent account of the parameters serving to control the kinetics of nonadiabatic proton transfer. A more rigorous test for the LH model will come when the kinetic deuterium isotope effects for benzophenone-A, A -dimethylaniline contact radical ions are examined as well as the temperature dependence of these processes are measured. 

When x > 1, the e.t reaction is adiabatic and the rate constant can be controlled by the solvent relaxation. There are of course intermediate cases when x 1, and the transition from adiabatic to nonadiabatic regime is not a step function. 

In general, for the types of linked donor-acceptor systems to be discussed in this review, electron transfer is assumed to occur in the nonadiabatic regime. That is, the mixing between the electronic state of the donor and acceptor before electron transfer occurs and the corresponding state after electron transfer is weak (< kBT) [9], The actual electron transfer event is assumed to be fast compared to the time scale of nuclear motions. Marcus has proposed [11, 15] that the electron transfer rate constant ke, is given by Eq. 1. 

One purpose of this paper is to examine the evidence that the rates of oxidation—reduction reactions are related to the conductivity of the medium separating the oxidant and reductant. This survey will then describe experiments now in progress to investigate systematically the nonadiabatic regime in oxidation—reduction reactions. First the relationship between what has loosely been referred to as the conductivity of the medium and the title term, nonadiabatic, should be defined. 

Before describing experiments designed to study the nonadiabatic regime for electron transfer in oxidation-reduction reactions systematically, some systems in which electron tunnelling, in the sense that it... 

H. Carlsen, E. Sjoqvist and O. Goscinski Quantal Trajectories for Adiabatic and Nonadiabatic Regimes of Vibronic Systems Int. J. Quantum Chem. 75, 409 (1999). 

In a series of papers, van der Zwan and Hynes used the Grote-Hynes theory Eq (5) to analyze charge transfer reactions in polar solvents. They found several important limiting regimes and analytic results for k. In the nonadiabatic regime, the reaction system sees a barrier in its short time motion. The reaction accurs in a "frozen" solvent and k is given by... 

It was found that the fate of a trajectory was very quickly decided, in 0.02 ps or less. On this time scale, there is negligible motion of the molecules that could change the solvent force exerted on the reaction system. Thus we are in the nonadiabatic regime described in general terms earlier, and the solvent is effectively frozen on the time scale during which the fate of the trajectories initiated at the barrier top is decided. 

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