Evans-Polanyi rule

A study directed toward understanding when gas phase dynamics closely resembles the dynamics of the same reaction in solution was performed by Li and Wilson. io In this work, they used a model asymmetric A -t- BC reaction. By using an asymmetric reaction, Li and Wilson were able to test the validity in the solution phase of the Evans—Polanyi rule,3n which has proven to be quite useful in understanding gas phase reaction dynamics. The Evans-Polanyi rule states for a collinear A -t- BC reaction, that if the barrier to reaction is located early in the reaction coordinate, then translational excitation of the reactants is necessary to climb this barrier and vibrational excitation of the products will result. Conversely, a late barrier to reaction requires vibrational excitation of the reactants and results in translational excitation of the products. This rule has been validated numerous times in the gas phase and is an ideal example of how a simple rule can explain the dynamics of a large number of reaction systems. 

To test the Evans—Polanyi rule in the solution phase, Li and Wilson performed simulations of the asymmetric A -I- BC solution in the gas phase and in a dense 100 Ar atom solvent. They began the dynamics at the transition state of the reaction and ran 1 ps of dynamics both forward and backward in time from those initial conditions. They calculated over 1700 reactive trajectories in both the solution phase and in the gas phase, monitoring the appropriate vibrational and translational energies. 

The gas phase results reflected the Evans-Polanyi rule very closely— primarily reactant translational energy needed for the early barrier and primarily vibrational energy for the late barrier, as shown in Figure 20. Li and Wilson ° also found that the gas phase and solution phase vibrational energies tracked each other almost perfectly over the 1 ps they studied, as shown in... 

Chemical intuition, which is very useful in the location of minima, usually fails in the search for saddle points. The symmetry of the transition-state structure was discussed and it was shown that many transition states exhibit low symmetry (130-132). Some empirical rules have been developed for approximate localization of the transition state. The rule referred to in the literature as the Bell-Evans- Polanyi-Leffler-Hammond rule is well known the more exoergic the process, the more the transition-state geometry resembles that structure which belongs to a higher energy minimum on the given potential energy surface. This idea has been supported by calculations on SN2-activated complexes (133). 

As reaction rates are often expressed in a modified Arrhenius form, simple approaches like those based on linear free energy relationships, such as Evans-Polanyi, are adopted (Susnow et al., 1997). Automatic generators usually refer to thermochemical kinetics methods (Benson, 1976) and the kinetic parameters rely on a limited number of reference rate constants and are extended to all the reactions of specific classes adopting analogy rules (Battin-LeClerc et al., 2000 Ranzi et al., 1995). Recently, extensive adoption of ab initio calculations of activation energies and reaction rates are adopted (Saeys et al., 2003, 2004, 2006). 

In this equation, ka and kb should remain nearly constant in the presence of hydrogen or deuterium, and thus these terms do not contribute to kinetic isotope effect. Small differences in kc can be estimated from the Evans-Polanyi-Semenov rule. (11)... 

Figure 5.5 Potential energy profile along the reaction coordinate for an early, midway, and late barrier. We show the two asymmetric cases as corresponding to an exoergic and endoergic reaction. The correlation between location of the barrier, shown by an arrow, and relative stability of reactants and products can be understood on the basis of the Evans-Polanyi mode/that we will discuss. The correlation shown is a useful rule of thumb, known in organic chemistry as Hammond s postulate. In structural terms this is sometimes stated as the more exoergic the reaction, the more the configuration at the barrier will be reactant-like.

Evans and Polanyi- have noted that in a homologous series of exothermic abstraction reactions (A + BC AB + C), the change in activation energy is related to the change in heat of reaction by the relation AAact = ofA act where a is a constant for a given series. The more recent and more accurate results on methyl radical abstractions would seem, however, to place limits on the quantitative value of the rule. Voevodskii has pro-... 

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