Electron localizability

It should be borne in mind that the resemblance of a Fermi hole density to that of a localized valence orbital is obtained only when the reference electron is placed in the neighbourhood of a local maximum in the VSCC. The Fermi hole and hence the density of the reference electron are much more delocalized for general positions throughout the valence region (see Fig. E7.4(f)). Localized molecular orbitals thus overemphasize electron localiz-ability and do not provide true representations of the extent to which electrons are spatially localized. 

In this equation, x, denotes the space (r ) and spin (o- ) coordinates of the electron labeled by i. As other examples of local functions, we can mention the local softness [41], the local hardness [36], the Fukui function [38], the Becke and Edgecombe electron localization function ELF [24], the spin pair composition [42], or the electron localizability indicator of Kohout et al. [43],... 

Kohout, M., Pemal, K., Wagner, F. R., Grin, Y. (2004). Electron localizability indicator for correlated wavefunctions. I. Parallel-spin pairs. Theor. Chem. Acc. 112,453-459. 

Fig. 2.10 Electron localizability indicator in Ba8Gc43 (top) the investigated fragment of the crystal structure (middle) distribution of ELI-D in the planes of Ba atoms (left) and in the plane of the defect hexagonal face of the tetrakaidecahedron (right), (bottom) isosurface of F= 1.25 visualizing the Ge-Ge bonds and lone pairs at the three-bonded germanium atoms...

The application of the electron localizability approach allows for studying details of the atomic interactions in intermetalhc clathrates. This may contribute to the understanding of structural features which cannot be achieved within the Zintl— Klemm concept. Another, from chemical point important, outcome of the electron localizabUity approach is the electron-locahzabihty-based oxidation number (ELIBON [77]) which is the real-space equivalent of the traditional oxidation numbers. Apphcation of oxidation numbers on intermetaUic clathrates allows for new ways of understanding of experimentally observed clathrate compositions and for novel redox routes for their preparation. 

Kohout M (2004) A measure of electron localizability. Int J Quantum Chem 97 651-658... 

Kohout M, Pemal K, Wagner FR, Grin Y (2004) Electron localizability indicator for correlated wavefunctions. i. parallel-spin pairs. Theoret Chem Acc 112 453—459... 

Delocalization indices have been also evaluated for the topological basins of the electron localizability indicator (ELI), whose topology defines partition of space into basins, representing various elements of chemical bonding, emerged from atomic shells cores, penultimate shells, lone pairs and bonds. 

Abstract The electron pair is a central object in chemist s view of the chemical bond. The definition and description of the electron pair in the position space is a complex problem within the quantum chemistry. Several different possibilities of how to accomplish this task, i.e., how to describe the localizability of an electron and electron pair, are given in a historical survey. The derivation of the electron localizability indicator (ELI) is presented and the application of ELI for the bonding analysis is examined for few systems. The importance of the ELI-q describing the singlet-coupled electron pairs and its connection to Lewis idea of bonding is highlighted. 

Keywords Correlation Electron localizability Electron pair ELI Fermi hole... 

In the following a special class of functions, termed electron localizability indicators [3-8], based on simultaneous evaluation of electron density and electron pair density will be described. This combination is utilized with the aim to analyze the correlation of electronic motion [9]. Apart from the density function point of view, the energy of a molecule can be thought as stemming from two parts - a one-particle terms in wide sense derived from the electron density and a two-particle terms derived from the electron pair density (of course, the full 2-matrix is stiU necessary today). The interplay between the electron density on the one hand and the electron pair density on the other hand could thus elucidate the situation in the molecular system. 

The definition of the electron localizability indicator (ELI) of Kohout was based on a different approach (inspired by Savin s suggestion [47] of a breathing sphere enclosing constant charge as well as Bader s proposition of correlation of electronic motion [9]). For ELI, first the whole space is partitioned at once into nonoverlapping compact regirais (called micro-cells) enclosing a fixed electron... 

The < RSP is the most important ingredient for the definition of whole family of functionals, one of which is the electron localizability indicator (ELI) [3]. The functionals are derived from the integrals of the so-called san ling function over the regions of the [Pg.140]

An interesting choice for the control function is, among others [25, 81], the electron pair density (respectively a specific part of it). Then, the rnRSP describes microcells enclosing fixed pair population. The procedure in which the distribution of certain variant of populations (e.g., the electronic charges) is determined over micro-cells controlled by (fixed) value of another population variant (e.g., electron pair population) is termed the restricted populations approach [68]. The electron localizability indicator ELI-D is a quasi-continuous rescaled distribution of charges over micro-cells enclosing fixed amount cod of electron pairs ... 

For all the abovementioned spin variants, the electron density can be chosen as the control function. The resulting electron localizability indicator ELI-q is a quasi-continuous rescaled distribution of pair populations over micro-cells enclosing fixed charge... 

In the preceding sections, the electron localizability indicator (ELI) was presented and applied to few systems. ELI includes in its definition integrals of both the electron density and the pair density. With this at hand, it is connected with the correlation of electronic motion, which is in certain sense a local description of electron pairing. It can be expected that specific ELI patterns will able to visualize (and possibly quantify) the bonding situation. This ability strongly depends on the ELI variant used to examine the system. 

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