William 6. Jensen University of Wisconsin Madison, WI 53706
I II
Extending Ball and Stick Models by Using ~hree-center, Two-Electron Bonding Components
Though some molecular model sets make an attempt to represent the delocalized a-electron systems found on benzene and other conjugated species, most are restricted to representing the localized honding components corresponding to the kernels, bonds, and lone electron pairs of classical structural theory (I). This restriction to localized bonding components is for the most part a natural consequence of the mechanical limitations inherent in the models themselves. It is important to realize, however, that a delocalized MO or boudine com~onentand a multicentered MO or honding compo~enta;e not necessarily the same thing. Thus hoth empirical experience and MO studies of the localized bonding (2) in certain classes of molecules suggest the existence of multicentered, hut localized, bonding components other than the two-center, two-electron (2c-2e) bonds and one-center, two-electron (lc-2e) lone pairs of conventional Lewis structures and hall and stick models. Once this distinction is made ~~~~-~ it becomes apparent that standard ball nnd stick models can he extended easilv and nrofitnl~lv " hv - incoraoratinr!- such Iocalized multicentered components without, at the same time, unduly increasing their mechanical complexity. ~~~~~~
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single or a bonds as well and again postulates the use of a 3c-2e bonding component in the initial complex to explain the apparent existence of pentavalent carbon without the necessity of invoking high-lying d orbitals. Thus in the nitration of CHI in liquid H F using the NOz+ cation as the attacking electrophile, one obtains
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Olah has also suggested that vonventionnl triv~lentrarhoI he valled carlwniwn ions, as they cornium ions IV.E., CH ; respond to prkonated carbeues (e.g., CHz), and that the term carhonium ion, in keeping with the terms ammonium ion (NH4+)and oxonium ion (H30+),be reserved for the corresponding protonated neutral hydrocarbons instead. The simplest member of this class would he the methonium cation
Use of Localized Multicentered Bonding Components
Perhaps the most common and best known of these components is the closed three-center, two-electron (3c-2e) hond found in localized borane and carborane structures and generally symbolized as
This component finds use not only in localized horane and carborane structures but in a numher of other inorganic species, such as Al2(CH&, [Be(CH3)2]1~,K[PtC13(CzH3],and BdC14. It is also employed in describing the honding in a number of donor-acceptor or charge-transfer complexes, such as that between the Ag+ ion and benzene
where broken lines are used in the 3c-2e symbol to represent its incipient nature relative to the other bonds in the benzene ring. Even more imaortantlv. .. the use of 3c-2e bonds is hecoming increasingly pre\.alent in organicchemistry, particularlv in the area of clectroahilic suhstitution and addition reactions. More than 30 years ago Dewar (3) proposed that electrophilic attack at a double bond proceeded initially through the formation of a weak a complex between the attacking electrophile and the multiple bond, a process involving 3c-2e hond formation. Thus in the case of addition of C12 over the double bond in ethene we would have
Olah (4) has extended this concept to electrophilic attack a t
Carbonium ions and carbeuium ions together would constitute the general class of carbocations in analogy with the term carhanion used to describe negatively-charged hydrocarbon ions. As with the methonium cation, carhonium ions in general would all have 3c-2e bonding components in their structures. Construction of Models In light of hoth the widespread use of the 3c-2e honding component in inorganic and organic chemistry and the long established use of a symbol to represent it, it is surprising that no commercially available molecular model kit appears to offer i t as a model component (5).We have constructed such a kit by modifying a standard student molecular model kit consisting of 3/4 in. wooden halls and spring connectors sold by Laboratory Supplies Co., Inc. of Hicksville, New York. Y-shaped 3c-2e bonding components were made by melting together sections of 1' s in. solid polyethylene tubing with a microtorch and then trimming off any excess with a razor knife. I t is necessary that these components be made of a flexible material as considerable bending, hoth in the plane and out of the plane of the Y, occurs in the construction of
Figure 1. lleh) AIdCH&
Figure 2. (right) Agt-benzene complex
Volume 57, Number 9, September 1980 / 637
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Figure 3 (left) Dewar n c o m p l e x f o r Clz-CzHn Figure 4 . (right) O l a h c o m p l e x for CHI-NO2+
The correct shapes. wrrr~~pondin:!to the polyhedra and polyhedral traementi oredictc.d t w Wade's rules ( 6 1 . natumll\. result fro; "inflaiing" these-styx structures, each boron having an approximately tetrahedral arrangement of bonds and the flexibility of the bonding components allowing for considerable distortion from the deal angles if necessarv. Use of any one of the many possible resonance styx structures for the higher boranes also gives the proper geometry for each species, the choice of the styx structure used being dictated by the absence of open 3c-2e bonds and (for aesthetic reasons) the symmetry of the components (7). Finally, Figure 6 shows a model for the carborane 2.4-C~BsH7based on the structure
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recently proposed by Lipscomb ( 2 ) on the basis of localized MO calculations. It is apparent from the above examples that commercial production of 3c-2e bonding components (and possibly other localized multicentered components such as the 4c-2e bonds in Pt4(CH3)16 and Lid(CH&) would substantially enhance the value of molecular model kits for the inorganic and organic chemist alike. The author would like to thank Mr. Russ Riley for his help in making the necessary bonding components and Dr. Glenn Dirreen for photographing the models.
Figure 5. (left) ( a ) BIHlo ( b )B s H x Figure 6. (right) 2.4-C&H7
also replaced by straight sections of polyethylene tubing to give a uniform representation of all bonding components. The 3c-2e components were cut so that each arch of the Y roughly spanned a distance equivalent to the longest straight line bonding component (about 1%in.). The tubing was slightly larger than the holes in the balls and trimming of the ends with a razor insured a secure fit for the bonding components. Some example models are shown in Figures 1 through 6. Figure 1 shows a model of Ala(CH&j, Figure 2 the Ag+-henzene complex in eqn. 2, Figure 3 the Dewar a complex in eqn. 3, and Figure 4 the CH4-N02+ intermediate in eqn. 4. Figure 5 shows models of B 4 H 1 0 and B e H 1 0 corresponding to thestyx structures (-21 -1
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638 / Journal of Chemical Education
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11) An extended survey of currently svailablecnmmercial model kits har- recently been given hy Wailon, A.,"Mc,lecular and Crystel Stmeture Mdels," Halbted Prescr, Chichenter. England. 1978. (2) Reade* interested in the theoretical jurtifieafinn nElncalized hundingeomlwnenfs land consequently uf ball and stick mudelr in general) and in the distinction between deIncalined, lueaiired, and multicentered should c o n u l t the review by England, w., Salmon,L.S.,andRuedenberg,K..Furbrhr.Chem Forsch.. 23.31 l1971l.Areview 01localized Mo results for multieenteied bonds in boranes and carboranes can he ~~ found by consultine Lip%cumb.W. N.. Arc. (7,nrn R e s , 6.257 119731. A B B R I Yd this work Lipscnmb has suggested ceitain modifications ui the eonventianal sly= picttms:see Eprtein. I. R. and Lipscomb. W. N..lnon. Chem.. 10,1921 l19711. Univemity Press. I31 Dpwar. M. J. S.. "The Elec~onieThpowofO~gsnicChemirfw."Oxford oxford,,949. I41 Oiah. G.. "Carhorationn and Eleetrophilie Reactions: Wilev, New York, 1974. 151 T h e only malecular modeis 1 nm aware of which attemptto represent 3e-2e bond3 are b a r d o n the tangent-sphere malelpopularized by Bent IseeBent, H.,Forischr. Chsm. Forsch.. 14, 1 119701! and commonly used t o represent Gillespie's VSEPR. rules for predicting molecular geometry. Model kit3 based 0" the use "f pla~tiesphere. and rubber bands have heen extensively used by King lkee King. L. C., Ch~misliy.37 121, 12 I19641l U represent such tangent-3pheredomains.and Sunderwfrth IseeSunderuirth.S. G., J. CHEM. EDUC.. 47.728 119701) hasgiven sometangent-sphere malelr of 3e-2e bonded fritermediates in organic chemistry. Ifii Wade, K..Chrm. Rrit., 11.177 (1976). 171 Lipscomb. W. N.,"Boron Hydrides," Benjamin. NewYork. 1963.
