Electronic localization function

Redress can be obtained by the electron localization function (ELF). It decomposes the electron density spatially into regions that correspond to the notion of electron pairs, and its results are compatible with the valence shell electron-pair repulsion theory. An electron has a certain electron density p, (x, y, z) at a site x, y, z this can be calculated with quantum mechanics. Take a small, spherical volume element AV around this site. The product nY(x, y, z) = p, (x, y, z)AV corresponds to the number of electrons in this volume element. For a given number of electrons the size of the sphere AV adapts itself to the electron density. For this given number of electrons one can calculate the probability w(x, y, z) of finding a second electron with the same spin within this very volume element. According to the Pauli principle this electron must belong to another electron pair. The electron localization function is defined with the aid of this probability ... 

The location of electrons linking more than three atoms cannot be illustrated as easily. The simple, descriptive models must give way to the theoretical treatment by molecular orbital theory. With its aid, however, certain electron counting rules have been deduced for cluster compounds that set up relations between the structure and the number of valence electrons. A bridge between molecular-orbital theory and vividness is offered by the electron-localization function (cf p. 89). 

According to calculations with the electron localization function (ELF) the electron pairs of the B6Hg cluster are essentially concentrated on top of the octahedron edges and faces (Fig. 13.12). 

Electron localization function for B6H6 (only valence electrons, without regions around the H atoms), shown as iso-surface with ELF = 0.80. (Reprinted from Angewandte Chemie [97] with permission from Wiley-VCH)... 

In this second edition the text has been revised and new scientific findings have been taken into consideration. For example, many recently discovered modifications of the elements have been included, most of which occur at high pressures. The treatment of symmetry has been shifted to the third chapter and the aspect of symmetry is given more attention in the following chapters. New sections deal with quasicrystals and other not strictly crystalline solids, with phase transitions and with the electron localization function. There is a new chapter on nanostructures. Nearly all figures have been redrawn. 

Distributed Electrostatic Moments Based on the Electron Localization Function Partition... 

Figure 6-4. Electron localization function domains (concentration of electrons) in glycine. Lone pair domains are displayed in red...

Pilme J, Piquemal J-P (2008) Advancing beyond charge analysis using the electronic localization function Chemically intuitive distribution of electrostatic moments. J Comput Chem 29 1440... 

Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371 683... 

Several methods have been used for analyzing the electron density in more detail than we have done in this paper. These methods are based on different functions of the electron density and also the kinetic energy of the electrons but they are beyond the scope of this article. They include the Laplacian of the electron density ( L = - V2p) (Bader, 1990 Popelier, 2000), the electron localization function ELF (Becke Edgecombe, 1990), and the localized orbital locator LOL (Schinder Becke, 2000). These methods could usefully be presented in advanced undergraduate quantum chemistry courses and at the graduate level. They provide further understanding of the physical basis of the VSEPR model, and give a more quantitative picture of electron pair domains. 

Fig. 2.7 Electron localization function (ELF) between the WAT oxygen atom and the y-phosphorus in the different steps of constrained AIMD at 2.2 A (a),... 

Fig. 2.8 The low-barrier hydrogen bond between Lysl6 and an oxygen atom of GTP /1-phosphate group. The electron localization function (ELF) is projected on the plane containing the three atoms involved in the LBHB. The red and yellow areas located between the... 

Kohout [10] used this function as an electron localization indicator (ELI). In the electron localization function (ELF), this function is scaled ... 

In a pericyclic reaction, the electron density is spread among the bonds involved in the rearrangement (the reason for aromatic TSs). On the other hand, pseudopericyclic reactions are characterized by electron accumulations and depletions on different atoms. Hence, the electron distributions in the TSs are not uniform for the bonds involved in the rearrangement. Recently some of us [121,122] showed that since the electron localization function (ELF), which measures the excess of kinetic energy density due to the Pauli repulsion, accounts for the electron distribution, we could expect connected (delocalized) pictures of bonds in pericyclic reactions, while pseudopericyclic reactions would give rise to disconnected (localized) pictures. Thus, ELF proves to be a valuable tool to differentiate between both reaction mechanisms. 

Introduces and analyzes the usefulness of local reactivity descriptors such as Fukui, shape, and electron localization functions... 

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