Current Organic Chemistry - Volume 15, Issue 20, 2011

The wave picture of the electron implies an always present electron delocalization. This electronic delocalization is not an observable, and therefore there is not an experimental property that allows measuring it directly. However, electronic delocalization reveals itself in several chemical phenomena that can be experimentally interrogated to have a measure of the degree of electron delocalization in our system. From a theoretical point of view, the fact that electron localization/delocalization is not an observable implies that there is not a unique and generally accepted measure of this property. A number of ways of putting this concept on a theoretically sound quantum mechanical basis have been developed, many of them based in one way or another on the concept of the Fermi hole. Tools such as the electron localization function (ELF), which provides a picture of the regions where the electron localization is high, or the quantum theory of atoms in molecules (QTAIM), which provides with a wealth of resources to tackle the electron structure in organic species, are nowadays routinely used in organic chemistry to rationalize a number of observable facts such as the molecular structure, stability, magnetic properties, and chemical reactivity of many molecules, in particular, π-conjugated molecules. Electron localization is also essential to know where local groups of electrons like core or valence electrons, electron pairs, bonding pairs, unpaired electrons, or π-electron subsystems are placed and, therefore, to discuss chemistry with the familiar organic way of thinking. In this issue devoted to “Electron Delocalization in Organic Chemistry”, we have gathered seven contributions showing several applications and developments of theoretical methods that account for electron delocalization. It is shown how these methods help to solve daily problems encountered in organic chemistry. Thus, Arrieta, de Cozar, and Cossío perform a critical review on the application of different geometric, energetic, magnetic, and electronic criteria to analyze the cyclic electron delocalization in an important group of pericyclic reactions. García-Revilla and Rocha-Rinza discuss the use of the ELF and delocalization indicators based on the QTAIM to quantify the relevance of electronic delocalization in electrophilic aromatic substitution reactions. Silva and de Lera make an exhaustive appraisal of the use of the bond ellipticity in the framework of the QTAIM to account for electron delocalization in structure and reactivity. Silvi and Reinhardt review the present situation of the electron localization function and show different examples in which this function can be helpful for quantum organic chemists. Fuentealba and Santos assess the application of this ELF and its decomposition into the π and σ parts as a measure of electron delocalization and aromaticity, while Andres, Berski, Domingo, Polo, and Silvi evaluate the use of the ELF to visualize the bond breaking/forming processes, forming/annihilation of lone pairs, and pair rearrangements along a reaction coordinate, thus providing a way to analyze the reaction mechanism at a molecular level. Finally, Angyan paves the way for future tools to measure electron delocalization as he suggests the use of a linear response function of the molecular charge density to an external perturbation as a new measure of electron delocalization in molecules. The present issue reveals many of the state-of-the-art methods used to account for electron delocalization in organic chemistry and, at the same time, we hope it will convince the reader about the importance of theoretical studies on electron localization/delocalization and how they significantly improve our understanding of many chemical processes.

The utility of the localization and localizability concepts for describing chemical situation is discussed. Two routes can be followed to get such a picture from wave functions which are in principle delocalized in nature. On the one hand are orbital localization techniques which are described in the context of their applicability to organic chemistry problems. On the other hand are methods relying on local functions which perform a partition of the molecular space into connected non overlapping regions. The Becke and Edgecombe localization function is presented in detail and its application to organic quantum chemistry reviewed.

Here, we provide an essay on the analysis of the reaction mechanism at the molecular level; in particular, the evolution of the electron pair, as it is provided by the ELF, is used to decribe the reaction pathway. Then, the reaction mechanism is determined by the topological changes of the ELF gradient field along a series of structural stability domains. From this analysis, concepts such as bond breaking/forming processes, formation/annihilation of lone pairs and other electron pair rearrangements arise naturally along the reaction progress simply in terms of the different ways of pairing up the electrons. To visualize these results some organic reaction mechanisms (the thermal ring aperture of cyclobutene and cyclohexa-1,3-diene) have been selected, indicating both the generality and utility of this type of analysis.

The ellipticity of the electron density at the bond critical points is a parameter computed in the framework of the Atoms in Molecules (AIM) analysis. This parameter provides a quantitative measurement of the anisotropy of the electron density at the BCP. The ellipticity has been originally associated to the π character of bonds, and therefore, it has been also employed as a measurement of delocalization and, ultimately, aromaticity. The number of applications of this parameter, however, has increased significantly in recent years and studies on the description of unusual bonds in charge transfer interactions, steric contacts, organometallic complexes, etc include the ellipticity as a useful chemical index. In this work a revision of the uses of ellipticity to characterize both molecular bonds and reactivity is provided.

Since in 1938 Evans and Warhurst established the analogy between electron delocalization in the transition structure of the Diels- Alder reaction and in benzene, many studies have been carried out to combine the concept of aromaticity with the Woodward- Hoffmann rules for thermally allowed pericyclic reactions. This review includes first a brief survey of the main aromaticity descriptors that have been applied successfully to the analysis of electron delocalization in the transition structures associated with pericyclic reactions. In the remaining sections pericyclic reactions such as cycloadditions, electrocyclizations, cheletropic reactions, the Claisen and Cope rearrangements and the ene reaction are covered. It is concluded that contemporary computational tools are reliable enough to quantify the magnitude of electron delocalization in thermally allowed pericyclic reactions. However, chemical variables such as regioand stereoselectivity are more difficult to correlate with aromaticity. In general, pericyclic and pseudopericyclic reactions can be distinguished using magnetic aromaticity descriptors: Transition structures associated with thermally allowed reactions are always Huckel or Mobius aromatic, whereas those associated with pseudopericyclic reactions exhibit low aromaticity, nonaromaticity or even low antiaromaticity.

The concept of localization and delocalization in molecules is discussed in terms of the response of the electronic system to an external perturbation. It is argued that both the spatial organization of electrons in pairs and the spatial distribution of the response intensity, reflect main features of the correlated motion of electrons, ultimately described by the pair distribution function of electrons. Various measures, derived from the linear charge density response function, are able to characterize localization in a rigorous way, in close analogy to the approach followed in solid state physics.

The Electron Localization Function (ELF) has played in the last time an important role in understanding the special characteristics of the chemical bond. The chemical interpretation of the ELF as an indicator of the regions of the space where it is most probable to find a localized electron pair has been of great value in order to understand some complex chemical bonds. In this work, the ELF has been used to study the delocalization and aromatic character of a diversity of molecules. It is shown that whereas the analysis of the total ELF does not provide clear information about aromaticity, the separation of the function on its σ and π parts yields indeed valuable information about it. Moreover, it is possible to construct a quantitative scale of aromaticity. It is also shown that the use of the ELF to understand aromaticity is complementary to other methodologies. The study includes mono substituted benzene derivatives, cyclic organic compounds, borazine molecule and the mechanism of acetylene trimerization.

Electron delocalization is a fundamental concept in chemistry. It is deeply rooted in many important chemical phenomena e.g. aromaticity, conjugation and the reactivity of a vast number of inorganic, organometallic and organic compounds. This review focuses on those theoretical studies in which electron delocalization indicators provide valuable insigths in the understanding of electrophilic aromatic substitutions. The considered approaches to deal with electron delocalization include primarily the quantum theory of atoms in molecules but also briefly the analysis of the electron localization function, the topography of the molecular electrostatic potential, the anisotropy of the induced current density and GIAO-derived charge delocalization modes. We go over the characterization of the electron delocalization in the most important intermediates of the electrophilic aromatic substitutions namely the Wheland intermediates and the π complexes formed by aromatic molecules and electrophiles. Then we discuss the relation between aromaticity and electrophilic aromatic substitutions. Finally, we give an account of the importance of the electron delocalization in the effect of the substituents on the regiochemistry and reactivity of an aromatic molecule towards an electrophilic attack. Besides reviewing the literature in an extensive way, it is our hope that this review will suggest directions of further progress in the field.