Bonding Zintl-Klemm concept

The Zintl-Klemm concept evolved from the seminal ideas of E. ZintI that explained the structural behavior of main-group (s-p) binary intermetaUics in terms of the presence of both ionic and covalent parts in their bonding description [31, 37]. Instead of using Hume-Rother/s idea of a valence electron concentration, ZintI proposed an electron transfer from the electropositive to the electronegative partner (ionic part) and related the anionic substructure to known isoelectronic elemental structures (covalent part), e.g., TK in NaTl is isoelectro-nic with C, Si and Ge, and consequenUy a diamond substructure is formed. ZintI hypothesized that the structures of this class of intermetallics would be salt-like [16b, 31 f, 37e]. 

G. A. Papoian, R. Hoffmann, Hypervalent bonding in one, two and three dimensions extending the Zintl-Klemm concept to nonclassical electron-rich networks. Angew. Chem. Int. Ed. 39 (2000) 2408. 

As mentioned in the Introduction, no structural information on these species was available for more than 40 years after the discovery of the first Zintl metal cluster anions, since no pure crystalline phases could be isolated and characterized structurally. Nevertheless, early efforts to rationalize the observed formulas and chemical bonding of these intermetallics and related molecules utilized the Zintl-Klemm concept [75, 76] and the Mooser-Pearson [77] extended (8 — N) rule. In this rule N refers to the number of valence electrons of the more electronegative metal (and thus anionic metal) in the intermetallic phases. 

The limitations of the simple Zintl-Klemm concept can be illustrated by differences in the two [MT1] intermetallics (M = Na [79] and Cs [80]). Complete electron transfer from M to T1 leads to [ M TI, where the Tl anion with four valence electrons is isoelectronic with a neutral group 14 atom and four bonds and needed to attain the octet configuration. Hence, the Tl- anion should form structures similar to allotropes of carbon or heavier group 14 elements. Indeed, [NaTl] has a stuffed diamond structure [79] with internal Na and an anionic (Tl-) lattice similar to diamond. However, the Tl- anions in [CsTl] form tetragonally compressed octahedra [80] unlike any structures of the allotropes of carbon or its heavier congeners. 

This chapter reviews the methods that are useful for understanding the structure and bonding in Zintl ions and related bare post-transition element clusters in approximate historical order. Thus, after briefly mentioning the early Zintl-Klemm concept, we proceed to discuss the Wade-Mingos rules and related ideas. We then conclude with a discussion of the jellium model and special methods pertaining to bare metal clusters with interstitial atoms. 

Early efforts to rationalize the observed formulas and chemical bonding of Zintl ions and related species used initially the Zintl-Klemm concept [10, 11] and subsequently the Mooser-Pearson [12] extended (8 — AO rule. In this rule, refers... 

The intermetallic phase [26] Na2Tl illustrates a simple application of the Zintl-Klemm concept to a group 13 metal cluster. Complete electron transfer from Na to T1 leads to the (Na" )2Tl formulation. The Tl dianion is isoelectronic with group 15 elements and thus should form similar tetrahedral structures with six two-center two-electron bonds along the edges of the tetrahedron. Indeed, the Tl anions in the Na2Tl phase form Tl4 tetrahedra, similar to the isoelectronic P4 and As4 units in white phosphorus and yellow arsenic. 

For a general formulation of the Zintl-Klemm concept, consider an intermetallic AmX phase, where A is the more electropositive element, t3 pically an alkali or an alkaline earth metal. Both A and X, viewed as individual atoms, are assumed to follow the octet rule leading to transfer of electrons from A to X, i.e., A AF, X —> X , so that mp = nq. The anionic unit X arising from this electron transfer is considered to be a pseudoatom, which exhibits a structural chemistry closely related to that of the isoelectronic elements [11]. Since bonding also is possible in the cationic units, the numbers of electrons involved in A-A and X-X bonds of various types (caa and exx> respectively) as well as the number of electrons e not involved in localized bonds can be generated from the numbers of valence electrons on A and X, namely and ex, respectively, by the following equations of balance ... 

The efforts to rationalize the formulas and structures of Zintl ions and related species predated extensive definitive structural information on anionic post-transition metal clusters obtained by Corbett and his group in the 1970s [8, 9]. After enough such structural information on the bare post-transition metal clusters became available, the resemblance of their polyhedra to the known polyhedral boranes became apparent. For this reason, the simple Zintl-Klemm concept has been largely superseded by newer, more advanced descriptions of chemical bonding in such clusters, initially those applied to the polyhedral boranes. 

The first question posed by this structure concerns the formal charge distribution between the two Gd, B6 and B2 units. If we naively apply the Zintl-Klemm concept we arrive at [Gd3+]2[B6, B2]6. The [B6]2 cluster with six external bonds obeys the cluster electron-counting rules. Consequently, the B2 fragment must have a charge of —4. This corresponds to saturated eight-electron B centers, and requires non-planar (tetrahedral) B centers. This does not agree with the observed planar B centers. But we know the metal does not need to be fully oxidized. Consider sp2-hybridized B atoms which satisfy the octet rule. This would lead to [Gd2+]2[B62 ][B22 ] and suggests a B=B double bond. OK, but planar B is... 

A general relationship between Zintl-Klemm concept and defect formation has been formulated [15, 16] recently. For a compoimd AaB, nstoichiometric numbers) the total number of valence electrons E per formula unit relates to the average number of bonds per atom N and to the number of defects d. 

On the silicon-rich side of the Ca/Mg/Si systems new phases have additionally been foimd. According to the Zintl-Klemm concept they must have a higher mean bond order than those discussed previously. 

The inherent basis of these procedures is the Zintl-Klemm concept and the Mooser-Pearson extended (8 — N) rule. Formerly applied only to classical two-center-two-electron bonds, the extended procedures comprise all varieties of bonding (multiple bonds, partial bonds, multicenter systems, radicals, and free electrons). Generally, for a compound AmB , an electron transfer A- A +, B- mp = nq ) to the more electronegative element B forms pseudoelements k, B that show the structural principles of the corresponding isoelectronic elements with the whole spread of homoatomic bond types. Alternatively, one can derive from the number of valence electrons e and cb according to the equation otca + nee + k = 3n the term k = saa + Y. bb - e, which accounts for the... 

Which, of course, brings me to the exception—the marvelous and useful Zintl concept.3 The simple notion, introduced by Zintl and popularized by Klemm, Busmann, Herbert Schafer, and others, is that in some compounds AxBy, where A is very electropositive relative to a main group element B, one could just think, that s all, think that the A atoms transfer their electrons to the B atoms, which then use them to form bonds. This very simple idea, in my opinion, is the single most important theoretical concept (and how not very theoretical it is ) in solid state chemistry of this century. And it is important not just because it explains so much chemistry, but because it forges a link between solid state chemistry and organic, or main group, chemistry. 

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