Figure 11.5 The second diagonal series.
Does Be–Al Isodiagonality Extend to Niobium? and to Tungsten?
There is some evidence for continuation of isodiagonality to niobium and tungsten. For example, both titanium and niobium form mixed metal oxides with a perovskite structure, such as CaTiO3 and LiNbO3, while tungsten(VI) oxide can adopt an analogous perovskite-like structure [28]. A key point to establishing the validity of an isodiagonal relationship is that of finding species unique to that linkage. Greenwood and Earnshaw have commented upon the relationship between the nonstoichiometric “bronzes” formed by titanium, niobium, and tungsten [29]. These compounds are characterized by very high electrical conductivities and intense colors. However, the diagonal similarities are better considered as two separate series: beryllium–aluminum and titanium–niobium–tungsten.
Isodiagonality of Boron and Silicon
A comparison of boron and silicon is the third common example of isodiagonality. This case is very different from the two other examples, for the chemistry of both elements involves essentially covalent bonding. Some of the similarities are listed here:
•Boron forms a solid acidic oxide, B2O3, like that of silicon, SiO2. The oxide of aluminum is amphoteric.
•Boric acid, H3BO3, is a very weak acid as is silicic acid, H4SiO4. Boric acid bears no resemblance to the amphoteric aluminum hydroxide, Al(OH)3.
•There are numerous polymeric borates and silicates that are constructed in similar ways, using shared oxygen atoms.
•Boron forms a range of flammable, gaseous hydrides, just as silicon does. There is only one aluminum hydride and that is a solid.
These similarities relate to covalent bonding. Unlike the explanations for the previous two pairs, there can be no justification in terms of cation charge density. Table 11.3 shows the element-oxygen single bond energy. Thus, it can be argued that it is the exceptional strength of the boron and silicon single bonds to oxygen that accounts for many of the diagonal similarities. This explanation would include the flammability of the hydrides to give the respective oxides.
There is more recent interest in diagonal relationships. A boron–silicon diagonal relationship has been claimed for a series of osmium organometallic compounds with boryl and corresponding dihydride silyl ligands [30]. While another diagonal connection is that boron and silicon are among the species to form heteropoly ions adopting Keggin structures [31].
Table 11.3 Element-oxygen single bond energy (kJ∙mol–1)
Isodiagonality of Carbon and Phosphorus
Inorganic chemists have seen the isodiagonal relationship primarily in terms of the three pairs earlier. A landmark advance was the synthesis of a ferrocene-like molecule in which the ring carbon atoms were replaced by phosphorus. Not only did this molecule resemble ferrocene, but it underwent a substitution reaction in a similar manner to ferrocene itself [32].
In recent years, organic chemists have been using the term “diagonal relationship” in the context of organophosphorus compounds. By 1998, there had been so much organophosphorus chemistry reported that a review book appeared with the title: Phosphorus: The Carbon Copy [33]. Some of the research has continued to cite the “diagonal relationship” as the underlying premise. For example, research published in 2000 describes the phospha-Wittig reaction [34]. Subsequently, the diagonal relationship was cited in the context of phosphorus-containing heterocycles [35] and in a review of poly-phospho-cation species [36].
Isodiagonality of Nitrogen and Sulfur
Greenwood and Earnshaw [37] suggested that similarities in charge densities and electronegativities between nitrogen and sulfur would lead to a diagonal relationship between these two elements. As evidence, they used the extensive range of cyclo binary sulfur nitrides. Greenwood and Earnshaw contended that the large number of permutations, or their interchangeability, indicated strong similarities between the two elements. Of particular relevance is the aromatic nature of the ion, suggesting the closeness in electronic energies of the two component atoms [38].
Isodiagonality of Vanadium and Molybdenum
Mitchell proposed a link between the chemistry of vanadium and molybdenum in 1974 [39]. At the time, he argued that, in its chemistry, vanadium more closely resembled molybdenum and tungsten than the other members of its own group. Mitchell also noted similarities between the chemistry of molybdenum and rhenium.
In 1986, it was reported that the nitrogenase enzyme was sometimes found with vanadium instead of molybdenum [40]. Subsequently, the vanadium–molybdenum link has also become of interest in the context of other enzymes that can utilize vanadium in place of molybdenum. Rehder proposed that, in early geological times, vanadium was more widely used than molybdenum in enzyme processes [41]. This complete diagonal series is shown in Figure 11.6.
In their aqueous chemistry, there are far more similarities of vanadium and molybdenum than of vanadium and niobium. At high pH, soluble vanadate ion, and molybdate ion, predominate. Then at intermediate pH, they both form soluble isopoly-oxo-anions. At low pH, vanadium forms a soluble cis-dioxo-cation, while molybdenum forms an insoluble trioxide at low pH and the corresponding cis-dioxo-cation, at very low pH (Table 11.4).
Figure 11.6 The Group 5–7 diagonal series.
Table 11.4 A comparison of aqueous vanadium and molybdenum species under oxidizing conditions
There are also analogous phosphorus-containing heteropoly-oxo-anions, including [PV14O42]9– and [PMo12O40]3–. By contrast, vanadium does not resemble niobium in its predominant species. For example, niobium forms insoluble niobium(V) oxide over much of the oxidized pH range [24]. Among other similarities between vanadium and molybdenum, vanadium(IV) and molybdenum(IV) form disulfides, VS2 and MoS2, with matching layer structures.
Does V–Mo Isodiagonality Extend to Rhenium?
Mitchell [39] alluded to a diagonal relationship between molybdenum and rhenium. One of several such similarities is the formation of analogous valence-isoelectronic chlorodimers containing quadruple bonds and eclipsed chlorine atoms: [Mo2Cl8]4– and [Re2Cl8]2–. There are also some features that encompass all three of the diagonal series, such as reduction under the same very acid conditions to the identical oxidation state: V3+, Mo3+, and Re3+. In addition, all three elements form corresponding valence-isoelectronic tetrathioanions: and [42].
Figure 11.7 The Group 16–17 lower diagonal series.
Table 11.5 A comparison of aqueous tellurium and astatine species under oxidizing conditions
Isodiagonality
