Anharmonicity reactions

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

Figure 5. Reaction probabilities for a given instance of the noise as a function of the total integration time Tint for different values of the anharmonic coupling constant k. The solid lines represent the forward and backward reaction probabilities calculated using the moving dividing surface and the dashed lines correspond to the results obtained from the standard fixed dividing surface. In the top panel the dotted lines display the analytic estimates provided by Eq. (52). The results were obtained from 15,000 barrier ensemble trajectories subject to the same noise sequence evolved on the reactive potential (48) with barrier frequency to, = 0.75, transverse frequency co-y = 1.5, a damping constant y = 0.2, and temperature k%T = 1. (From Ref. 39.)...

The second set of problems in dynamics are those of scattering theory where the Hamiltonian is of the form H = H0 + V and the interaction V vanishes when the colliding particles are far apart. It is usually assumed that the H0 part is already solved and that the interesting or the hard part is to account for the role of V. For realistic systems, which are anharmonic, even the role of H() can be quite significant. An example that has received much recent attention is the reaction of vibrationally excited HOD with H atoms (Sinha et al., 1991 Figure 8.2). The large difference in the OH and OD vibrational frequencies means that the stretch overtones of HOD are primarily local in character (cf. Section 4.21). It follows that one can excite HOD to overtones localized preferentially on either one of the two bonds and that an approaching H atom will abstract prefer-... 

One might ask how the Marcus case of crossing in the harmonic region can arise. In a sense, that is the surprising situation. How can significant reaction occur without reaching the anharmonic part of the potential To think of this, it is probably wise to remember that Marcus theory was first applied to electron transfer of the outer-sphere variety. Albery answers by pointing out that a reaction coordinate which is constructed from the intersection of parabolic surfaces for several... 

The force controls the remarkably persistent coherence in products, a feature that was unexpected, especially in view of the fact that all trajectory calculations are normally averaged (by Monte Carlo methods) without such coherences. Only recently has theory addressed this point and emphasized the importance of the transverse force, that is, the degree of anharmonicity perpendicular to the reaction coordinate. The same type of coherence along the reaction coordinate, first observed in 1987 by our group, was found for reactions in solutions, in clusters, and in solids, offering a new opportunity for examining solvent effects on reaction dynamics in the transition-state region. 

Such a method has recently been developed by Miller. et. al. (28). It uses short lengths of classical trajectory, calculated on an upside-down potential energy surface, to obtain a nonlocal correction to the classical (canonical) equilibrium probability density Peq(p, ) at each point then uses this corrected density to evaluate the rate constant via eq. 4. The method appears to handle the anharmonic tunneling in the reactions H+HH and D+HH fairly well (28), and can... 

Schmidt81 has commented that symmetry-forbidden, concerted modes of reaction may be quite accessible if the reaction path is short, the force constants in reactant and product are both small, and the anharmonicities large. He cites a case where a forbidden reaction occurs readily with an activation energy of only 25 kJ mol-1. 

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