Electron charge concentration repulsion

Fig. 5 A simple model of electron repulsion and screening, (a) Electron charge concentrated firt a sphere of radius a (b) Electrostatic potential of an additional electron, given by eqns 5.9 and 5.10. (c) Effective nuclear charge as a function of clstance, for an atom with atomic number Z and Z-1 hner electrons concentrated on the sphere.

Note e = electron charge NA = Avogadro s number z, = charge of ion of type Mt = molar concentration of ions in the bulk e = dielectric constant of the medium 4 = energy of attraction A = Hamaker constant d = distance between the surfaces 4 = energy of repulsion = ionic concentration (in number/volume) T0 1 17 = viscosity of the liquid u = electrophoretic mobility... 

An unshared pair of electrons repels other pairs more than a shared pair of electrons does. This seems reasonable because a shared pair, which also spends time around another atom, should not offer as much charge concentration for repulsion as a pair of electrons that is not shared and therefore spends all of its time around the atom. 

The Laplacian thus displays where the electronic charge is locally concentrated or depleted [25, 26]. The topology of the valence shell charge concentration (VSCC), the region of the outer shell of an atom over which V p < 0, is in accordance with the Lewis and valence shell electron pair repulsion model. To each local maximum in the VSCC, a pair of bonded or non-bonded electrons can be assigned (Fig. 2). 

The Laplacian of the electronic charge density (V p(r)) describes two extreme situations, hi the first p r) is locally concentrated (V p(r) < 0) and in the second it is locally depleted (V p(r) > 0). Thus, a value of V p(r) < 0 at a BCP is unambiguously related to a covalent bond, showing that a sharing of charge has taken place. In a closed-shell interaction a value of V p(r) > 0 is expected, as found in noble gas repulsive states, in ionic bonds, in hydrogen bonds and in van der Waals molecules. 

Electron density maps based on theoretical calculations (methods in parentheses) are given in [22] (SCF-MO [23] also for the highest occupied MO 5ai), in [24] (SCF and Cl also for the three valence orbitals), in [10] (SCF-Xa-SW for the valence orbitals and the total valence shell), in [25] (SCF and SCGF [self-consistent group function]), and in [26] (united atom). The Laplacian V p of the charge density p showed four local concentrations of electronic charge in the valence shell of the central P atom in accordance with the VSEPR (valence shell electron pair repulsion) model [27] for this latter model and its application to PH3, see [28 to 31]. 

Knowledge of the accurate electron density is decisive especially for the development of chemical concepts that are based on the analysis of this observable. Such concepts are Gillespie s valence-shell electron-pair repulsion model [1149] or the ligand-induced charge concentrations [880,1150-1152] that are designed to predict molecular structures and even chemical reactivity. Both approaches can be related to Bader s theory of atoms in molecules [1153], for which relativistic generalizations have been discussed in the literature [1154,1155]. 

Lone pairs of electrons have a more concentrated electron charge cloud than bonding pairs of electrons. Their cloud charges are wider and slightly closer to the nucleus of the central atom. This results in a different amount of repulsion between different types of electron pairs. 

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