New insights in conceptual DFT: New model for the calculation of local reactivity indices based on the Sanderson's principle

Abstract

In the present study, a new model mainly based on the Sanderson's principle for estimating important reactivity descriptors, such as the local hardness and the local electrophilicity, is introduced. New approximations and corrections were taken into account, which led to a significantly different development, obtaining more realistic results than the previous ones used. The Fukui condensed-to-atom indices: f − and f + have been used in this model, but their role is clearly described in the development, reducing therefore, the ambiguity of previous developments where the indices could be arbitrarily used. It is important to underline that the proposed model is relatively simple, but leads to qualitatively correct results. It also makes it possible to interpret the hard-soft acid base principle in local terms, as can be seen in the sample set of reactions (Diels-Alder type) selected as an example in the present study, and which provides very coherent results with the expected experimental reactivity. K E Y W O R D S conceptual DFT, HSAB principle, reactivity descriptors, Sanderson's principle, UCA-FUKUI

Density functional theory, chemical reactivity, and the Fukui functions

“…We have reviewed some of the works which led towards the development of Conceptual Density Functional Theory in problems of chemical reactivity. Recent developments of these studies (Kaya et al 2018;Miranda-Quintana et al 2018b, a;Echegaray et al 2017;Lamine et al 2019;Fuentealba et al 2016;Gázquez et al 2018;Coulibaly et al 2019;Lee et al 2019;Sánchez-Márquez et al 2018) demonstrate the ongoing interest in this field.…”

Introducing a new model based on electronegativity equalization principle for the analysis of the natural bond orbital reactivity in the c‐DFT background

“…Now, by solving Equation ( 26) we obtain Equation (27). Figure 1 represents the main parameters of Equations ( 25)- (27). Note that in the new…”

Correlations between Fukui Indices and Reactivity Descriptors Based on Sanderson’s Principle

“…In a previous study, we introduced a very simple model mainly based on Sanderson’s principle (or the principle of electronegativity equalization), − and we have used this model to estimate several reactivity descriptors, for example well-known atomic parameters such as local hardness − or local electrophilicity, − as well as to define new parameters. In addition, it made it possible to obtain several types of functions to describe reactivity.…”

“…Note that a quadratic expansion was used to describe the global variation of energy Δ E as a function of the charge variation Δ N and the global parameters μ 0 and η. This expansion is truncated from the second derivative, thus neglecting the effect of the third derivative, and this is consistent with the work of Fuentealba et al However, at the local level we have used a cubic expansion; if we use a quadratic expansion at the local level, we obtain an important incoherence as set forth in the Appendix III that was included with a previous publication …”