Electronic distribution electron localization function

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

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... 

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. 

FIGURE 5. Summary of electronic distribution in aniline, (a) Bond distances (A), NBO charges [bracket, in au] and Wiberg indices (parentheses, in au). (b) Topology of the electron density determined from atom-in-molecule calculations p(r) = electron density, L = Laplacian of the density defined as L(r) = —V2p(r) and e = ellipticity of the bond critical point, (c) Laplacian map of the density, (d) Iso-surfaces of the electron localization function, ELF = 0.87 the values are the populations of the valence basins... 

FIGURE 20. Aspects of the electronic distribution in the vertical triplet aniline (triplet state at the singlet ground-state geometry) (a) Differential density Pink represents the Ap(r) = 0.005 an, and blue represents the Ap(r) = —0.005 an isosurface of the differential density, (b) ELF = 0.87 isosurfaces of the electron localization function. Values correspond to basin populations and integrated spin densities (s values)... 

At a microscopic level, two kinds of functions can be derived from quantum mechanics. On the one hand are those corresponding to global properties such as the energy, expectation values of operators, chemical potential, or global hardness as defined within the conceptual DFT context [35] and on the other hand are local properties such as electron density distributions, the electron localization function ELF [24], local hardness [36,37], and the Fukui functions [38,39],... 

FIGURE 5.4 The differences in electron localization functions (ELFs) between the Becke-Edgecombe (BE) and Markovian (Ml) and (M2) formulations of Eqs. (5.388), (5.416), and (5.417), in left and right respectively, versus the homogeneous (/j-parameter) and inhomogeneous (g-parameter) influences on electronic distribution (Putz, 2009). 

Presents the Fokker-Planck quantum description of open systems, by considering the drift and diffusion contributions in quantum evolution, as based on a non-equilibrium Lagrangian, lading with generating of the so called Markovian families of electronic localization functions, accommodating the Thom s catastrophe theory in an iimovative maimer, thus directly describing the atomic valence distribution as well as the molecular formation. 

Therefore, the analysis of the electron density distribution of the molecular aggregates held together through non-covalent interaction can provide valuable information on both their properties and how these change with respect to the isolated building blocks. This analysis can be carried out by means of different techniques, the most popular of which are the Quantum Theory of Atoms in Molecules (QTAIM) theory [76, 77], the Electron Localization Function (ELF) [78-80] and the Natural Bond Orbital (NBO) method [81]. 

So, the localization functions indicate the ratio of the non-uniformly localized electronic distribution to the uniform delocalization of the electronic gas, accordingly with the Heisenberg quantum principle of delocalization and that of the Pauli indiscemibility. It was however proved, through a series of hydracids molecules that the atoms-in-molecule electronic localization function in its exponential form and with error interpretation, as recently recommended by the authors recipe, see the Volume II of the present five-volume book, stands as a viable quantum tool for identifying bonds within the bonding space. 

Illumination creates excess electrons and holes which populate the extended and localized states at the band edges and give rise to photoconductivity. The ability to sustain a large excess mobile carrier concentration is crucial for efficient solar cells and light sensors and depends on the carriers having a long recombination lifetime. The carrier lifetime is a sensitive function of the density and distribution of localized gap states, so that the study of recombination in a-Si H gives much information about the nature of the gap states as well as about the recombination mechanisms. 

Interest in the electronic properties of interfaces centers around a-Si H/Si3N4, because this combination is used in multilayers (Section 9.4) and field effect transistors (Section 10.1.2). The electronic structure of the interface is illustrated in Fig. 9.18. Apart from the band offset which confines carriers to the a-Si H layer, the distribution of localized interface states and the band bending are the main factors which govern the electronic properties of the interface. The large bulk defect density of the SijN also has an effect on the electronic properties near the interface. Band bending near the interface may result from the different work functions of the two materials or from an extrinsic source of interface charge - for example, interface states. 

---