8.6.2: Heavier Elements of Group 13 and the Inert Pair Effect

The group 13 metals also form conventional compounds as well as M-X-M type bridge bonds and metal-like clusters.

The group 13 metals form a wide variety of compounds that may be explained in terms of ionic or pairwise covalent bonding. These oxides can generally be explained as ionic. Thallium's main oxide, Tl₂O, crystallizes in the CdI₂ lattice, and consists of layers of edge-linked octahedra, as shown in Figure \(\sf{\PageIndex{1A}}\), while the most stable form of Al₂O₃ , corundum, consists of layers of edge-linked AlO₆ octahedra vertex-linked to adjacent layers as shown in Figure \(\sf{\PageIndex{1B}}\).

Figure \(\sf{\PageIndex{1}}\). (A) The CdI₂ structure adopted by Tl₂O showing layers of edge-linked Tl₆O octahedra and (B) Corundum Al₂O₃ structure consisting of layers of edge-linked AlO₆ octahedra (in the horizontal) vertex-linked adjacent layers (in the vertical direction). The CdI₂ structure image is by Speedpera / CC BY (https://creativecommons.org/licenses/by/4.0 and the Corundrum Al₂O₃ image is is by Materialscientist at English Wikipedia / CC BY-SA (https://creativecommons.org/licenses/by-sa/3.0)

Nevertheless, although it is possible to explain the structural chemistry of Al₂O₃ as involving an ionic lattice, Al does form covalently-bonded oxyanions just as boron does. A particularly well known example is the Al₆O₁₈^18- anion, which contains AlO₄ tetrahedra covalently vertex-linked into an Al₆O₆ ring as shown in Scheme \(\sf{\PageIndex{I}}\). The calcium salt of this anion is found in tricalcium aluminate cements, which as the name suggests are formed by mixing 3 equivalents of CaO with one of Al₂O_3^.

Scheme \(\sf{\PageIndex{I}}\). Two views of the Al₆O₁₈^18- anion.

Figure \(\sf{\PageIndex{2}}\) is illustrative. It forms a network structure as a solid, as liquid exists as a E₂X₆ dimer, and in the gas phase is a mixture of dimers and monomers, ultimately giving the monomer only at high temperatures.

Figure \(\sf{\PageIndex{2}}\). Representative group 13 trihalides. The solid state structure and text are adapted from an image by Benjah-bmm27 taken from https://upload.wikimedia.org/Wikipedia/commons/4/42/Aluminium-trichloride-3D-structures.png.

The aluminum trihalides are effective Lewis acids. This property serves as the basis for their use as a catalyst in Friedel-Crafts alkylations and acylations. In these reactions, AlCl₃ acts as a Lewis base to abstract a chloride ion from an alkyl or acyl halide, generating a carbon-based cation that can add to an aromatic ring in an electrophilic aromatic substitution reaction (Scheme \(\sf{\PageIndex{II}}\)).

Scheme \(\sf{\PageIndex{II}}\). AlCl₃ acts as a Lewis acid catalyst in facilitating Friedel Crafts acylation.

Trialkyl group 13 compounds also exist as monomers and dimers, although the monomer-dimer preference increasingly shifts towards monomer on going from Al to In. In general, GaR₃ and InR₃ species exist as monomers, while for Al the monomer and dimer are often in equilibrium (Scheme \(\sf{\PageIndex{II}}\)) for smaller alkyl groups, shifting towards monomer with bulky ones.

Scheme \(\sf{\PageIndex{II}}\). Dimer-monomer equilibrium of trimethyl aluminum.

As with their boron analogues, trialkyl aluminum and trialkylgallium compounds are effective Lewis acids, reacting with Lewis bases at the group 13 element to give tetrahedral species.

The low electronegativity of the group 13 metals also means that the alkyl groups of group 13 trialkyl complexes are nucleophilic and basic. This reactivity is employed in the commercial use of GaR₃ species for the chemical vapor deposition of semiconductor-grade GaAs via reaction of GaR₃ with AsH₃.

\[\sf{Ga(CH_3)_3~~+~~AsH_3~~\longrightarrow~~GaAs(s)~~+~~3~CH_4} \nonumber \]

Compounds containing Al-Al and Ga-Ga single and multiple bonds can be prepared, although Al≡Al bonds have so far only been demonstrated in the gas phase.¹ In the case of Ga, multiple bonds can be formed by reduction of compounds of type RGaX₂ by using extremely bulky R groups to prevent dimerization of any Ga=Ga or Ga≡Ga species formed. The nature of the multiply-bonded species formed this way have been the subject of much theoretical investigation. The 1997 report of the synthesis of a gallyne² in particular set off a storm of controversy about the nature of its Ga-Ga bond, leading to competing claims that the bond should be understood as involving single, triple, or even double bond interactions. Some of the options are depicted in Figure \(\sf{\PageIndex{3A}}\). Although no clear consensus has yet emerged, recent experimental and theoretical work³ has pointed to the description of bonding as involving a \(\sigma\) bond, a conventional \(\pi\) bond, and a Klinkhammer-type slipped \(\pi\) bond, as shown in Figure \(\sf{\PageIndex{3}}\).

Figure \(\sf{\PageIndex{3}}\). (A) Two Lewis depictions of possible bonding arrangements in Robinson's Gallyne, in which the bond between the Ga atoms has been proposed to consist of (B) an overlap between \(\sigma\) type and p orbitals on the two Ga atoms, equivalent to the \(\sigma\) bond and a Klinkhammer-type slipped \(\pi\) bond. (C) The third bond of the triple bond is a conventional \(\pi\) bond perpendicular to the \(\sigma\) and slipped \(\pi\) bond and, in common with other \(\pi\) interactions involving row 3+ elements, features relatively weak overlap. The dotted lines to the Na⁺ ions are intended to show the location of these ions in the structure without implying anything about how they participate in the bonding.

Aluminum and gallium are also known to form atomic clusters. There are two types:

1. Naked metal clusters

Examples include anions like Tl₇^7- , Ga₁₁^7- , and Tl₁₃^11- formed by reaction of the metal or metal halide with a powerful reductant (usually an alkali or similar highly reducing metal) and "magic clusters" containing unusually stable species like Al₇⁺ and Al₁₃^- formed by laser sputtering of aluminum (i.e., irradiating an Al surface with a laser and watching what sort of clusters come off). Among these, Al₁₃^- is so stable that it can even be prepared by solution phase reduction of dendrimer-encapsulated AlCl₃ by ketyl radicals. The chemical behavior of the Al₁₃^- anion may be rationalized by thinking about it as analogous to a "halide," specifically of the superatom Al₁₃. Superatoms like Al₁₃ are clusters that possess well-defined energy levels and directional valence orbitals just as atoms do; consequently, they exhibit atom-like reactivity in tending to gain, lose, or share electrons to fill a shell of low energy orbitals. In the case of Al₁₁, its reactivity mimics that of the halogens and so it is described as a superhalogen.

Examples of naked metal cluster structures are given in Figure \(\sf{\PageIndex{4}}\).

Figure \(\sf{\PageIndex{4}}\). Structures of some naked metal clusters. The shapes of these are often analogous to those of stable boranes, although in many of them, one of the atoms occupies the cluster interior.

As may be seen from the structures in Figure \(\sf{\PageIndex{4}}\), these clusters adopt shapes similar to those of the boranes, although as is the case with Tl₁₃^11- and Al₁₃^- sometimes one of the metal atoms resides in the cluster interior. As might be expected, the stability of many of these clusters is analogous to that of the boranes in being explicable in terms of Wade's rules, although given that Tl₁₃^11- and Al₁₃^- are isostructural and both stable while differing in their valence electron counts by ten electrons it is clear that this is not always the case.

The existence of multiple stable electron counts in group 13 superatom clusters like Al₁₃^- has been explained by the jellium model of cluster stability, which treats clusters like Al₁₃^- as consisting of an "ionic core" consisting of the nuclei and their core electrons (Al³⁺)₁₃ surrounded by the "jelly" of valence electrons. In the case of Al₁₃ clusters, this model gives stable sets of energy levels allowing for configurations containing the "magic numbers" of 2, 8, 18, 20, 34, or 40 electrons. In this model, the 40 valence electrons in Al₁₃^- correspond to the last of these stable states. Thus Tl₁₃^11- and Al₁₃^- represent different regimes of stability, one consistent with a Wade-type cluster similar to the boranes explicable in terms of molecular orbitals formed by combinations of atomic orbitals and the other one explicable in terms of the orbitals given by treating Al₁₃ as a superatom in the jellium model.

2. Metalloid clusters

Metalloid clusters consist of a small particle of metal surrounded by ligands. Some such Al and Ga clusters even contain upwards of 69 atoms. Examples include clusters with formulas [Al₆₉{N(SiMe₃)₂}₁₈]^3- and [Al₇₇N(SiMe₃)₂}₂₀]^2-. The structure of a relatively small example is given in Figure \(\sf{\PageIndex{5}}\).

Figure \(\sf{\PageIndex{5}}\). Structure of Cp*₁₀Al₅₀ (Cp* = C₅(CH₃)₅^-). By Smokefoot - Own work, CC BY-SA 4.0, commons.wikimedia.org/w/inde...curid=87686580

Although the group 13 metals have varying tendencies to form covalent bonds, they tend to act chemically as metals.

Some representative features of these elements illustrative of their chemistry are summarized in Table \(\sf{\PageIndex{1}}\).

Table \(\sf{\PageIndex{1}}\). Illustrative properties of the group 13 metals.^9,10

Group 13 Metal	Natural Source	Oxides (major product of reaction of the element with O2 is given in bold)	Illustrative Stable Mononuclear Halides	Redox Behavior in Acidic Solution
Aluminum, Al	Aluminosilicates like feldspars of formula MAlSi3O8 or M'Al2Si2O8 where M = alkali metal and M' = alkaline earth metal clays like kaolinite, Al2Si2O5(OH)4 Bauxites containing Al2O3·xH2O	Al2O3	AlX3 (X = F, Cl, Br, I)
Gallium, Ga	As impurities in Aluminum and Fe/Zn ores Bauxites, Al2O3·xH2O Sphalerites, ZnS Small amounts in Gallite, CuGaS2	Ga2O3 Ga2O	Network covalent GaF3 Dimeric Ga2X6 (X = Cl, Br, I) Ga^IGa^III2Cl7 Ga^IGa^IIIX4 (X = Cl, Br, I)
Indium, In	As impurities in Zn and Cu/Fe ores Sphalerites, ZnS Chalcopyrite, CuFeS2	In2O3	InX3 (X = F, Cl, Br, I) In^I3(In^IIIX6)(X = Cl, Br) In^IIn^IIIX4 (X = Br, I) InX (X = Cl, Br, I)
Thallium, Tl	As impurities in sulfide-rich ores CuFeS2, CuS, Cu2S PbS ZnS small amounts in minerals like TlCu7Se4, TlPbAs5S9, others	Tl2O3 Tl2O	TlF3 TlX (X = F, Cl, Br, I) thallium(I) triiodide, Tl^I(I3)

As may be seen from the data in Table \(\sf{\PageIndex{1}}\), on moving down group 13 from Al to Tl

1. Geologic occurrence of the elements in oxide ores (Al, Ga) becomes increasingly replaced by a preference for occurrence in sulfides and selenides (Ga, In, Tl). This is consistent with increasing softness on moving down group 13.
2. There is an increasing preference for the +1 oxidation state. This may be seen from

• the standard potentials for reduction of M³⁺ and M⁺ to the metal. These show a decrease in the stability of the +3 ion on going down the group. In the case of Tl, Tl³⁺(aq) is even less stable than Tl⁺(aq).
• an increase in prevalence of the +1 oxidation state in the monomeric halides. The aluminum monohalides, AlX, are highly unstable; the bromide and chloride of Ga^I stabilizable (but perhaps not monomeric); the In^I halides stable only for the less oxidizing halogens Cl, Br, and I; and for  thallium, TlF₃ is the only stable Tl³⁺ halide.

This increasing preference for an oxidation state two lower than maximum valence is not restricted to the group 13 elements. It is a common feature of post transition element chemistry that these elements can act as if their ns² valence electrons are inert, on account of which this tendency has been referred to somewhat misleadingly as the inert pair effect.

Post-transition metals exhibit the inert pair effect, in which they act as if their ns² valence electrons do not contribute to bonding.

Metals and metalloids of the p block commonly possess two stable oxidation states, with one corresponding to the loss of all their ns and np valence electrons and one the loss of two fewer electrons. This is evident from the well-known ions and oxidation states observed for the group 13, 14, and 15 metals and metalloids shown in Scheme \(\sf{\PageIndex{III}}\).

Scheme \(\sf{\PageIndex{III}}\). Common oxidation states of group 13, 14, and 15 metals and metalloids.

Moreover, there is an increasing preference for the lower oxidation state on going down a group in the periodic table so that

• The higher (n+) oxidation state is favored for lighter elements so that the order of preference is

Al³⁺ > Ga³⁺ > In³⁺ > Tl³⁺

• The lower (n - 2)+ oxidation state is favored for heavier elements

Al⁺ < Ga⁺ < In⁺ < Tl⁺

This is why the most stable oxide and chloride of Al are Al₂O₃ and AlCl₃ while the most stable oxides and Cl of Tl are Tl₂O and TlCl.

The classical explanation for the existence of this behavior is to postulate that the heavier elements' ns² valence electrons are chemically inert - i.e., an inert pair. For this reason the observation that many post transition elements have stable n+ and (n-2)+ oxidation states and that there is an increasing preference for the lower oxidation state on moving down a group has been termed the inert pair effect.

The inert pair effect is due to the decrease in bond energies down a group.

However, the term inert pair effect is a misnomer. There are two reasons for this

1. The ns electrons do not become significantly more inert (a.k.a. lower in energy) as one descends the groups of the periodic table. A cursory look at the valence s and p orbital energies of the main group elements reveals that it is simply not the case that the ns orbitals become lower in energy on going down a group of the periodic table. As may be seen from the energies given in Figure \(\sf{\PageIndex{6}}\), the energy of the ns orbitals is generally lowest for period 1 and 2 elements, after which the only overall trend that may be noted is that the ns orbital energies of the rows 3-6 elements generally do not differ by more than 20% across the entire range.

Figure \(\sf{\PageIndex{6}}\). Valence orbital energies of the main group elements and transition metals in eV. By Emily V Eames and taken from http://www.graylark.com/eve/orbital-energies-table.html

2. The inert pair effect is due to the decrease in bond energies as bond lengths increase down a group of the periodic table. To see how this leads to the appearance of ns electron inertness as one descends the periodic table, consider that the process of forming an E-X bond generally involves

• endergonic oxidation of the metal
• exergonic formation of a M-X bond

Consider the interplay between these two energies in the case of forming the monohalides and trihalides of the group 13 elements. The cost of oxidation of the metal reflects a balance between the ionization energies given in Table \(\sf{\PageIndex{2}}\) and bond energies given in Table \(\sf{\PageIndex{3}}\).¹⁵

Table \(\sf{\PageIndex{2}}\). Ionization energy costs for formation of M⁺ and M³⁺. Recalculated from the similar table of ionization energies at en.Wikipedia.org/wiki/Inert_pair_effect.

Process	B	Al	Ga	In	Tl
M \(\rightarrow\) M^+ IE1 (kJ/mol)	800	577	578	558	589
​​​​​​M \(\rightarrow\) M^3+ IE1​ + IE2 + IE3 (kJ/mol)	6886	5137	5520	5082	5438
Inert pair oxidation: M^+ \(\rightarrow\) M^3+ IE2 + IE3 (kJ/mol)	6,086	4,560	4,942	4,524	4,849

Table \(\sf{\PageIndex{3}}\). M-Cl homolytic bond energies in kJ/mol.¹⁵

Bond	B-Cl	Al-Cl	Ga-Cl	In-Cl	Tl-Cl
Typical E-Cl Bond Dissociation energy (kJ/mol)	536	494	481	439	372.8

As may be seen from Table \(\sf{\PageIndex{3}}\), the energy cost for ionization of the "inert pair" is greatest for boron, drops by ~25% on going to Al, and then remains approximately constant for the remaining members of the group. In contrast, the compensating bond dissociation energies drop more slowly on going from B to Tl, with successive ~10% and ~20% decreases on going from Ga to In and In to Tl. Because bond energies drop on going from Al to Tl while ionization energies do not, it is thought that the inert pair effect isn't due to the inertness of the ns electrons but rather due to the weakening of bond energies. When the stabilization energy due to M-E bond formation is no longer enough to pay the cost needed to oxidize away the ns electrons, the lower oxidation state will be more stable than the higher one, just as it would if the ns electrons really were inert.

The inert pair of electrons exerts structural effects.

Regardless of the origin of the inert pair effect, the inert pair of electrons influences the structure of compounds in the (n-2)+ oxidation state. Electron pairs that do this by altering the observed geometry of compounds are said to be stereochemically active inert pairs. The lone pairs of Sn^IICl₂ are the classic example. As shown in Figure \(\sf{\PageIndex{7A}}\), gas phase Sn^IICl₂ exhibits an AX₂E VSEPR geometry, while Sn^IICl₂ in its solid state, hydrates, and salts all exhibit AX₃E geometries, consistent with the influence of a lone pair of electrons.

Figure \(\sf{\PageIndex{7}}\). (A) Steroechemically active inert pairs in SnCl₂ and several of its Lewis base adducts. (B) Stereochemically inert lone pairs in BiI₃. The SnCl₂ image is by Hbf878 - Own work, CC0, commons.wikimedia.org/w/inde...curid=64768302. The BiI₃ image is adapted from the structure drawn by Ben Mills, Benjah-bmm27 / Public domain, and taken from commons.wikimedia.org/wiki/F...r-3D-balls.png.

Sometimes the coordination geometry of an element is exactly that which would be expected if the inert pair were not present. In such cases the inert pair is said to be stereochemically inert. In general, when the element's coordination number is less than six, the inert pairs will be stereochemically active, while for coordination numbers of six or more the pair may be stereochemically active or stereochemically inert.

Even when an inert pair appears stereochemically inert, it does not mean that it exerts no effect on the structure of the compound. It may be that the pair is simply fluxional and only appears to be inert because it is rapidly adjusting its position among possible locations. For instance, in the structure of BiI₃ shown in Figure \(\sf{\PageIndex{7B}}\), the lone pair is likely interchanging between the six faces of the octahedron defining the coordination sphere, as is the case for XeF₆ (Figure \(\sf{\PageIndex{8}}\)).

Figure \(\sf{\PageIndex{8}}\). The appearance of stereochmeical inactivity on the part of the inert pair in BiI₃ can likely be explained in terms of fluxional behavior similar to that believed to take place in XeF₆. (A) If the lone pair of XeF₆ were stereochemically inactive, the compound would possess true O_h symmetry. (B) The opening of a face of XeF₆'s coordination octahedron by a stereochemically active lone-pair reduces the symmetry of the octahedron to C_3v symmetry, (C) as may be seen in that F atoms on opposite faces no longer interchange under an S₈ operation. (D) However, fluxionality in XeF₆ involving interchange of the stereochemically active lone pair among the six faces of the XeF₆ octahedron is so fast that on most timescales the opening of all six faces is averaged and the structure appears octahedral.

Notes and References

1. Zhang, X.; Popov, I. A.; Lundell, K. A.; Wang, H.; Mu, C.; Wang, W.; Schnöckel, H.; Boldyrev, A. I.; Bowen, K. H., Realization of an Al≡Al Triple Bond in the Gas-Phase Na3Al2− Cluster via Double Electronic Transmutation. Angewandte Chemie International Edition 2018, 57 (43), 14060-14064.

2. Su, J.; Li, X.-W.; Crittendon, R. C.; Robinson, G. H., How Short is a -Ga⋮Ga- Triple Bond? Synthesis and Molecular Structure of Na2[Mes*2C6H3-Ga⋮Ga-C6H3Mes*2] (Mes* = 2,4,6-i-Pr3C6H2):  The First Gallyne. Journal of the American Chemical Society 1997, 119 (23), 5471-5472.

3. Kobera, L.; Southern, S. A.; Rao, G. K.; Richeson, D. S.; Bryce, D. L., New Experimental Insight into the Nature of Metal−Metal Bonds in Digallium Compounds: J Coupling between Quadrupolar Nuclei. Chemistry – A European Journal 2016, 22 (28), 9565-9573.

4. Klinkhammer, K. W., How Can One Recognize a Triple Bond between Main Group Elements? Angewandte Chemie International Edition in English 1997, 36 (21), 2320-2322.

5. Kambe, T.; Haruta, N.; Imaoka, T.; Yamamoto, K., Solution-phase synthesis of Al13− using a dendrimer template. Nature Communications 2017, 8 (1), 2046.

6. Schnepf A. (2016) Metalloid Clusters. In: Dehnen S. (eds) Clusters – Contemporary Insight in Structure and Bonding. Structure and Bonding, vol 174. Springer, 135-200.

7. Schnöckel, H., Structures and Properties of Metalloid Al and Ga Clusters Open Our Eyes to the Diversity and Complexity of Fundamental Chemical and Physical Processes during Formation and Dissolution of Metals. Chemical Reviews 2010, 110 (7), 4125-4163.

8. Köhnlein, H.; Purath, A.; Klemp, C.; Baum, E.; Krossing, I.; Stösser, G.; Schnöckel, H., Synthesis and Characterization of an Al₆₉^3- Cluster with 51 Naked Al Atoms:  Analogies and Differences to the Previously Characterized Al₇₇^2- Cluster. Inorganic Chemistry 2001, 40 (19), 4830-4838.

9. The list of halides are selected from those listed in references 4-6 and element halide Wikipedia pages, checked against the original literature. The specific pages used include en.Wikipedia.org/wiki/Aluminium_halide, en.Wikipedia.org/wiki/Gallium_halides, en.Wikipedia.org/wiki/Indium_halides, and en.Wikipedia.org/wiki/Thallium_halides.

10. All potentials are taken from Bard, A. J.; Parsons, R.; Jordan, J. Standard potentials in aqueous solution. M. Dekker: New York, 1985. Note that this reference reports a Ga^2+/0 potential in addition to the Ga^3+/0​ potential given​​​​​​. This couple was not included since the nature of the Ga²⁺ species referenced (GaCl₂ produced by reacting Ga and GaCl₃) was unclear (i.e., it may be a Ga^IGa^III species or possess a Ga-Ga bond).

11. Greenwood, N. N.; Earnshaw, A., Chemistry of the elements. 2nd ed.; Butterworth-Heinemann: Oxford ; Boston, 1997.

12. Cotton, F. A.; Cotton, F. A., Advanced inorganic chemistry. 6th ed.; Wiley: New York, 1999; p xv, 1355 p.

13. Pardoe, J.; Downs, A., Development of the Chemistry of Indium in Formal Oxidation States Lower than +3 †. Chemical reviews 2007, 107, 2-45.

14. Aldridge, S.; Downs, A. J. The Group 13 Metals Aluminium, Gallium, Indium and Thallium: Chemical Patterns and Peculiarities, Wiley, 2011.

15. Bond energies are taken from Table 4.11 of Dean, J. A.; Lange, N. A., Lange's handbook of chemistry, 14th ed. McGraw-Hill: New York, 1992.

Contributors and Attributions

Stephen Contakes, Westmont College