Crossover adiabatic-nonadiabatic

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. 

Note that in this particular intersystem crossing process the nuclear coordinate Q is less than Q0 in both initial and final states. We call eq. (7-12) nonadiabatic intersystem crossover, since the process initiates on the E(Y) curve and ends up on the (11) curve. We call the process (7-9) an adiabatic intersystem crossover, since it follows curve E ) only. 

Applications are then presented in Section IV. These examples should served as a guide as to what kinds of problems can be studied with these techniques and the limitations and possibilities for these methods. We present three examples (1) a dynamical test of the centroid quantum transition-state theory for electron transfer (ET) reactions in the crossover regime between adiabatic and nonadiabatic electron transfer, (2) the primary electron transfer reaction in bacterial photosynthesis, and (3) the diffusion kinetics of a Brownian particle in a periodic potential. Finally, Section V offers an outlook and a perspective of the current status of the field from our vantage point. 

We have studied the usefulness of this factorization in the crossover region between the nonadiabatic and adiabatic limits [26]. The starting point for these rate calculations is the exact quantum expression for the... 

In the normal region, the crossover between the nonadiabatic dynamic solvent control regime and the adiabatic regime is smooth, because in both cases the reaction rate is determined by the diffusive delivery of the reactive wave packet to the transition state. However, the situation is radically different in the inverted region, where the reaction is always nonadiabatic... 

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