Quantitative Theories of Spontaneous Decomposition

The first quantitative formulation of the decomposition process was made by Marcellin, who did not attempt a solution. An interesting analysis was later made by Polanyi and Wigner, who treated the molecule as an elastic medium in which decomposition occurred when certain elastic waves (equivalent to the atomic vibrations) reinforced each other sufficiently to break a bond. The form of the law they then deduced was the same as that derived from discrete models and has been of considerable use in discussing the decomposition of unstable atomic nuclei, which is a related problem. 

The first usable results were obtained by Rice and Ramsperger and Kassel,who were able to deduce from a simplified model of a molecule, consisting of a set of harmonic oscillators, that 

The essential correctness of Eq. (V.5.1) for reactions that give the Arrhenius equation as a high-pressure limit has been demonstrated by Slater.- The proof is accomplished by a Laplace transform of the equation 

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