Atomic configurations, tunneling reactions

The common character of the phenomenon stimulated the introduction of quantum notions into the theory of chemical reactions, notions that up to the second half of the 1970s were based exclusively on the one-dimensional tunneling model. Though in the frameworks of this model one may attempt to explain a strong dependence of reaction rates on the medium properties by the existence of the barrier whose parameter spectrum is determined by the distribution of reagent configurations, the insufficiency of such treatment is shown by quantitative comparison with experiment even in the case of reactions with H-atom transfer. 

The one-dimensional potential along the tunneling coordinate, represented by t/c(x) in Eq. (29.20), is a crude-adiabatic potential evaluated with the heavy atoms fixed in the equilibrium configuration, i.e. with y = Ay ,y5 = Ay it is equivalent to the potential along the linear reaction path. This symmetric doubleminimum potential has a maximum U (0) = Ug at x = 0, minima U( ( Ax) = 0 at X = +Ax, and a curvature in the minima given by the effective frequency Qq which accounts for the contribution of the normal modes of the minima to the reaction coordinate [27]. Eor the shape of the potential in the intermediate points we use an interpolation formula based on the calculated energies and curvatures near the stationary points. We have found that in many cases the simple quartic potential of the form... 

Tx represent the mass, frequency and distance traversed by the heavy atoms that control the distance between the H-donor and acceptor (such that Ar = ro — r ). According to this model, the configuration at which tunneling occurs is comprised of three coordinate systems (i) the environmental or solvent coordinate parametrized by the reaction driving force (AG°) and environmental reorganization (A) ... 

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