Periodic Table, The: Past, Present, And Future

diagonal demarcation” [5]. Similarly, the elements often considered to be semimetals fall on a roughly diagonal boundary between the metals and nonmetals, see Chapter 5 [6].

Figure 11.3 Rich’s version of the periodic table to emphasize isodiagonal relationships (from Ref. [4]).

A related phenomenon, the change in bonding type across Periods, similarly lies upon a diagonal [7]. The pattern is usually for a change from ionic (to the left) to small-molecule covalent (to the right) with a species that can be assigned as possessing network covalent bonding at the transition point. As was shown in Chapter 7, for 2nd Period and 3rd Period oxides, this intermediate bond type occurs with B₂O₃ and SiO₂. For fluorides, the transition is displaced left by one group so that it occurs with BeF₂ and AlF₃, and similarly for hydrides with (BeH₂)_x and (AlH₃)_x.

Explanations for Isodiagonality

Cartledge, in 1928, was the first to suggest a possible explanation for isodiagonality [8]. He proposed that the phenomenon could be explained in terms of ionic potential, Z/r, what is now more commonly known as charge–radius ratio. The ionic potential was recalculated by Hanusa using Shannon–Prewitt ionic radii and these values correlated well with isodiagonal links for some pairs, but not others [9]. As an example, the ionic potential for Be²⁺ of 74 nm⁻¹ is very close to the value of 77 nm⁻¹ for Al³⁺. However, there is no match in the values for the pair of Li⁺ (17 nm⁻¹) and Mg²⁺ (35 nm⁻¹). The same ratio, but called polarizing power, was qualitatively used to explain isodiagonality by Puddephatt and Monaghan [10].

Lee provided a variety of explanations [11]. He first proposed polarizing power, then suggested radius similarities for the Li⁺–Mg²⁺ link; and charge per unit area to explain the Be²⁺–Al³⁺ link; but commented that electronegativity similarities was another possible explanation. Finally, in the context of the Be²⁺–Al³⁺ link, Lee stated:

Just as was the case with lithium and magnesium, the similarity in atomic and ionic sizes is the main factor underlying this relationship.

King also favored electronegativity as an explanation [12]. Housecroft and Sharpe, by contrast, proposed that isodiagonality could be explained in terms of similarities in ionic radius [13]. However, this contradicted Hanusa’s conclusions, as ion radius and ionic potential are reciprocal relationships.

Rayner-Canham and Overton found that charge density is a useful parameter for predicting ionic versus covalent behavior in simple binary compounds and that it could also account for the diagonal Li⁺–Mg²⁺ and Be²⁺–Al³⁺ links [14]. This term, charge density, dates back to at least the 1960s [15]. It is defined as:

The charge density of a real or hypothetical ion is defined as the ion charge divided by the ion volume.

In order to obtain numbers in meaningful units and, at the same time, avoid the need for enormous exponents, Rayner-Canham and Overton utilized the electron charge in Coulombs and the ionic radius in millimeters. Thus, for each real or theoretical ion, the integer ion charge was multiplied by the electron charge and divided by 4/3π times the ion volume to give values in C⋅mm⁻³.

Unfortunately, some sources confuse charge density with charge–radius ratio. For example, Rogers stated that charge density was defined as “charge on a metal cation over its ionic radius” [16]. This parameter is, in fact, correctly named charge–radius ratio.

Despite this confusion, Rogers provides one of the more comprehensive discussions of isodiagonality. He correlated the parameters of ionic radius, charge–radius ratio, and electronegativity for the Li–Mg, Be–Al, and B–Si pairs:

There appear to be three principal factors why these pairs — take beryllium and aluminum as a representative example — have so much chemistry in common. One factor is ionic size; the others are charge density (or charge-radius-ratio, Z/r) and electronegativity. … The two metal ions, then, will similarly polarize the X atom in an M−X bond and give rise to a similar additional covalent character on that basis.

He added the caveats:

First, keep in mind that group relationships (for example, between beryllium and magnesium) are still the dominant factor. … Second, the ions … particularly the highly charged B³⁺, C⁴⁺, and Si⁴⁺ really do not exist as such. … Nevertheless, even with these warnings, the diagonal relationship remains a good organizing principle.

Table 11.1 shows some of the parameters for these eight ions. The ionic radii in pm (Shannon–Prewitt), both for 4- and 6-coordination are from Ref. [17]; charge–radius ratio values are calculated from the Shannon–Prewitt ion radius values for 6-coordination (in nm⁻¹); charge density values are from Ref. [14] (in C⋅mm⁻³); and Allred–Rochow electronegativity values are from Ref. [18].

It is difficult to attribute any one parameter as a ubiquitous explanation for all isodiagonal resemblances. This is not surprising, considering the Li–Mg pair are predominantly ionic in behavior while B–Si are totally covalent in their properties. In the following sections, individual pairs of elements will be compared and contrasted in terms of possible isodiagonal relationships.

Table 11.1 Parameter values for the early 2nd Period and 3rd Period elements

Isodiagonality of Lithium and Magnesium

Though lithium and magnesium are often taken as the prototypical isodiagonal pair, it more highlights the 2nd Period Anomaly: that the 2nd Period elements are uniquely different to the lower members of their group (see Chapter 7). As we see in the following, there are indeed specific similarities between lithium and magnesium, though on the basis of free energies of formation of compounds, Hanusa found a closer resemblance of lithium with calcium [9]. On the other hand, Greenwood and Earnshaw contended that magnesium is atypical of Group 2 (though beryllium is even more so) and that lithium does match well and uniquely with magnesium [19].

General Resemblance of Lithium to Group 2 Elements

First, there are resemblances between lithium and the Group 2 elements as a whole:

•Lithium does not form an isolatable hydrogen carbonate whereas solid hydrogen carbonate salts can be obtained for the other Group 1 metals. Solid hydrogen carbonates cannot be isolated for the Group 2 metals.

•Lithium salts tend to be hydrated (often as a trihydrate) whereas the salts of the other