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 and concluded the following one to be the best [35]:
Because of the Pauli Exclusion Principle, electrons with parallel (unpaired) spins tend to avoid each other, thus decreasing the electrostatic repulsion between them. This will be the situation when filling the first half of the shell. When electrons are forced to doubly occupy orbitals in the second half, their spins are constrained to be paired (antiparallel). Because they are no longer obliged to avoid each other, the [inter-electron] electrostatic repulsion increases.
In Figure 2.5, the IE1 are shown for the 2p and 3p block elements. Continuing the line of the p1 to p3 configurations, a line parallel to the actual p4 to p6 values is obtained. The difference between the two represents the coulombic repulsion between pairs of electrons within the same orbital. For the 2p series, this amounts to about 430 kJ⋅mol−1, while for the 3p series it is 250 kJ⋅mol−1. Cann attributed the difference between the two series to the more diffuse 3p orbitals compared with the 2p orbitals. Thus, any paired 3p electrons are sharing a larger volume of space and therefore have less mutual repulsive forces.
Figure 2.5 First ionization energy for the p-block elements of the 2nd and 3rd Periods (adapted from Ref. [35]).
To review, there is nothing exceptional about the “half-filled shell.” It is instead the interelectron repulsive forces between the electron pairs beyond the p3 configuration, which result in a lower ionization energy. To reinforce the point, as Rich and Suter added [36]:
Likewise, when one compares the energy to remove an electron from the half-filled p subshell with that needed for a p2 structure, nothing special is found.
Rich and Suter then referred to the claimed stability of the “filled shell.” They continued [36]:
Similarly, the large energy difference between electrons in 3s1 and 2p6 configurations is readily explained by the difference in principal quantum number; this again indicates no more “extra” stability of a filled p shell than it does for a p5 or any other structure in which the electron being removed is at the lower principal number.
3d-Series Metal Ionization Energies
The 1st and 2nd ionization
