Electron localization function ELF

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 ... 

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). 

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. 

The study of chemical reactions requires the definition of simple concepts associated with the properties ofthe system. Topological approaches of bonding, based on the analysis of the gradient field of well-defined local functions, evaluated from any quantum mechanical method are close to chemists intuition and experience and provide method-independent techniques [4-7]. In this work, we have used the concepts developed in the Bonding Evolution Theory [8] (BET, see Appendix B), applied to the Electron Localization Function (ELF, see Appendix A) [9]. This method has been applied successfully to proton transfer mechanism [10,11] as well as isomerization reaction [12]. The latter approach focuses on the evolution of chemical properties by assuming an isomorphism between chemical structures and the molecular graph defined in Appendix C. 

The question remains whether the nodal planes, essential for the qualitative analysis, remain in the more advanced calculations of wavefunctions. To test this point, the electronic localization function (ELF) as implemented by B. Silvi and A. Savin [24] is used. In Figure 3 we summarize the results. 

Fig. 2. We show the electron localization function (ELF) of (from left to right and from above to below) the Cl-, the AlCLj-, the 12 1 , the A12C17-, and the AI4CI13- species. The purple colored space indicates high values of ELF or electron pairs. Therefore, electron deficiency can be recognized from the half open spheres.

To understand chemical processes, it is useful to have information besides total energies. Electron localization methods provide insight on the behavior of electrons in molecules. Properties, such as electron density, spin density, and the electron pair localization function (EPLF) [33], can routinely be computed by post-processing. The EPLF provides a quantitative description of electron pairing in molecular systems and has similarities to the electron localization function (ELF) of Becke and Edgecombe [34]. The QMC method is a particularly well-suited approach for obtaining such information because the simple and general definition of EPLF is easily evaluated in QMC. 

The pair density description of aromaticity of the chalcogenophenes was calculated using the atoms-in-molecules (AIM) and electron localization function (ELF) methods, with both methods yielding equal results for the formally single C-C single bond but differing for almost all other bonds <2000CPF1(257)175>. The molecular parameters of the... 

Several alternatives to the Mulliken population have been presented that attempt to provide more rigorous estimates of the charges on atoms in molecules or clusters although not all have been applied in chemisorption and catalysis. We quote the Natural Bond Order analysis, and the elegant topological analysis of the electron density or of the electron localization function, ELF, introduced by Becke and Edgecombe. " ELF analysis has... 

Fig. 3b. Electron localization function (ELF) in the plane of the Si,2 entities the white areas indicate large electron localization and denote regions of bonds and lone electron pairs the small isolated circular regions between the ring systems are cores of magnesium atoms...

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