Calculation of activation energy

The a priori calculation of activation energies or potential energy surfaces for radical—molecule reactions is still beyond the present scope of quantum mechanics despite the use of large computers [382]. One of the more successful of several empirical or semi-empirical attempts to calculate activation energies of H-abstraction reactions is the bond energy-bond order (BEBO) method developed by Johnston [382]. There are no adjustable parameters involved but rather empirical relations of a non-kinetic type. For the general situation 

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Simple collision theory does not provide a detailed interpretation of the energy barrier or a method for the calculation of activation energy. It also fails to lead to interpretations in terms of molecular structure. The notable feature of collision theoiy is that, with very simple means, it provides one basis for defining typical or normal kinetic behavior, thereby directing attention to unusual behavior. 

All rate constants are in units of 1. mole i sec."L Rate constants quoted for vinyl acetate at 30°C have been interpolated from reported values at 25°C. Measurements at temperatures other than 30° and 60°C have been included for the calculation of activation energies and frequency factors. 

The semiempirical nature of the methods used to construct multidimensional potential energy surfaces makes the quantitative validity of the results questionable. Hence the present state of the theoretical calculation of activation energies is unsatisfactory. 

Note that the transition path sampling method can be also used for the calculation of activation energies (as opposed to activation free energies) [29]. This approach is useful for systems in which it is not possible to identify transition states. 

The IPM as a semiempirical model of an elementary bimolecular reaction appeared to be very useful and efficient in the analysis and calculation of the activation energies for a wide variety of radical abstraction and addition reactions [108-113]. As a result, it became possible to classify diverse radical abstraction reactions and to differentiate in each class the groups of isotypical reactions. Later this conception was applied to the calculations of activation energies and rate constants of bimolecular reactions of chain generation [114]. In the IPM, the radical abstraction reaction, for example,... 

The parameters used for calculations of activation energies and rate constants are summarized in Table 15.16. The calculated values of E and k for the reaction of ozone with antioxidants are given in the handbook [4], They are in good agreement with the experimental data [113]. 

Calculation of Activation Energy from the JMAK Model and the Arrhenius Equation... 

For accurate comparison of relative energies, one must add to the BO-optimized energy the zero-point vibrational energy (ZPVE), which in the harmonic approximation is half the sum of the fundamental frequencies. This correction is most critical for the calculation of activation energies. The contribution of the ZPVE of the mode corresponding most closely to the reaction coordinate is lost completely. Processes that involve breaking of a bond to H are the most seriously affected torsional changes are the least affected. 

R-H BDEs energies are certainly one parameter that has to be taken into account when discussing H-transfer reactions, yet many other aspects have to be considered to account for the kinetics of such a reaction (for the calculation of activation energies in H-abstraction reactions, see Zavitsas and Chatgilialoglu 1995). 

The significance of this type of curve in chemical problems and in photochemistry was stressed by Franck.6 The curve is also of great importance in calculating specific heats and thermodynamic quantities. We are interested in it here because it is essential in the semi-empirical calculation of activation energies. 

In Table II are given the three fundamental constants for a number of atom pairs which are of interest in chemical kinetics. From these constants Morse curves can be constructed as just shown for bromine, and these, in turn, are necessary for the calculation of activation energies of chemical reactions. 

It has been emphasized that these calculations of activation energies are only approximate, commonly involving an error of 3,000 calories or more. Frequently the data for the constants D, r0 and co0 are not known with accuracy and the assumption of the fourteen per cent coulombic energy and the plotting of the empirical Morse curves are subject to considerable uncertainty. In some cases the calculations are quite tedious but frequently some type of symmetry greatly reduces the labor of computations and after some experience one finds it sufficient to select for computation only a limited number of points in the neighborhood of the... 

An alternative equation, also derived by Marcus18, is from Johnston s19 BEBO calculation of activation energies. It is specifically useful for these H atom transfer processes. This is Eq. (5), with the terms as above. 

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