Relation between activation and threshold energies

Question

Activation energy $E_\mathrm{a}$ and threshold energy $E_0$ appear to be equivalent quantities:

In particle physics, the threshold energy for production of a particle is the minimum kinetic energy a pair of traveling particles must have when they collide.

In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction.

How are activation energy and threshold energy defined, exactly? Why do both terms exist? Is there a context where both terms are used, and they refer to different aspects of the same phenomenon?

Answer 1

The activation energy $E_a$ of a reaction is the amount of energy required to take reactants to products across some reaction coordinate. The threshold energy $E_0$ is related, but defined as the minimum kinetic energy of a particle in order to bring about collisions where atom-exchange is possible. The terms are mostly used in different contexts (activation energy is common in discussions of organic synthesis, but kinetic energy of particles isn't) but they also are not fully congruent. Specifically, reactions that don't require much collision for reaction progress may not have them congruent.

For example, the activation energy of thymine-thymine dimerization in DNA strands is large—this energetic barrier is surpassed when ultraviolet light excites the appropriate electrons and initiates the dimerization. This process is ambivalent to kinetic energy (inside the DNA strand, the nucleic acid residues do not move very much.)

Regardless, the concepts are very close and mostly a matter of context. Threshold energy can more easily be extrapolated to other contexts, like particle physics. Chemical reactions are a subset of particle collisions, and the term is more relevant there.

Answer 2

Arrhenius activation energy $E_\mathrm{A}$ is one more closely related quantity that needs to be distinguished from activation and threshhold energies. The difference between the quantities is briefly outlined in IUPAC Green Book [1, pp. 64, 67]:

The term activation energy is also used for an energy threshold appearing in the electronic potential (the height of the electronic energy barrier). For this “activation energy” the symbol $E_0$ and the term threshold energy is preferred, but $E_\mathrm{a}$ is also commonly used. Furthermore, $E_0$ may or may not include a correction for zero point energies of reactants and the transition state. It is thus recommended to specify in any given context exactly which activation energy is meant and to reserve (Arrhenius) activation energy only and exactly for the quantity defined in the table. $E_\mathrm{A}$ depends on temperature and may be written $E_\mathrm{A}(T).$

$E_0$ is the threshold energy for reaction, below which no reaction is assumed to occur. In transition state theory, it is the difference of the zero-point level of the transition state and the zero-point level of reactants.

Reference

1. IUPAC. Quantities, Units and Symbols in Physical Chemistry (the “Green Book”), 3rd ed.; Cohen, R. E., Cvitaš, T., Frey, J. G., Holmström, B., Kuchitsu, K., Marquardt, R., Mills, I., Pavese, F., Quack, M., Stohner, J., Strauss, H. L., Takami, M., Thor, A. J., Eds.; RSC Publishing: Cambridge, UK, 2007. ISBN 978-0-85404-433-7.