Engineering approximations for activation energies in hydrogen transfer reactions

Previous investigators have often used the Polanyi relationship, extensions due to Seminov, or the BOC-MP/UBI-QEP relationship to estimate activation barriers in complex reaction networks. However, these relationships are not accurate for many reactions. In this article, a new engineering approximation for the estimate of activation barriers is presented. The approximation allows one to estimate barriers analytically, using known heats of reaction and one adjustable parameter, the intrinsic barrier. The equation was fit to the recommended values of activation energies for all 151 independent hydrogen transfer reactions in the NIST tables. All but nine of the reactions are fit within ± 4 kcal/mol. Of the nine failures, seven of the data points came from previous estimates, and may not be accurate. By comparison, Seminov's relationship fails for 47 of the reactions even though the Seminov relationship has three adjustable parameters compared to one in our approximation. The BOC-MP/UBI-QEP method gives errors of more than 10 kcal/mol for all 151 reactions and errors of more than 30 kcal/mol for many of the reactions. These results show that the new approximation is a significant improvement over the approximations that are currently in use.