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

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.

The electronic temperature and the effective chemical potential parameters of an atom in a molecule. A Fermi-Dirac semi-local variational approach

We developed a numerical procedure to compute the electronic temperature and the effective (local) chemical potential undergone by electrons belonging to a particular molecular species. Our strategy relies on consider atomic basins as open quantum (sub)systems within the context of the quantum theory of atoms in molecules. Each basin is represented by the two parameters, the electronic temperature and the effective chemical potential, which are determined by distributing electrons (fermions) imbedded in each atomic region, through a Fermi-Dirac semi-local variational procedure. The results obtained for 40 different chemical species show that the effective chemical potential is a useful tool to reveal the most acidic/basic atoms in a molecule while the electronic temperature is closely related to the concept of chemical hardness at the local level. Our numerical data also indicate that the electronic temperature values undergone by electrons imbedded in atomic basins are way beyond the room temperature condition, allowing to fractionally occupy several of the one-particle quantum states. In this context, we developed two new indexes useful to reveal outstanding orbitals involved in the chemical reactivity of atoms in molecules.

Local electrophilicity

In this work some possibilities for deriving a local electrophilicity are studied. First, we consider the original definition proposed by Chattaraj, Maiti, and Sarkar (J Phys Chem A 107:4973, 2003), in which the local electrophilicity is given by the product of the global electrophilicity, and the Fukui function for charge acceptance is derived by two different approaches, making use of the chain rule for functional derivatives. We also modify the proposals based on the electron density so as to have a definition with the same units of the original definition, which also introduces a dependence in the Fukui function for charge donation. Additionally, we also explore other possibilities using the tools of information theory and the temperature dependent reactivity indices of the density functional theory of chemical reactivity. The poor results obtained from the last two approaches lead us to conjecture that this is due to the fact that the global electrophilicity is not a derivative, like most of the other reactivity indices. The conclusion is that Chattaraj's suggestion seems to be the simplest, but at the same time a very reliable approach to this important property.

Comment on “Revisiting the definition of local hardness and hardness kernel” by C. A. Polanco-Ramirez, M. Franco-Pérez, J. Carmona-Espíndola, J. L. Gázquez and P. W. Ayers, Phys. Chem. Chem. Phys., 2017, 19, 12355

In this comment we show that the derivation proposed Polanco-Ramirez et al. appears naturally in the Taylor expansion of the energy, showing that their whole construction is not artificially built.

Reply to the ‘Comment on “Revisiting the definition of local hardness and hardness kernel”’ by C. Morell, F. Guégan, W. Lamine, and H. Chermette, Phys. Chem. Chem. Phys., 2018, 20, DOI: 10.1039/C7CP04100D

Starting from the chain rule for functional derivatives we develop a general procedure to define the local and non-local counterparts of a global reactivity indicator.

New Fukui, dual and hyper-dual kernels as bond reactivity descriptors

We define three new linear response indices with promising applications for bond reactivity using the mathematical framework of τ-CRT (finite temperature chemical reactivity theory). The τ-Fukui kernel is defined as the ratio between the fluctuations of the average electron density at two different points in the space and the fluctuations in the average electron number and is designed to integrate to the finite-temperature definition of the electronic Fukui function. When this kernel is condensed, it can be interpreted as a site-reactivity descriptor of the boundary region between two atoms. The τ-dual kernel corresponds to the first order response of the Fukui kernel and is designed to integrate to the finite temperature definition of the dual descriptor; it indicates the ambiphilic reactivity of a specific bond and enriches the traditional dual descriptor by allowing one to distinguish between the electron-accepting and electron-donating processes. Finally, the τ-hyper dual kernel is defined as the second-order derivative of the Fukui kernel and is proposed as a measure of the strength of ambiphilic bonding interactions. Although these quantities have never been proposed, our results for the τ-Fukui kernel and for τ-dual kernel can be derived in zero-temperature formulation of the chemical reactivity theory with, among other things, the widely-used parabolic interpolation model.

Local chemical potential, local hardness, and dual descriptors in temperature dependent chemical reactivity theory

From the definition of a local chemical potential, well-behaved expressions for the local hardness and the dual descriptors are derived.