Quantum mechanical activation barrier

G. A. Voth and E. V. O Gorman, J. Chem. Phys., 94, 7342 (1991). An Effective Barrier Model for Describing Quantum Mechanical Activated Rate Processes in Condensed Phases. 

Changes in the degrees of freedom in a reaction can be classified in two ways (1) classical over the barrier for frequencies o) such that hot) < kBT and (2) quantum mechanical through the barrier for two > kBT. In ETR, only the electron may move by (1) all the rest move by (2). Thus, the activated complex is generated by thermal fluctuations of all subsystems (solvent plus reactants) for which two < kBT. Within the activated complex, the electron may penetrate the barrier with a transmission coefficient determined entirely by the overlap of the wavefunctions of the quantum subsystems, while the activation energy is determined entirely by the motion in the classical subsystem. 

It is important to note that as early as 1931, the density of electronic states in metals, the distribution of electronic states of ions in solution, and the effect of adsorption of species on metal electrode surfaces on activation barriers were adequately taken into account in the seminal Gurney-Butler nonquadratic quantum mechanical treatments, which provide excellent agreement with the observed current-overpotential dependence. 

Third, with recent advances made in theoretical and computational quantum mechanics, it is possible to estimate thermochemical information via electronic structure calculations (Dewar, 1975 Dunning et al., 1988). Such a capability, together with the transition state theory (TST) (Eyring, 1935), also allows the determination of the rate parameters of elementary reactions from first principles. Our ability to estimate activation energy barriers is... 

This simplified approach is analogous to the more rigorous absolute rate treatment. The important conclusion is that the bimolecular rate constant is related to the magnitude of the barrier that must be surmounted to reach the transition state. Note that there is no activation barrier (/.e., that AG = 0) in cases where no chemical bond is broken prior to chemical reaction. One example is the combination of free radicals. (In other cases where electrons and hydrogen ions can undergo quantum mechanical tunneling, the width of the reaction barrier becomes more important than the height.)... 

Computational studies of the CH3CCI to vinyl chloride rearrangement (Scheme 7.17) provide an activation energy that can be compared to those measured by LFP experiments.The gas phase computed a is 11.5 kcal/ mol, which is reduced to 9.3 kcal/mol in (simulated) heptane." The experimental value in isooctane is 4.9 kcal/mol. Some of the 4.4 kcal/mol difference between the computed and observed a can be narrowed if quantum mechanical tunneling (QMT) is included in the calculations The migrant H atom can tunnel through the activation barrier as well as chmb over The... 

A key point that must be made is diat quantum mechanical tunneling through the Marcus-theory barrier when it is non-zero can increase the rate for electron transfer just as is true for any other activated process. Because the electron is so light a particle, tunneling can be a major contributor to die overall rate. Models for electron tunneling will not, however, be presented here. 

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