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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1971 Feb;68(2):402–405. doi: 10.1073/pnas.68.2.402

Calculation of the Reaction Cross Section from a Rate Constant by the Method of Steepest-Descent

S H Lin 1,2, H Eyring 1,2
PMCID: PMC388948  PMID: 16591906

Abstract

The reaction cross section of a bimolecular reaction has been calculated from the corresponding rate constant by the inverse Laplace transform. In carrying out the inverse Laplace transform, the method of steepest-descent has been used. As applications, the reaction cross sections for the rate constant of k(T) = kTne-E0/kT and for the rate constant of the absolute reaction rate theory have been calculated. The computation of the energy density function associated with the definition of the weighted-average cross section has also been discussed.

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