Electron localization function kinetic energy density

LT2A Local square kinetic energy density exchange functional depending only on Ihe kinetic energy density (i.e.. not at all on the electron density). Maximoff, S. N., Enzerhof, M., Scuseria, G. E. 2002. 7. Chem. Phys., 117, 3074. 

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. 

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. 

We have used transferable atom equivalent (TAE) descriptors [116,117] that encode the distributions of electron density based molecular properties, such as kinetic energy densities, local average ionization potentials, Fukui functions, electron density gradients, and second derivatives as well as the density itself. In addition autocorrelation descriptors (RAD) were used and represent the molecular geometry characteristics of the molecules, while they are also canonical and independent of 3D coordinates. The 2D descriptors alone or in combination with the latter 3D descriptors were calculated for 26 data sets collated by us from numerous publications. These data sets encompass various ADME/TOX-related enzymes, transporters, and ion channels as... 

Most importantly, these systems are amenable to the Electron Localization Function (ELF) method [21]. This is a local measure based on the reduced second-order density matrix, which as pioneered by Lennard-Jones [22] should retain the chemical significance and at the same time reduce the complexity of the information contained in the square of the wave function ELF is defined in terms of the excess of local kinetic energy density due to the Pauli exclusion principle, T r), and the Thomas-Fermi kinetic energy density, Th(r) ... 

These functions provide a local measure of the effect of the Pauli repulsion on the kinetic energy density. In the region of space where the Pauli repulsion is weaker than in a uniform electron gas of identical density, we should say where the local parallel pairing is lower, i/ji r) and are... 

The term meta-GGAs is, however, often also used for fimctionals that include dependences on local kinetic-energy densities. It may be observed that - from a formal point of view - the solutions to the single-particle, so-called Kohn-Sham equations (13) also are functionals of the electron density and, therefore, Ee may include dependences on those. The quantity... 

Apart from these indexes, the electron localization function (ELF) is another approach to measure aromaticity [34]. It is based on the properties of the electron density. Introduced by Becke and Edgecombe [34(a)], ELE is defined in terms of excess local kinetic energy density due to Pauli exclusion principle, T[p(f)], and Thomas-Fermi kinetic energy density, Th[p(r)], as follows ... 

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