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 pK a 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 10 25 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.Résumé : La théorie sans barrière fournit d'une part une façon qualitative de réfléchir sur ce qui fait qu'une réaction est rapide ou lente et d'autre part une façon quantitative de calculer la constante de vitesse (énergie libre d'activation) correspondant à un mécanisme particulier. On passe en revue l'origine et le développement de cette idée et on présente des exemples de son utilisation dans la compréhension qualitative avant de l'appliquer à un ensemble de décarboxylations. On a tiré de la littérature un ensemble des meilleures valeurs pour les constantes de vitesse de décarboxylation. Des modèles de mécanismes réactionnels détaillés ont été développés pour des réactions conduisant à des anions délocalisés ou localisés. Il était nécessaire d'avoir les valeurs de pK a pour l'ionisation des acides carboniques correspondants à chacune des espèces et celles-ci ont été sélectionnées à partir de la littérature ou elles ont été évaluées par des relations d'énergie linéaires ou elles ont été occasionnellement calculées à partir de données d'échange de proton. Sur l'ensemble complet des constantes de vitesse de décarboxylation, une plage de constantes de vitesse relatives s'étalant de 1 à 10 25 , les valeurs calculées ont en bon accord avec les valeurs expérimentales, à deux exceptions près: le dianion de l'acide malonique a été rapporté, mais qui n'a probablement pas été mesuré et la glycine pour laquelle il est possible qu'un mécanisme différent soit impliqué, un mécanisme qu'on ne peut malheureusement pas encore traiter par la théorie sans barrière. La théorie sans barrière (TSB) est un outil qualitativement et quantitativement utile pour la compréhension de la chimie.Mots-clés : décarbox...

Equilibrium constants for enolization in solution by computation alone

“…Cyclohexanone enol has a pK a of 11.70 while 3‐hydroxy‐2‐cyclohexen‐1‐one (the enol of 1,3‐cyclohexanedione) has a pK a of 4.34, for a difference of 7.4. The pK a of the enol of a carboxylic acid ester is approximately 6; the effect of conjugation to an ester may well be smaller than for conjugation to a ketone so that the expected pK a for Meldrum's enol would be somewhat greater than −1.4, consistent with the value of 1.9 obtained above. The enol content of dialkyl malonate is unknown, but Graham and Williams suggested that it is near pK E = 11, based on the assumption of diffusion control for a reaction known to be close to diffusion control.…”

Ab initio study of the mechanism of carboxylic acids cross-ketonization on monoclinic zirconia via condensation to beta-keto acids followed by decarboxylation

“…Decarboxylation of beta-keto acids, by itself, is an important reaction in connection with catalysis by enzymes, the mechanism of which has been debated for almost a century [21,22]. The reaction has been extensively studied in a solution [23][24][25][26][27], and in the gas phase [28].…”

“…Guthrie in his No Barrier Theory analysis of the beta-keto acids decarboxylation has discussed the most energy demanding electronic and structural changes required to occur when going through the transition state [23,27]. They include stretching C-C bond, changing hybridization of the carboxylic carbon from sp 2 to sp, that of the alpha carbon from sp 3 to sp 2 , and transferring the proton.…”

Hydration of nitriles: an examination in terms of No Barrier Theory

“…No Barrier Theory proposes that for a simple process, there is no kinetic barrier but simply a quadratic potential. A simple process is defined as one for which the energy is a quadratic function of a suitable progress variable The kinetic barriers that are observed for essentially all real chemical reactions result from the need for more than one simple process to occur more or less simultaneously for the overall reaction to take place.…”

“…We have computed the thermodynamic properties of nitriles, imidic acids, and amides studied in this work and, from these, the equilibrium free energies of reaction for both stages of nitrile hydrolysis. We wish to report that the rate constants for nitrile hydrolysis in acid or base have been calculated using No Barrier Theory (NBT), leading to the computed rate constants in satisfactory agreement with experiment. These calculations cover the range of reactivity thus far reported.…”