Rate constants for decarboxylation reactions calculated using no barrier theory

Abstract

No barrier theory (NBT) provides both a qualitative way of thinking about what makes a reaction fast or slow and a quantitative way of calculating the rate constant (free energy of activation) corresponding to a particular mechanism. The origin and development of this idea are reviewed and examples of its use for qualitative understanding are presented before applying it to a set of decarboxylations. From the literature, a set of best values for rate constants for decarboxylation was picked. Detailed mechanistic models were developed for reactions leading to delocalized “anions” or to localized anions. It was necessary to have pKa values for ionizaion of the carbon acids corresponding to all of these species and these were selected from the literature or estimated by linear free energy relations (or occasionally calculated from proton exchange data). Over the entire range of measured decarboxylation rate constants, a range of 1025 in rate constant, the calculated values were in good agreement with experiment, with two exceptions: malonate dianion, which has been reported but probably not measured, and glycine, where it is possible that a different mechanism is being followed, unfortunately, one which we do not yet know how to treat by NBT. NBT is both a qualitatively and quantitatively useful tool for understanding chemistry.