Up to this point, similarities have been considered among valence-isoelectronic series, such as Be2+, Al3+, and Ti4+. However, titanium also readily forms an ion Ti3+. Thus, in this (and the later example of vanadium and molybdenum), matching compounds in the same oxidation can be considered. As an example here, titanium, like aluminum, forms alums such as CsTi(SO4)2∙12H2O, analogous to CsAl(SO4)2∙12H2O.
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 of Tellurium and Astatine
It is likely that other examples of isodiagonality remain to be explored. In fact, isodiagonality seems to occur in many parts of the Periodic Table. For example, there are similarities between the chemistry of tellurium(VI) and astatine(VII) (Figure 11.7).
These resemblances are not just in formulas, but also in the pH dependence of the oxo-anions (Table 11.5).
Evidence-Based Isodiagonality
It is probable that at least one similarity could be found between any pair of elements. Thus, it is important to define criteria that can be used to establish an isodiagonal relationship as a real phenomenon. There seems to be three separate ways that can be used individually — or preferably in combination — to define elements as having an isodiagonal relationship.
•That for several compounds, there are diagonal similarities in physical and/or chemical properties. This is the classic definition used for the Li–Mg, Be–Al, and B–Si relationships.
•That very unusual chemical structures are shared in a diagonal pattern. Examples of these would be the tricarbide(4−) found
for the Li–Mg pair and the cis-dioxocations of the V–Mo pair.
•That in a few cases, there is an isodiagonal relationship between two elements that share the same biological function or occupy the same enzyme site. Examples of this would be the Li–Mg pair and the V–Mo pair, both discussed earlier.
Evidence of isodiagonality is usually found by considering valence-isoelectronic species, but for elements that have more than one oxidation state, similarities can sometimes be found for a common oxidation state.
Commentary
It would be nice to discover an all-encompassing explanation for isodiagonal relationships. As they are an upper-left–lower-right pattern, electronegativity might be used to account for some of the resemblances, while similarities in ionic radius and/or charge density might explain others. However, there seems to be no simple general “explanation” for isodiagonality. From the perspective of this series, however, the more important task is to define and clarify the isodiagonal relationship as one of the valid linkages among the chemical elements — and not just limited to the upper-left corner of the Periodic Table.
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Chapter 12
Lanthanoids, Group 3, and Their Connections
The short form of the conventional Periodic Table may be convenient and compact, but it results in a marginalization of the lanthanoids (and of the actinoids, covered in Chapter 13). Not only do they appear to be the orphan elements, but in undergraduate chemistry courses, if they are mentioned at all, they are dismissed in the closing lecture(s) of the course as being boring and of little interest. Yet this is not the case. In addition to some trends, there are also interesting and curious exceptions. Lanthanoid chemistry is most definitely worthy of study.
In Chapter 5, the rare earth metals were defined as the lanthanoids (see in the following) plus the two earlier Group 3 elements of scandium and yttrium. Cotton has referred to these two elements as “The Misfits” of the Periodic Table [1] and these two elements will be discussed first.
Yttrium and Scandium
In the debate on the 6th Period and 7th Period members of Group 3 (see Chapter 4), the 4th Period and 5th Period members of the Group are often overlooked
. In Chapter 8, scandium and yttrium were rejected from membership of the transition metals. They have found a home in this book by joining the lanthanoids as part of the rare earth metal grouping.
Yttrium
The yttrium 3+ ion resembles the lanthanoid 3+ ions so closely that it is best regarded as a later lanthanoid. For example, yttrium’s standard reduction potential is −2.37 V compared with −2.37 V for lanthanum and −2.30 V for lutetium. Also, the yttrium 3+ ion has an ionic radius of 90.0 pm compared with 90.1 pm for holmium.
In the context of its chemistry, the yttrium(III) halides are isostructural with all the lanthanoid(III) halides from dysprosium to lutetium. The yttrium(III) ion exists as an octahydrate is aqueous solution, [Y(OH2)8]3+, as do many of the lanthanoids. The major interest in ytterbium has been for yttrium oxosulfide, Y2O2S, doped with later lanthanoid(III) ions as long-lasting phosphors [2].
Though yttrium seems “more comfortable” with the latter lanthanoids, curiously, yttrium in minerals is usually associated with the earlier lanthanoids. Two examples of these are bastnäsite, (Ce,La,Y)CO3F, and gadolinite (which contains no gadolinium), (Ce,La,Nd,Y)2FeBe2Si2O10.
Though yttrium does seem to be predominantly lanthanoid-like, there seems to be a significant resemblance in chemistry to its (n + 10) Group 13, analog, indium (see Chapter 9). Interestingly, research on inorganic polymers has also found some similarities of yttrium and indium [3].
Scandium
While yttrium behaves unambiguously like a lanthanoid, the much smaller scandium(III) ion (74.5 pm) has resemblances to — and differences from — both transition metals and lanthanoids. In fact, Cotton’s term of “misfit” does indeed apply to this element. For example, like the transition metal ions from titanium(III) to cobalt(III), scandium(III) forms a three-coordinate silylamide, Sc[N(Si(CH3)3)2]3. However, while the transition metal complexes are planar, that of scandium is pyramidal. Despite the difference in ion size, scandium can be found with yttrium in such ores as thortveitite, (Sc,Y)2Si2O7.
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