Tangent-sphere models of molecules, V Henry A. Bent
University of Minnesota Minneapolis 55455
Alfred Werner and the Doctrine of Coordination
Packing models are widely used, in science as in everyday life, to account for the existence of stable structures. For many years, for example, packing models have been used to describe the structures of ionic and molecular crystals. Recently, Pauling has suggested that packing models might be useful in describing the structures of atomic nuclei (1). And their use to describe the electronic structures of atoms has been considered (2). Currently, packing models are extensively used in molecular biology (5). I n previous articles of this series (4), it has been suggested that packing models may be used to describe the electronic structures of covalent molecules. These "tangenbsphere models" may be viewed from several points of view. They may be viewed as a geometrical expression of the exclusio~~ principle (4a). They may be viewed as a quantum-mechanical refinement of Lewis's interpretation of the graphic formulas of classical structural theory (5). Or, as we now show, the tangentsphere models may be viewed as a generalization of the coordination theory of Alfred Werner. Werner's Theory of Valence
Werner's coordination theory, which he came to view as practically, if not quite, a general theory of valence, grew out of his early work as an organic chemist-one might say, as a theoretical organic chemist. For Werner's first, and still most famous, paper in organic chemistry, published when he was 24 years old, "On the Spatial Arrangement of Atoms in Nitrogen-Containing Molecules," with Hantzsch, in 1890 (6), was based entirely upon a study of the published literature. Noting that "all previous considerations of spatial isomerism have concerued only the carbon atom," Werner speculated that t,he cause of isomerism in compounds that
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contain nitmgen and in addition either a double bond between a nitrogen atom and a carbon atom or a double bond hemight be due to a different spatial tween two nitrogen atoms arrangement of the groups hound t o the nitrogen atom with respect to this atom itself. In other words, the task was to investigate whether the hypothesis developed by van't Haff and Wislicenus for the carbon atom could not also be extended to the nitrogen atom and finally perhaps even to other polyvalent a t o m [italics added].
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Three years later, reasoning from the properties of inorganic compounds, Werner published his "ingenious impudence," the Principle of Coordination (7). Here Kekule's doctrine of constant valency, so applicable to carbon, but not to most other atoms, was replaced by the doctrine of constant coordination. I n Werner's own words: 512
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The nnn~berof atomic groups which can become itnited to sn atom. I term the co-ordination number of the given atom: an atom with co-ordination number 6 has the pmperty of directly binding or o-ordinalzng six groups. The podion oecopied by onesuch gmup I terma eo-ordinalion sile.
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Werner's Principle of Coordination might have served as a rallying point for inorganic chemists, but it did not in his life time (8),partly because it was not supported by any experimental work of his own, being based entirely upon the experimental researches of others, particularly those of his later, ardent foe, S. M. Jijrgensen (9),and, probably more importantly, because it ran counter to widely accepted catenation-type formulas, which earlier had done good servire in organic vhenlistry (10). To the development and perfection of his Principle of Coordination Weruer devoted the remainder of his life (11). Extensive experimental work culminated, in the years 1907-1914, in convinciug demonstratiorls of the usefulness of the geometrical implications of the doctrine of coordination, through the isolation from wordination compounds of predicted cis-transisomers and carbon-free optical isomers (12). Through Werner's insight the facts of isomerism contributed to the development of structural inorganic chemistry as earlier; t,hrough van't Hoff's, they had contributed to the development of structural organic chemistry (15). In 1913 Weruer received the Nobel Prize in Chemistry "in recognition of his work on the linkage of atoms in molecules, by which he has thrown fresh light on old problems and opened up new fields of research, especially i n inorganic chemistry" (14). Werner's general views on the liukage of atoms in n~oleculesare set forth in his best,-known work, "New Ideas on Illorganic Chemistry" (15). I n t,his stillvaluable classic, first published in 1905, Werner deduces from the almost countless facts of inorganic chemistry a coucrete (yet suitably flexible (16)) solution to what was, in his view, "the most important and pressing problem of valence:. . . [findiug] a theoretical co~mectiol~ . . . between the doctrine of valence and that of coordination" (17). Koting that (18)
. . . the maximum co-ordination number of the vast majority of those elements far which it was possible to accurately obtain this value is six, and that only a few of the elements, members of the seoond group in the periodic system, viz. those with the s m l ~ l l e ~ t atomic volume, had the lower value of four. . .
Werner suggests that: "the marimum coordinatin number must be c o n s i d e d as hauing refwmee to the space a r w n d the s u ~ f a c eof the atom."
Wcruer's suggestion is so simple that it is not a t first glance illuminating. And yet, as we ran see today (4c), and as Werner himself emphasized, "The maximum co-ordination number, when considered sparially, provides a means by which a very great number of phenomena may be grouped together, and is the first clear explanation to give any idea of the combiniug possibilities of the atom" (19). The full meaning of Werner's statemmts beconles appareut when they are viewed from the vantage point of later developments in rhemistry and physics. Coordination Theory:
A Modern View
Wenier, had he been still scientifically active, would have liked 1,ewis's 1916 model of the electronic st,ructure of chemically rombined at,oms (20), particularly Lewis's electron-pair model of the valence strokes of elassioal strurtural theory, and the extension of that model t,o coordinat,ion rompounds hy Huggins (21) and Sidgwick (22), just as later Lewis must have looked with interest up011 the discovery by physicists of the wave, spin, and exrlusion properties of electrons, which were implicit in, if not exactly anticipat.ed by, his st,atic model of the atom. For, from the viewpoint of atomic cores and localized, uon-interpenetrating, valenre-shell electron pairs, all compounds are coo~dinatin con2pounds. All compounds are the product of the coordination of negat,ively charged elect,rons by smaller, positively charged atomic cores. I n particular, t.he bond diagrams of rlassical organic chemistry are nothing more (or less) than coordination diagrams, diagrams that show the coordination by small carbon cores of four valence-shell elertron pairs. In the language of Werner and Lewis, carbon in chemical compounds has an electrou pair coordination number of four. When applied a t the level of atomic cores and individual electron pairs, the doctrine of coordination summarizes in one simple, useful word, the word roovdination, all of the major ideas of modern electron physics as they bear on structural chemistry. "Coordination" reflects: 1 1 ) The presence in molemlrs of at,tractive irrkr~vt,ions
(among positively charged atomic cores and negatively charged electrons). ( 2 ) The wave character of electrons (which produces atomic cores and coordinated valence-shell electrons that are finite in size). (3) The Exclusion Principle (which permits t,wo but no rnox than two electrons to share the same region of space, and which t,herefore prevents electron pairs-r, in t h e i ~ classical representation, valence stmkea-fmm interpenetrating).
Without attract,ive interactions, without particles of finite size, and without spatial exclusion, one could hardly speak of "coordination" (or of tangent spheres). The presence of attractive interactions Wenier had had to postulat,e but could not explain. Their existence raised another question, however. What keeps t,he electrons of Lewis's electron-dot formulas suspended in space? One might equally well ask: What keeps the ions in sodium chloride apart? The two questions have the same answer: The wave character of electrons, and the Exclusion Principle. Use of the Exclusion Principle in a strong form (electron clouds of electrons whose spins are parallel do not interpenetrate) is suggested by the fact that, if the electron clouds of electrons whose spins are parallel
reall) could interpenetrate, one might suppose that, for the myriads of organic compounds known, it would be useful in some instances to draw structural formulas that rontairi valence strokes that cross each other, yet that is not the case. I t is a well-known, if unstated, rule of structural theory that valence strokes do not pass through each other. The doctrine of coordination emphasizes that chemiral bonding is an electrostatic phenomenon. From the point of viewof the doctrine of coordinationas developed by Werner, partirularized by Lewis, and refined through use of the ideas of de Broglie, Schrodinger, and Pauli (41, the valence strokes of classical structural theory represent negative ions-the "electride ions" of charge cloud models-and their points of intersection, where often are placed the syn~bolsof the elements, represent positive i o n s t h e atomic cores. From the Werner1,ewis-de Broglie-Schrodinger-Pauli point of view, all compounds are ' i n ' compounds. The doctrine of coordination in its modern form permits, indeed, all the insights of the ionic model of inorganic compounds to be applied to the classical bond diagrams of covalent rompounds (23). Additionally, it opens up a new field of research: the determination of the sizes and shapes of atomic cores and of coordinatedvalence-shell electrons. Pauli Mechanics
The modern doctrine of coordination explains how a centrally symmetric potential function about an atomic core produces in concert with the Exclusion Principle the two most salient features of chemical a f h i t y : saturation and directional character. The following quotation from Werner (24), in which one small, but significant, change has been made (for the word "atom" we have substituted the phrase "atomic core") summarizes the inlport.ant structural features of the modern doctrine of coordination. For tbe sake of simp1icit.ywe ran suppose the atomic core to he a sphere. Such a supposibion simplifies our mechanical picture
of thestructure of the molec~tle. We will also make the following supposition on affinity. Affinity is rtn attractive force which acts from the centre of the atomic core, and [according to Coulomb's Law]is of equal value at all points on its surface. The amount of affinity saturated by the linking up of two atomic mres [through shared electrons] is distributed on a definite cirenlnr segment of the surface of the atomic mre (binding zone), and varies within wide limits with the nature of these atomic cores.
From the viewpoint of the modern doctrine of coordination, the saturation and directional character of chemical affinity is not produced solely by the wave character of electrons. Quantum mechanics alone does not account for the saturation and directional character of chemical affinity. Another principle is required. That principle, which governs the behavior of all matter, is the Exclusion Principle. From the viewpoint of theoretical physics-more especially, of Pauli-The Doctrine of Coordination is a mechanics of the Exclusion Principle. This mechanics, which chemistry has been articulating slowly but surely for over a century, is most useful in the study of complex systems of strongly interacting fermions, such as electrons, i.e., in the study of chemical compounds. Unlike other kinds of mechanics, it has the peculiar, hut to chemists familiar, feature that it Volume 44, Number 9, September 1967
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produces stable structures. The salient features of these structures can be usefully, if not yet perfectly, described by simple packing models (4). Because this mechanics is grounded in the Exclusion Principle, it approprial,ely may be called Pauli Mechanics. Literature Cited (1) PAULING, L., Science, 150,297 (1965). (2) STEVENS,P. S., PTOC.Nat. Acad. Sci., 56, 789 (1966); GAMBA, A,, Phya. Lelters, 24A, 64 (1967). (3) WATSON,J. D., "Molecular Biology of the Gene," W. A. Benjamin, Inc., New York, 1965. ~~, (4) (a) BENT,H.A., J. CHEM.E D U C . , 446(1963); (b) ibid, 40,523 (1963); (c) ibid, 42,302 (1965); (d) ibid, 42,348 (1965). (5) BENT, H. A., Chemistry 39, no. 12, 9 (1966); 40, no. 1, R(lCl6il. ~-...,.
(6) Translated by KAUFFMAN, G. B., J. CHEM.EDUC., 43, 156 (1966). (7) WERNER,A,, Z. anorg. Chem., 3, 267 (1893); translated (in part) by PALMER, W. G., "A History of the Concept of Valencv to 1930." Cambridee Universitv Press. London. 116. ~ n g l s n h1962, , (8) SODDY,F., "The Interpretation of the Atam," G. P. Pub nsm's Sons, N. Y., 1932, p. 269;
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IHDE, A. F.. "The Development of Modern Chemistry,'' Harper and Row, 1964, p. 585. (9) KAUFFMAN, G. B., J. CHEM.EDUC.,36, 521 (1959). (10) See translations of papers by KEKULEand by COUPER in "Classics in the Theory of Chemical Combination" (Edilor: BENFEY,0. T.), Dover Publications, Inc., New York, 1963, Papers 5 and 6. (11) K A U F ~ A G. N ,B., "Alfred Werner: Founder of Coordination Chemistry," Springer-Verlag, New York, 1966, p. 33. (12) KING,V. L., J. CHEM.EDUC.,19,345(1942). (13) Ref. (101, Paper8. (14) Itef.(lI), p.94. (15) WERNER, A., "New Ideas on Inorganic Chemistry," translated by HEDLEY,E. P., Longmans, Green, and CO., New York, 1911. (16) ZWICKY, F., Phys. Rev., 43,1030(1933). (17) Ref.(I5),p. 15. (18) Ref. (161, p. 53. (19) Ref. (M), p. 54. (20) LEWIS,G. N., J . Am. Chem. Soe., 38, 762 (1916). (21) HUQGINS,M. L., Science, 55, 459 (1922). N. V., J. Chem. Soc., 123, 725 (1933). (22) SIDGWICK, (23) BENT, H. A,, "Ionic Models of Covalent Compounds," Symposium on "Models far the Discussion of Molecular Structure," Am. Chem. Soc. Meeting, Chicago, Ill., September, 1967. (24) Ref.(M),p. 73.
