Theoretical Calculation of Activation Energies

The practical importance of the Arrhenius equation k = se EIRT has been stressed in previous lectures. The quantities 5 and E depend only slightly on temperature, and within a factor of ten or so s can often be estimated as 1013 for unimolecular reactions and 109 for bimolecular reactions, when concentrations are expressed in moles per liter. An estimation of E, then, permits a prediction of reaction rates at different temperatures. 

Because the temperature variation of 5 is to be compared with the strong exponential variation of e EIRT it is difficult to separate from experimental data the temperature dependence of 5 and E. For this reason it is a convenient working rule to assume that 5 is a constant. The activation energy E is then given by the slope of the line obtained by plotting 2.303 R log k against 1/T, as shown in Fig. 5. In most cases little error will be introduced by this simplification. 

Many reactions follow neither the first order nor the second order equation but the evidence more and more seems to support the view that most reactions are fundamentally unimolecular or bimolecular and that the complex reactions which follow neither first order nor second order equations consist really of two or more simple reactions of the uni- or bimolecular type. Eventually, perhaps, these intermediate steps can be independently determined. 

The important thing in predicting reaction rates is to determine the activation energy E of the reaction—or, in the case of composite reactions, to determine the activation energy of the slowest reaction step. Because the equation is of the exponential type, s need not be known very accurately and the quantity of limiting accuracy is E. It is the purpose of these next lectures to show how E can be estimated and how these estimates are useful 

2 Pelzer and Wigner, Z. physik. Chem., B15, 445 (1932) Born and Oppen-heimer, Ann. Phys., 84, 457 (1927). 

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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. 

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