Electronic nonadiabatic barriers

From the point of view of associative desorption, this reaction is an early barrier reaction. That is, the transition state resembles the reactants.46 Early barrier reactions are well known to channel large amounts of the reaction exoergicity into product vibration. For example, the famous chemical-laser reaction, F + H2 — HF(u) + H, is such a reaction producing a highly inverted HF vibrational distribution.47-50 Luntz and co-workers carried out classical trajectory calculation on the Born-Oppenheimer potential energy surface of Fig. 3(c) and found indeed that the properties of this early barrier reaction do include an inverted N2 vibrational distribution that peaks near v = 6 and extends to v = 11 (see Fig. 3(a)). In marked contrast to these theoretical predictions, the experimentally observed N2 vibrational distribution shown in Fig. 3(d) is skewed towards low values of v. The authors of Ref. 44 also employed the electronic friction theory of Tully and Head-Gordon35 in an attempt to model electronically nonadiabatic influences to the reaction. The results of these calculations are shown in... 

A treatment of electronically nonadiabatic transitions in molecular collisions is possible on the basis of an extension of Miller s classical S-matrix method /106b/. This means using complex valued classical trajectories which go from one to another adiabatic surface through thisir (complex) crossing point. Quantum effects, such as tunneling through or reflection above a potential barrier also can be incorporated in the theory of nonadiabatic transitions. 

The transition between adiabatic PT and electronically non-adiabatic CPET can also be incorporated in the adiabatic PT rate constant using the electronic nonadiabatic factor Xei, that depends on (XeiVei)/vv in the same way as IkgsI depends on pi x- Additionally, we include in the energy barrier the contributions from the reorganizations of the parts of the molecular system involved in the synchronous proton and electron transfer, and express the rate constant for nonadiabatic CPET as... 

With the radical atom in a state, there is no electronically nonadiabatic route for vibrational relaxation. This is a simplifying feature, but the mechanism responsible for removal of HX+ by H or D atoms remains unclear, largely because of uncertainty over the barrier heights for the abstraction and exchange processes, i.e.. 

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

The effects of deviations from the Born-Oppenheimer approximation (BOA) due to the interaction of the electron in the sub-barrier region with the local vibrations of the donor or the acceptor were considered for electron transfer processes in Ref. 68. It was shown that these effects are of importance for long-distance electron transfer since in this case the time when the electron is in the sub-barrier region may be long as compared to the period of the local vibration.68 A similar approach has been used in Ref. 65 to treat non-adiabatic effects in the sub-barrier region in atom transfer processes. However, nonadiabatic effects in the classically attainable region may also be of importance in atom transfer processes. In the harmonic approximation, when these effects are taken into account exactly, they manifest themselves in the noncoincidence of the... 

R to P is slow, even when the isoenergetic conditions in the solvent allow the ET via the Franck-Condon principle. The TST rate for this case contains in its prefactor an electronic transmission coefficient Kd, which is proportional to the square of the small electronic coupling [28], But as first described by Zusman [32], if the solvation dynamics are sufficiently slow, the passage up to (and down from [33]) the nonadiabatic curve intersection can influence the rate. This has to do with solvent dynamics in the solvent wells (this is opposed to the barrier top description given above). We say no more about this here [8,11,32-36]. 

There is one experimental parameter that does serve to distinguish between the semiclassical model and the quantum model for nonadiabatic proton transfer. In the semiclassical model, if one assumes that the magnitude of the electronic barrier directly correlates with the thermodynamic driving force, a statement of the Hammond postulate, then as the driving force increases the rate of reaction increases, eventually reaching a maximum rate. The quantum model has a... 

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