Electron localizability indicator

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...

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. 

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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