Electron sharing indexes

Matito, E., Sola, M., Salvador, R, Duran, M. (2007). Electron sharing indexes at the correlated level. Application to aromaticity calculations. Faraday Discuss. 135,325-345. Mebkhout, M. (1979). Algebraic theory of the chemical potential in the case of the usual gauge group. H /j. Pl s. 123(2), 317-329. 

Matito E, Sola M, Salvador P, Duran M (2007) Electron sharing indexes at the correlated level, application to aromaticity measures. Earaday Discuss 135 325-345... 

As may be seen, the charge transfer form by geometrical mean Eq. (3.229) is richer than that provided by the additive model equation (3.185) for atoms-in-molecule because containing also the equilibrium information through the parameter (3.227). Consequently, the electronic sharing index of atoms-in-molecule by geometric mean (3.229) becomes... 

Del Re and coworkers [131] were concerned with the relation of s character in hybrids to bond angles and have considered hybridization as described by local orbitals, determined by requiring that hybrids on different atoms have minimal overlap unless they participate in the same bond. Alternate approaches are provided by the bond index of Wiberg [132] and by the Trindle-Sinanoglu procedure [133] for the application of the physical criterion of Lennard-Jones and Pople [134,135], requiring that an electron in a localized orbital interact maximally with the electron sharing that orbital. 

The bond index is a function of the square of the charge density matrix elements, whereas the bond order is defined in terms of the charge density matrix elements themselves. It is a measure of the extent of electron sharing between two atoms, but it has the disadvantage that it is always positive and hence cannot describe antibonding situations. 

Variants and generalizations of the bond index were proposed by Mayer [Mayer, 1986b, 1986a Wang and Werstiuk, 2003 Ponec and Cooper, 2005]. For example, in the framework of the AIM theory, starting from the correlation function characterizing the extent of the electron sharing and defined as... 

Shghtly earher than the appearance of NICS, attempts to construct numerical characteristics of the electron delocalization based on Bader s quantum theory of atoms in molecules (QTAIM) (1990MI) or electron localization function (ELF) (1990JCP5397) had begun. The most important for aromaticity description are electron sharing indices. For example, the delocalization index (DI) provides a value 6(A,B) which is the number of electrons delocalized or shared between atoms A and B. The next useful aromaticity... 

The results of Eqs. (3.232) and (3.233) are nevertheless a quarter of the electronic sharing indices within the additive model of atoms-in-mole-cules, (3.217) and (3.220), respectively, modeling therefore weaker bonds. Nevertheless, the geometrical mean model still prescribes the sharing index as behaving like the bonding softness, within equilibrated atoms-in-molecule, i.e., the states ( ), being this way superior to the additive... 

Characterizes molecular stmcture also by their propensity to engage chemical reactivity, with specific frontier measure appropriately modeled by the Fukui function (the density to number of electrons derivatives) as well as the chemical hardness iteratively evolution among adducts in a complex chemical interaction or through various chemical interactions channels (so explaining by quantum chemical reactivity principles the Le Chatelier-Braim principle of reactive equilibrium and bonding, or the electronic delocalization by novel sharing index, just to name few preeminent applications) ... 

The basin of the penultimate (3rd) shell in fee Cu is populated by 16.40 e but the localization index is only 13.64. An analysis of the de-localization indices shows that it is mainly due to the electron sharing with its core basin (5 = 2.56) as well as nearest valence basins (5 = 0.26). Direct electron exchange with the penultimate shell of the nearest Cu atom is in order of magnitude smaller (5 = 0.03). 

Because the H2 molecule contains just one electron of each spin, its EBO can be computed analytically and is identically equal to 1 for any of the above choices of projector. The closely related shared electron distribution index (SEDI) measures the number of electrons shared between two atoms irrespective of the spins at e and Because this correlation decreases... 

As has just been described, when a covalent bond forms between two atoms, there is no reason to assume that the pair of electrons is shared equally between the atoms. What is needed is some sort of way to provide a relative index of the ability of an atom to attract electrons. Linus Pauling developed an approach to this problem by describing a property now known as the electronegativity of an atom. This property gives a measure of the tendency of an atom in a molecule to attract electrons. Pauling devised a way to give numerical values to describe this property that makes use of the fact that the covalent bonds between atoms of different electronegativity are more stable than if they were purely... 

Note that the bond order index defined by Mayer accounts for the covalent contribution to the bond (this is why of late it is often mentioned as shared electron pair density index, SEDI). As such, the index cannot be expected to produce the integer values corresponding to the Lewis picture if a bond has a significant ionic contribution. The bond order index defined in this way measures the degree of correlation of the fluctuation of electron densities on the two atoms in question [7]. 

The bond order traditionally means the number of electron pairs shared between two bonded atoms. The sharing of eleetrons between any two atoms in a molecule is measured by the deloealisation index 8 A,B). This index is the magnitude of the exchange of the eleetrons in the basin of atom A with those in the basin of atom [111] ... 

SEDI = shared-dectron distribution index —> quantum-chemical descriptors ( electron density)... 

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