Global and Local Reactivity Descriptors Based on Quadratic and Linear Energy Models for α,β-Unsaturated Organic Compounds

<div>Global and local descriptors of chemical reactivity can be derived from conceptual density functional theory. Their explicit form, however, depends on how the energy is defined as a function of the number of electrons. Within the existing interpolation models, here, the quadratic and the linear energy model were used to derive global descriptors as the electrophilicity and nucleophilicity (defined as the negative of the ionization potential) and local descriptors employing either the corresponding condensed fukui function in the linear model or the local response of the global descriptor in the quadratic model. The ability of these descriptors to predict the reactivity of molecules with more than one reactive site was first studied on a set of α ,β -unsaturated ketones, where experimental rate constants for the nucleophilic attack is known. With the validated descriptors the reactivity of α ,β -unsaturated carboxylic compounds with different heteroatoms as α ,β -unsaturated thioesters, esters and amides as alternative substrates for the enzymatic CO<sub>2</sub> fixation studied experimentally by Erb <i>et al.</i> was addressed. The carbon dioxide fixation involves the reduction of the neutral α ,β -unsaturated carboxylic compounds by a nucleophilic attack of a hydride anion from NADPH and the following electrophilic attack by carbon dioxide. It was found that condensed values of the linear fukui function within the fragment of molecular response approximation describe best the reactivity of α ,β -unsaturated ketones. For the two relevant processes involved in CO<sub>2</sub> fixation the amides present the largest reactivity in vacuum and in aqueous solution compared to the esters and thioesters and may, therefore, serve as alternative sustrates of carboxylases.</div>