Sodium electron repulsions

Unfortunately, the Schrodinger equation for multi-electron atoms and, for that matter, all molecules cannot be solved exactly and does not lead to an analogous expression to Equation 4.5 for the quantised energy levels. Even for simple atoms such as sodium the number of interactions between the particles increases rapidly. Sodium contains 11 electrons and so the correct quantum mechanical description of the atom has to include 11 nucleus-electron interactions, 55 electron-electron repulsion interactions and the correct description of the kinetic energy of the nucleus and the electrons - a further 12 terms in the Hamiltonian. The analysis of many-electron atomic spectra is complicated and beyond the scope of this book, but it was one such analysis performed by Sir Norman Lockyer that led to the discovery of helium on the Sun before it was discovered on the Earth. 

Figure 5 shows the temperature dependence of disproportionation of the sodium salts of radical anions of tetraphenylethene. Several conclusions may be drawn from these data. Both disproportionations are endothermic, as shown by their enthalpy changes (AH) AH18 = 19 2 kcal/mol, and AH 19 = 13 2 kcal/mol. These observations may not be surprising because the electron-electron repulsion in the dianion may account for the endo-thermicity of the disproportionation. However, the large entropy gain (AS)... 

Two classes of charged radicals derived from ketones have been well studied. Ketyls are radical anions formed by one-electron reduction of carbonyl compounds. The formation of the benzophenone radical anion by reduction with sodium metal is an example. This radical anion is deep blue in color and is veiy reactive toward both oxygen and protons. Many detailed studies on the structure and spectral properties of this and related radical anions have been carried out. A common chemical reaction of the ketyl radicals is coupling to form a diamagnetic dianion. This occurs reversibly for simple aromatic ketyls. The dimerization is promoted by protonation of one or both of the ketyls because the electrostatic repulsion is then removed. The coupling process leads to reductive dimerization of carbonyl compounds, a reaction that will be discussed in detail in Section 5.5.3 of Part B. 

For sodium cations and chloride anions, q = + and q2 — - 1. To complete the calculation, we need to know how closely the ions approach each other before their mutual attraction is balanced by electron cloud repulsion. In the sodium chloride crystal this distance is 313 pm. Using this value for r, we can calculate the energy released in... 

The authors proposed the following picture of the silylene anion-radical formation. Treatment of the starting material by the naphthalene anion-radical salt with lithium or sodium (the metals are denoted here as M) results in two-electron reduction of >Si=Si< bond with the formation of >SiM—MSi< intermediate. The existence of this intermediate was experimentally proven. The crown ether removes the alkali cation, leaving behind the >Si - Si< counterpart. This sharply increases electrostatic repulsion within the silicon-silicon bond and generates the driving force for its dissociation. In a control experiment, with the alkali cation inserted into the crown ether, >Si — Si< species does dissociate into two [>Si ] particles. 

Close-packed spheres occupy 74.04% of a total volume, hence the hard-sphere radius of I" in these 2 1 salts in 2.03 A. Correction for the electrostatic attraction alone would give a monovalent iodide radius of about 2.24, an opposite repulsion-correction for the different co-ordination number would reduce this to about 2.10 A for the monovalent sodium-chloride type (see Appendix). Such values are consistent with our earlier estimates, but incompatible with the electron-density minimum value (4) of 1.94 A. 

Why is carbon so versatile in its ability to bond to very different kinds of elements The special properties of carbon can be attributed to its being a relatively small atom with four valence electrons. To form simple saltlike compounds such as sodium chloride, Na Cle, carbon would have to either lose the four valence electrons to an element such as fluorine and be converted to a quadripositive ion, C4 , or acquire four electrons from an element such as lithium and form a quadrinegative ion, C40. Gain of four electrons would be energetically very unfavorable because of mutual repulsion between the electrons. 

Before presenting the results which have been obtained for sodium chloride it is necessary to indicate the sources of the data used for this salt. Van der Waals coefficients were taken from a tabulation by Mayer (11) and electronic polarizabilities of the ions at zero frequency from the work of Tessman, Kahn, and Shockley (13). A value of 4.802 X 10-10 e.s.u. was used for the charge of the electron and the repulsive parameters by and p were taken from recent publications by Cubicciotti (5, 6). A value of a — 2.794 A. was computed for the nearest... 

It will be assumed that the ions are non-distorted the problem of polarization will be discussed later. In addition to the attraction between the ions there will be a repulsion caused by the completed electronic shells of the sodium and chloride ions. The transfer of paired electrons, as we have seen in Chapter 3, leads to a repulsion energy. Exact calculation of this energy is difficult but it may be done by an approximate method. The error involved does not significantly affect the result, as the repulsion energy is small in comparison with the energy of attraction. In Chapter 3 it was shown that the exchange energy of repulsion decreased exponentially with the distance between the atoms ... 

The theory of Born and Mayer has been extended by the work of Landshoff using the methods of quantum mechanics. Taking sodium chloride as an example, Landshoff accepts the assumption that the lattice consists of Na+ and Cl ions and calculates the ionic interaction energy on the basis of the Heitler-London theory using the known distributions of electrons in the Na+ and Cl " ions. In addition to the correction terms of Bom and Mayer, additional interactions related to the superposition of the electron clouds, the attraction between electrons and nuclei and the mutual repulsion of electrons are incorporated. The values obtained by this more exact method, however, differ from the values given in Table CXLVII by only a few kcals, the value for sodium chloride being 183 kcals. 

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