Chemical Reactivity in the {N, NS, v(r)} Space

Electrophilicity index revisited

This review aims to be a comprehensive, authoritative, critical, and accessible review of general interest to the chemistry community; because the electrophilicity index is a very useful global reactivity descriptor defined within a conceptual density functional theory framework. Our group has also introduced electrophilicity based new global and local reactivity descriptors and also new associated electronic structure principles, which are important indicators of structure, stability, bonding, reactivity, interactions, and dynamics in a wide variety of physico-chemical systems and processes. This index along with its local counterpart augmented by the associated electronic structure principles could properly explain molecular vibrations, internal rotations and various types of chemical reactions. The concept of the electrophilicity index has been extended to dynamical processes, excited states, confined environment, spin-dependent and temperature-dependent situations, biological activity, site selectivity, aromaticity, charge removal and acceptance, presence of external perturbation through solvents, external electric and magnetic fields, and so forth. Although electrophilicity and its local variant can adequately interpret the behavior of a wide variety of systems and different physico-chemical processes involving them, their predictive potential remains to be explored. An exhaustive review on all these aspects will set the tone of the future research in that direction.

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.

A computational investigation of the selectivity and mechanism of the Lewis acid catalyzed oxa-Diels-Alder cycloaddition of substituted diene with benzaldehyde

The selectivity and the mechanism of the uncatalyzed and AlCl₃ catalyzed hetero-Diels-Alder reaction (HDR) between ([E]-4-methylpenta-2,4-dienyloxy)(tert-butyl)dimethylsilane 1 and benzaldehyde 2 have been studied using density functional theory at the MPWB1K/6-31G(d) level of theory. The uncatalyzed HDR between diene 1 and alkene 2 is characterized by a polar character and proceeds via an asynchronous one-step mechanism for the meta paths and synchronous for the ortho ones. In the presence of AlCl₃ catalyst, the mechanism changes to be stepwise, while the first step is the rate-determining step. The activation energies widely decrease, and the polar character increases dramatically. A large analysis of the mechanism is performed using the activation strain model/energy decomposition analysis (ASM/EDA) model, the natural bond orbital (NBO) and state specific dual descriptors (SSDDs). The obtained results indicate that the combined interaction energy associated with the distortion of the reactants in these HDR are at the origin of the observed kinetics. NBO analyses were applied to estimate the Lewis-acid catalyst donor-acceptor interaction with the molecular system. The SSDD analysis shed light into the orientation effects on the reaction kinetics by providing important information about charge transfer interactions during the chemical reaction. It indicates that the more favorable HDR pathway have the lowest excitation energies, facilitating the interaction between diene 1 and benzaldehyde 2 moieties. Non-covalent interaction (NCI) and QTAIM analyses of the meta-endo structure indicate that the presence of several weak NCIs formed at this approach is at the origin of the meta-endo selectivity.

How predictive could alchemical derivatives be?

The chemical space contains all possible compounds that can be imagined. Its size easily equals the number of fundamental particles in the observable universe. Rational design of compounds aims to find those sectors of the chemical space where compounds optimize a set of desired properties. Then, rational design demands tools to efficiently navigate the chemical space. Ab initio alchemical derivatives offer the possibility to navigate, without empiricism, the energy landscape through alchemical transformations. An alchemical transformation is any process, physical or fictitious, that connects to points in the chemical space. In this work, those transformations are constructed as a perturbative expansion of the energy with respect to perturbations in the stoichiometry. The response functions of that expansion are what is called alchemical derivatives. In this work we assess how effective alchemical derivatives are in predicting energy changes associated to changes in the composition. We do this by including in the expansion, for the first time, electrostatic, polarization and electron-transfer effects. The system we chose is one that challenges alchemical derivatives because none of these effects dominates its behavior. The transmutations studied here correspond to substitutional doping of Al₁₃ with up to four atoms of Si, Al_13-nSi_n. Two types of transformations are considered, those in which the number of electrons remains constant and those in which the number of electrons also changes. It is found that contrary to what has been reported before, polarization cannot be neglected. If polarization is not included, alchemical derivatives fail to predict the change of energy and the relative energy between isomers. For isoelectronic substitution of four or more atoms, the perturbative approach collapses because the strength of the perturbation becomes too strong to guarantee convergence of the series. It is shown, however, that if only one atom is mutated at a time, alchemical derivatives rank pretty well the isomers of Al_13-nSi_n according to their energy. In the case of non-isoelectronic transformations, it is observed that the series rapidly diverges with increasing number of electrons. In this situation, it becomes more important to keep the degree of transmutation of the parent system small.

Condensed-to-atoms electronic Fukui functions within the framework of spin-polarized density-functional theory

A simple formalism devised to calculate the condensed-to-atoms Fukui function [R. R. Contreras, P. Fuentealba, M. Galván, and P. Pérez, Chem. Phys. Lett. 304, 405 (1999)] has been further analyzed within a spin-polarized density-functional theory framework. The model is based on a frozen-core approximation to these local reactivity indices [M. Galván, A. Vela, and J. L. Gázquez, J. Phys. Chem. 92, 6470 (1988)], giving us an extended local reactivity description of systems based on the frontier spin-up and spin-down molecular orbitals. Degenerate molecular spin orbitals have been explicitly included in our model equations. Computational results for the nitric oxide (NO) and some simple carbene systems are presented in order to test the model. These quantities have been discussed in the context of changes both in charge density and spin density within the context of electron charge transfer or spin-polarization processes.

Philicity indices within the spin-polarized density-functional theory framework

The electrophilicity index is analyzed within the framework of spin-polarized density-functional theory. In this context, constrained philicities, omega(N) identical with (mu(N))(2)(2eta(NN)), are introduced in order to define the capability of a system to acquire or donate electrons in a process at constant spin number. The spin-philicity/spin-donicity indices, omega(S)(+/-) identical with (mu(S) (+/-))(2)(2eta(SS)), are examined and rationalized here as the philicity of a given system to change its spin-polarization state, as being defined through the spin potential mu(S) and spin hardness eta(SS) for a process at constant number of electrons. The local extension of these indices has been also outlined and numerical results have been discussed on the analysis of the electrophilic nature of some simple carbene systems both in the singlet and triplet states.

Hardness and softness reactivity kernels within the spin-polarized density-functional theory

Generalized hardness and softness reactivity kernels are defined within a spin-polarized density-functional theory (SP-DFT) conceptual framework. These quantities constitute the basis for the global, local (i.e., r-position dependent), and nonlocal (i.e., r and r'-position dependents) indices devoted to the treatment of both charge-transfer and spin-polarization processes in such a reactivity framework. The exact relationships between these descriptors within a SP-DFT framework are derived and the implications for chemical reactivity in such context are outlined.

Do Fukui Function Maxima Relate to Sites of Metabolism? A Critical Case Study

The usefulness of local reactivity descriptors for understanding drug metabolism is investigated. Electrophilic Fukui functions are calculated for 18 drugs and 11 agrochemicals and their relation to experimentally observed metabolites is discussed. Maxima of the Fukui functions correspond to major sites of metabolic attack in many examples, facilitating a posteriori understanding of experimental findings. In the second part of the paper, the nature of the electrophilic oxidant species in cytochromes, called "Compound I" (Cpd I), is investigated within the Fukui framework. Nucleophilic Fukui functions are calculated involving the relevant spin states of Cpd I, allowing a more qualitative, intuitive understanding of its reactivity.