The ensemble theorem establishes that at 0 K, the dependence of the energy, or any other size extensive property, on the fractional occupation is given by a set of straight lines connected at integer number of electrons, implying that these functions are non-differentiable in these points. On the other hand, several important chemical concepts and principles have found theoretical support using the well known and widely used quadratic interpolation model proposed in 1983 by Parr and Pearson (PP model). By construction, the PP model has continuous first derivatives and, consequently, is in conflict with the ensemble theorem. In this work we show that a way to circumvent this drawback is by means of the 2-parabola model that satisfies the discontinuity condition dictated by the ensemble theorem, and also assuming the existence of the second derivative, the hardness, with respect to the number of electrons. This model leads to the definition of the electrodonating and electroaccepting powers, chemical reactivity descriptors that have been used in the recent literature. Inspired by these ideas, we present a global and local partitioning of the charge transferred predicted by the PP model that allow us to determine which direction of electron transfer, electrophilic or nucleophilic, prevails in a given reaction. Several applications to well known reactions like complexation, hydration of aldehydes and ketones, addition of Br2 to alkenes and Diels-Alder cycloaddtions will be presented. The model also serves to explain and quantify back-donation as it is illustrated in its application to the reaction between phosphines and a transition metal atoms. To show the potentiality of this approach, the partitioning of the amount of electrons transferred is applied to the interaction of the iron-sulfur ferrodoxin and a set of imidazopyridines, aiding to determine the action mechanism of these compounds.

Incorporating charge transfer directionality in a global and local charge transfer model

255th National Meeting (2018)

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