Electrons localization

Summarizing, both kinds of electron-electron interactions (exchange and correlation, X and C) have to be accounted for in order to yield a satisfying description of atoms, molecules, and solids, at least in principle. Practical experience has shown that different approaches have been followed to deal with these effects, and molecules and solids have also been treated differently. 

The physical nature of a solid (metal, semiconductor, insulator) also suggests different strategies for the proper inclusion of exchange and correlation. 

19) For example, the complete set of atomic shells caimot be resolved for very heavy atoms. In addition, ant/ such decomposition is somewhat arbitrary (see Section 2.7). 

The evaluation of P r,rs) using Hartree-Fock theory (full inclusion of exchange interactions, see Section 2.11.3) and by spherically averaging up to tg can be written as a Taylor series in tg, and the first nonzero entry of the pair probability of like spins, which is quadratic in rj, reads 

The crucial interpretative step now consists in assuming that the lower the pair probability of finding a second like-spin in the proximity of the left reference spin-up electron (this is what D(r) measures inside the grey region in 

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Wimmer E, Fu C L and Freeman A J 1985 Catalytic promotion and poisoning all-electron local-density-functional theory of CO on Ni(001) surfaces coadsorbed with K or S Phys. Rev. Lett. 55 2618-21... 

Whitten J L and Pakkanen T A 1980 Chemisorption theory for metallic surfaces Electron localization and the description of surface interactions Phys. Rev. B 21 4357-67... 

Electrophilic substitution reactions of unsubstituted quinoxaline or phenazine are unusual however, in view of the increased resonance possibilities in the transition states leading to the products one would predict that electrophilic substitution should be more facile than with pyrazine itself (c/. the relationship between pyridine and quinoline). In the case of quinoxaline, electron localization calculations (57JCS2521) indicate the highest electron density at positions 5 and 8 and substitution would be expected to occur at these positions. Nitration is only effected under forcing conditions, e.g. with concentrated nitric acid and oleum at 90 °C for 24 hours a 1.5% yield of 5-nitroquinoxaline (19) is obtained. The major product is 5,6-dinitroquinoxaline (20), formed in 24% yield. 

Examine the geometry of the most stable radical. Is the bonding in the aromatic ring fuUy delocalized (compare to model alpha-tocopherol), or is it localized Also, examine the spin density surface of the most stable radical. Is the unpaired electron localized on the carbon (oxygen) where bond cleavage occurred, or is it delocalized Draw all of the resonance contributors necessary for a full description of the radical s geometry and electronic structure. 

The process is exothermic, suggesting that the phenoxy radical is particularly stable. Display the spin density surface for phenoxy radical. Is the unpaired electron localized or delocalized over several centers Is the unpaired electron in the a or 7t system Draw appropriate Lewis structures that account for your data. 

Examine the spin density surface for BHT radical. Is the unpaired electron localized or delocalized Examine BHT radical as a space-filling model. What effect do the bulky tert-butyl groups have on the chemistry of the species (Hint BHT radical does not readily add to alkenes or abstract hydrogens from other molecules.)... 

The electrons occupy the in-phase combined orbital after the interaction. They are distribnted not only in the orbital occnpied prior to the interaction, bnt also in the overlap region and the orbital vacant prior to the interaction. The electrons localized in the occupied orbital before the interaction delocalize to the overlap region and the vacant orbital after the interaction (Scheme 13). 

The antibonding properties of the geminal a-a interactions has recently led to a theory of electron localization and its successful application to blue-shifting hydrogen bonds [129],... 

At the equilibrium inter-atomic distance R, two paired electrons of occupy the bonding orbital with a closed-shell low-spin singlet (S = 0). When the bond length is further increased, the chemical bond becomes weaker. The dissociation limit of corresponds to a diradical with two unpaired electrons localized at each atom (Fig. 1). In this case, the singlet (S spin-antiparaUel) and triplet (T spin-parallel) states are nearly degenerate. Different from such a pure diradical with... 

Figure 9.28. One-dimensional cuts through Figure 9.27 (a) X2 (b) Xj is the reaction coordinate with the charge and the electron localized.

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... 

Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92 5397... 

Savin A, Had OJ, Andersen J, Preuss H,Von Schering HG, Angew (1992) Electron localization in solid-state. Structures for the elements the diamond. Chem Int 31 187... 

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

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