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[31]:

       The oxidation state of an atom is the change of this atom after ionic approximation of its heteronuclear bonds. Bonds between atoms of the same element are not replaced by ionic ones: they are always divided equally.

      In many cases, both the algebraic and the electronegativity–Lewis structure approach give the same result. For example, in the sulfate ion, both methods assign an oxidation state of +6 for sulfur. However, very different results are obtained where there are two (or more) atoms of the same element in different environments.

      An example is provided by the thiosulfate ion, S₂O₃²⁻, with a peripheral and a central sulfur atom. When this ion decomposes in acid, the fates of the two sulfur atoms are quite different, indicating that they have come from very different environments and oxidation states in the thiosulfate ion itself. However, the algebraic calculation provides an average oxidation state of +2 for each sulfur atom. The Lewis structure of the ion (Figure 2.3) confirms the experimental finding of two very different electron environments for the sulfur atoms. Utilizing the Pauling/Loock electronegativity–Lewis structure approach, the central sulfur atom is assigned an oxidation state of +5 while the peripheral one has a resulting oxidation state of −1. These values make much more chemical sense.

      Figure 2.3 Electron assignment for the thiosulfate ion to use for electronegativity determination by the Pauling/Loock deductive method.

       Abegg’s Rule

The range of oxidation states for a specific element is sometimes alluded to in introductory chemistry. As examples, values for sulfur range from −2 to +6, while for chlorine the range is from −1 to +7. It was Abegg who, in 1904, noticed that the sum of the extreme oxidation states of an element often equaled eight. The popularization of this observation did not happen until 1916, in a long-overlooked contribution to chemical bonding by Lewis [32]. The rule can be states as follows:

      Abegg’s Law states that, for a main group element, the total difference between the maximum negative and positive oxidation states of an element is frequently eight and is in no case more than eight.

      As an example, sulfur has the oxidation state limits of −2 and +6. Thus, applying Abegg’s law: [{+6} − {−2}] = +8.

Electron Gain and Loss

      Having devoted the first part of this chapter to the variously defined concept of electronegativity, the second part will be on the very specifically defined topics of ionization energy and electron affinity. Values of which are mostly known to considerable precision.

      First a comment upon a statement that appears in many introductory chemistry texts: “Ionic compounds form because metals want to give up valence electrons and non-metals want to gain valence electrons.” The statement is a convenient fiction for students starting out in chemistry, but nothing could be farther from the truth! This false explanation can be demolished by simply considering the ionization energy (IE₁) and electron affinity (EA₁) of the sodium atom:

As can be seen from the values, sodium actually “wants” to gain an electron not lose one! It is only the fact that the nonmetal counter-atom has a higher electron affinity that “forces” sodium to lose its valence electron. That is, ionic bonding is not benign, but atomic “nature red in tooth and claw,” in other words, a competition for the valence electrons [33]. The two related phenomena are discussed in the following.

       Ionization Energy

One pattern explicable in terms of electron configuration is that of ionization energy. Usually we are interested in the 1st ionization energy. As the orbital occupancy may change between the neutral atom and the ionized ion, a correct definition is as follows [34]:

      The experimental 1st ionization energy is equal to the difference between the total electronic energy of the atom X and the total electronic energy of the ion X⁺, both in their ground states. That is, X(g) → X⁺(g) + e⁻

       Periodic Trends in Ionization Energy

Unlike the molecule-dependent values of covalent radii, ionization energies can be measured with great precision. Figure 2.4 shows the IE₁ for the 1st, 2nd, and 3rd Period elements. As can be seen, the pattern is repetitious, the Group 1 elements at the low point and the Group 18 elements at the peaks. Most of the variations can be explained in terms of screening/shielding from the nucleus of the outermost electron by the inner electrons [35].

      Figure 2.4 1st ionization energy for the first 19 elements (adapted from Ref. [35]).

      Instead of discussing IE₁ of each element shown, one cycle will be chosen for examination: that of the 2nd Period elements. The patterns can be explained as follows:

      •Lithium has a small IE₁ as the 2s electron is largely shielded from the nuclear attraction by the 1s²:

      [He]2s¹ → [He]

      •Beryllium has a larger IE₁ primarily as a result of the greater effective nuclear charge:

      [He]2s² → [He]2s¹

      •Boron has a lower IE₁ as, even though there is an increase in nuclear charge, the 2p electron is partially shielded by the 2s² electrons:

      [He]2s²2p¹ → [He]2s²

      •Carbon has a higher IE₁ primarily as a result of the greater effective nuclear charge:

      [He]2s²2p² → [He]2s²2p¹

      •Nitrogen has a higher IE₁ primarily as a result of the greater effective nuclear charge:

      [He]2s²2p³ → [He]2s²2p²

      •Oxygen has a lower IE₁ which will be discussed separately in the following:

      [He]2s²2p⁴ → [He]2s²2p³

      •Fluorine has a higher IE₁ primarily as a result of the greater effective nuclear charge:

      [He]2s²2p⁵ → [He]2s²2p⁴

      •Neon has a much higher IE₁ primarily as a result of the greater effective nuclear charge:

      [He]2s²2p⁶ → [He]2s²2p⁵

       The Half-Filled Shell Myth

      Ingrained in the vocabulary of chemistry is the term “the stability of the half-filled shell.” However, it is not the “stability” of the p³ configuration, but the reduced “stability” of the subsequent electrons, which accounts for the break in near-linearity of the plot. Cann has compared some of the explanations for the discontinuity

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