Coulombic attraction

Madeluag constant For an ionic crystal composed of cations and anions of respective change z + and z, the la ttice energy Vq may be derived as the balance between the coulombic attractive and repulsive forces. This approach yields the Born-Lande equation,... 

Thus E. is the average value of the kinetic energy plus the Coulombic attraction to the nuclei for an electron in ( ). plus the sum over all of the spin orbitals occupied in of the Coulomb minus exchange interactions. If is an occupied spin orbital, the temi [J.. - K..] disappears and the latter sum represents the Coulomb minus exchange interaction of ( ). with all of the 1 other occupied spin orbitals. If is a virtual spin orbital, this cancellation does not occur, and one obtains the Coulomb minus exchange interaction of cji. with all N of the occupied spin orbitals. 

The simplest example is that of tire shallow P donor in Si. Four of its five valence electrons participate in tire covalent bonding to its four Si nearest neighbours at tire substitutional site. The energy of tire fiftli electron which, at 0 K, is in an energy level just below tire minimum of tire CB, is approximated by rrt /2wCplus tire screened Coulomb attraction to tire ion, e /sr, where is tire dielectric constant or the frequency-dependent dielectric function. The Sclirodinger equation for tliis electron reduces to tliat of tlie hydrogen atom, but m replaces tlie electronic mass and screens the Coulomb attraction. 

The ability of living organisms to differentiate between the chemically similar sodium and potassium ions must depend upon some difference between these two ions in aqueous solution. Essentially, this difference is one of size of the hydrated ions, which in turn means a difference in the force of electrostatic (coulombic) attraction between the hydrated cation and a negatively-charged site in the cell membrane thus a site may be able to accept the smaller ion Na (aq) and reject the larger K (aq). This same mechanism of selectivity operates in other ion-selection processes, notably in ion-exchange resins. 

Every electron in a molecule has a Coulombic attraction to its own nucleus Hii = J iH idx. In addition, it has an athaction to all other nuclei in the molecule Hij = J Coulombic attraction between nuclei and the electrons normally... 

The first three terms in Eq. (10-26), the election kinetic energy, the nucleus-election Coulombic attraction, and the repulsion term between charge distributions at points Ti and V2, are classical terms. All of the quantum effects are included in the exchange-correlation potential... 

Were we to simply add the ionization energy of sodium (496 kJ/mol) and the electron affin ity of chlorine (—349 kJ/mol) we would conclude that the overall process is endothermic with AH° = +147 kJ/mol The energy liberated by adding an electron to chlorine is msuf ficient to override the energy required to remove an electron from sodium This analysis however fails to consider the force of attraction between the oppositely charged ions Na" and Cl which exceeds 500 kJ/mol and is more than sufficient to make the overall process exothermic Attractive forces between oppositely charged particles are termed electrostatic, or coulombic, attractions and are what we mean by an ionic bond between two atoms... 

To conclude this section let us note that already, with this very simple model, we find a variety of behaviors. There is a clear effect of the asymmetry of the ions. We have obtained a simple description of the role of the major constituents of the phenomena—coulombic interaction, ideal entropy, and specific interaction. In the Lie group invariant (78) Coulombic attraction leads to the term -cr /2. Ideal entropy yields a contribution proportional to the kinetic pressure 2 g +g ) and the specific part yields a contribution which retains the bilinear form a g +a g g + a g. At high charge densities the asymptotic behavior is determined by the opposition of the coulombic and specific non-coulombic contributions. At low charge densities the entropic contribution is important and, in the case of a totally symmetric electrolyte, the effect of the specific non-coulombic interaction is cancelled so that the behavior of the system is determined by coulombic and entropic contributions. 

The first two terms represent the kinetic energy of the nuclei A and B (each of mass M), whilst the fourth term represents the kinetic energy of the electron (of mass m). The fifth and sixth (negative) terms give the Coulomb attraction between the nuclei and the electron. The third term is the Coulomb repulsion between the nuclei. 1 have used the subscript tot to mean nuclei plus electron, and used a capital I. ... 

Acid catalysis increases reactivity both para and ortho to the site of protonation. Coulombic attraction of an anionic nucleophile to the vicinity of the positive center will to some extent remove the proton (65), forming the less reactive azine and the nucleophile s... 

The dominant force in ionic liquids is Coulombic attraction between ions. The Coulombic attraction term is given by Equation (3.1-2) ... 

Thus in water at room temperature the work done in separating the charges against the forces of their mutual Coulomb attraction will be equal to 73 per cent of the quantity —T S, since, in accordance with (24) the term —TSS will be 1.36 times the increment in the free energy. Now when we come to apply these considerations to ions that are not... 

The Orientation of Water Molecules Adjacent to an Ion. Order and Disorder in the Vicinity of Solute Particles. Coulomb Attraction and Repulsion between Ions. Activity Coefficients. The Distance of Closest Approach. Activity Coefficients of Various Solutes. Forces Superimposed on the Coulomb Forces. 

According to a large number of experimental studies, the most stable phologen-erated species in the lowest excited stales of conjugated chains are electron-hole pairs bound by Coulomb attraction and associated to a local deformation of the backbone, i.e., polaron-excilons [18]. A good insight into the properties of these species can be provided by quantum-chemical calculations our recent theoretical... 

Salts of diazonium ions with certain arenesulfonate ions also have a relatively high stability in the solid state. They are also used for inhibiting the decomposition of diazonium ions in solution. The most recent experimental data (Roller and Zollinger, 1970 Kampar et al., 1977) point to the formation of molecular complexes of the diazonium ions with the arenesulfonates rather than to diazosulfonates (ArN2 —0S02Ar ) as previously thought. For a diazonium ion in acetic acid/water (4 1) solutions of naphthalene derivatives, the complex equilibrium constants are found to increase in the order naphthalene < 1-methylnaphthalene < naphthalene-1-sulfonic acid < 1-naphthylmethanesulfonic acid. The sequence reflects the combined effects of the electron donor properties of these compounds and the Coulomb attraction between the diazonium cation and the sulfonate anions (where present). Arenediazonium salt solutions are also stabilized by crown ethers (see Sec. 11.2). 

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