Activation energy empirical estimates

Empirical methods are of two types those that permit potential energy surfaces to be calculated and those that only allow activation energies to be estimated. Laidler has reviewed these. A typical approach is to establish a relationship between experimental activation energies and some other quantity, such as heats of reaction, and then to use this correlation to predict additional activation energies. In Section 5.3 we will encounter a different type of empirical potential energy surface. 

Fundamental advances are offered by the knowledge of energy states and their electronic distributions in organic compounds and the relationship of these to reaction mechanisms. The development, for example, of even an empirical and approximate general scheme for the estimation of activation energies would indeed be most notable. 

Activation Energy Considerations. Activation energy considerations can provide a basis for eliminating certain elementary reactions from a sequence of reactions. Unfortunately, the necessary activation energy data is seldom available, and one must estimate these parameters by empirical rules and generalizations that are of doubtful reliability. 

These results confirm the important role of the force constant of the reacting bonds in the formation of the activation barrier. The activation energies Ee0 for the R + RX reactions can easily be estimated from the empirical formulas [17] (units are given in brackets) ... 

The results of the experimental estimation of rate constants for all these reactions prove that larger the volume V4 of TS, lower the rate constant and higher the activation energy for reconstruction of the shape of the cage to form an appropriate orientation of polymer segments around TS. An empirical linear correlation between AEot = RT ln(/ci//cs) and the volume Vu of TS was found [8] as follows ... 

At present rate parameters for cis-trans isomerization reactions can be estimated by using the empirical model involving biradical transition states (Benson, 1976). That is, the transition state can be viewed as the —C —C — biradical, which rapidly rotates. Experimental rate parameters for a variety of cis-trans isomerization reactions are presented in Table XL As seen from this table, the A factors for these reactions are consistent with a tight transition-state model. Although not directly evident from Table XI, activation energies... 

Several empirical rules also exist for the estimation of activation energies of metathesis reactions. A useful method involves the consideration of the following prototype reaction written in the exothermic direction ... 

The bond-energy bond-order (BEBO) method developed by Johnston and Parr (1963), in spite of its nonkinetic basis, represents a broadly applicable empirical approach to estimating activation energies of metathesis reactions. 

Computational details of the BEBO method are discussed in Johnston (1966) and Brown (1981). As is evident from the foregoing discussion, although the BEBO method represents a general method to estimate activation energies, it is strictly apphcable to bimolecular metathesis reactions. In addition, in spite of its computational rigor, the BEBO method often does not lead to the determination of activation energies that are more accurate than the other empirical methods discussed earlier. 

Alfassi, Z. B., and Benson, S. W., A simple empirical method for the estimation of activation energies in radical molecule metathesis reactions, Int. J. Chem. Kinetics S, 879 (1973). Allara, D. L., and Edelson, D., A computational analysis of a chemical switch mechanism. Catalysis-inhibition effects in a copper surface-catalyzed oxidation, J. Phys. Chem. 81, 2443 (1977). 

The activation energy, E2, is not known. The empirical Semenov-Polanyi equation (46) (E = 11.5 + 0.25 AH) gives 8 E 10 kcal. per mole, depending on the nature of the C—H bond broken. Heicklen (29) prefers E = 5 kcal. per mole. Values of 6 to 8 kcal. per mole (Table I) have therefore been assumed. Benson (12) estimates that A2 — 10 12 2 cc. molecule 1 sec."1 hence, k2 has been calculated (Table I). 

There have been many attempts, some completely empirical, some less so, to calculate activation energies, but none of them has been able to give results reliable to better than a roughly estimated 10 Kcal/mole, which is useless for quantitative work. Glasstone et al., loc. cii.y outline a method which is the same as that used to get the molecular constants of the transition complex given above. 

In principle, equation (2) should provide a numerical estimate for Vq. However, in practice, values of w are so uncertain (see Appendix B) that equation (2) is more useful for estimating w from experimental values of Vq. A useful way to deduce an overall order and an overall activation energy for a reaction is to measure the T and p dependences of Vq and to correlate these empirically with equation (3) by adjusting n and E. ... 

The empirical equation (1) used in estimating activation energies for the reverse ene reactions shows some promise in yielding reasonable activation energy estimates for Cope and Claisen type rearrangements as well (Table 131). However, additional data are needed before the usefulness of equation (1) can be assessed. 

In the estimation methods discussed so far the quantities estimated have either been the rate constant or the pre-exponential factor in the Arrhenius expression. Methods for estimating the activation energy of bimolecular reactions are much less developed. Theoretical prediction, at the level required, is beyond current computational techniques except in some exceptional, simple cases. However, there have been empirical attempts to relate the activation energy for a series of related reactions e.g., H abstraction by methyl radicals from hydrocarbons, to the thermodynamics of the process. 

Both A and E may also be temperatme dependent. We can estimate the activation energy from either potential energy smfaces or various empirical relationships and the frequency factor from either collision theory, transition state theory or from computational chemistry software (see Appendix J). 

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