Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Abstract

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles

“…Superscript "0" indicates that the term is evaluated for the isolated reagent; subscripts index the reagents. As explained in (Miranda-Quintana et al, 2022b), Eq. 3 can be iterated.…”

“…3 and the equation Eq. 33 in (Miranda-Quintana et al, 2022b), is that last it was assumed that ΔN A −ΔN B . That is, every electron that leaves one reagent goes to the other reagent, and the number of electrons in the combined system does not change.…”

“…Early attempts at quantifying well-matchedness were made by Berkowitz, Geerlings, and then, much later, by one of the present authors (Berkowitz, 1987;Langenaeker et al, 1995;Anderson et al, 2007a;Ayers, 2007;Anderson et al, 2007b;Ayers and Cardenas, 2013). In the first paper of this series (Miranda-Quintana et al, 2022b), we derived a general expression for the interaction energy between two reagents using DFT-CR and drew the links to other, more computational, DFT theories like density-functional embedding (Cortona, 1991;Vaidehi et al, 1992;Wesolowski and Warshel, 1993;Govind et al, 1999;Wesolowski, 2004;Wesolowski and Leszczynski, 2006), electronegativity equalization molecular mechanics (Yang and Mortier, 1986;Mortier et al, 1985;Mortier et al, 1986;Yang and Mortier, s1986;Mortier, 1987;Rappe and Goddard, 1991;Bultinck et al, 2002a;Bultinck et al, 2002b;Verstraelen et al, 2013), and density-based energy decomposition analysis (Wu et al, 2009).…”

Can we predict ambident regioselectivity using the chemical hardness?

“…Finally, it could be the case that we have to reinterpret the local HSAB principle in terms of ''charge-controlled bases prefer charge-controlled acids'' and ''frontier-controlled bases prefer frontier-controlled acids'', which is more in line with the more detailed treatments of C-DFT that have been recently proposed to account for the interaction between the reagents in a more detailed way. 104,105 This perspective has appeared in one way or another in previous studies, [106][107][108][109] and we will explore it in forthcoming contributions.…”

“…To evaluate this expression we first need to calculate the chemical potential of the product (an alternative derivation is provided in the Appendix). We can do this starting from the chemical potentials (eqn (19)) and hardnesses of the moieties A 1 B 1 and A 2 B 2 : 51,103–105 Then:Now we can calculate how the number of electrons changed for each of the four reactive centers (A 1 , A 2 , B 1 , and B 2 ) from their initial state in the reactants to their final state in the products:Then, with the help of eqn (1) and (21) turns into:Substituting eqn (23) and (24) in the above expression we get:While this is an expression for the energy difference between the reactants and products (as opposed to Ponti's), it is easy to see that it will not allow us to determine the regioselectivity of the cycloaddition reaction. The reason for this is that eqn (26) is independent of the orientation of the reactants; in other words, if we interchange the B 1 and B 2 indices, we will get exactly the same expression.…”