Isomers of Benzene I. Gutman Faculty of Science, University of Kragujevac, P.O. Box 60, YU-34000 Kragujevac, Yugoslavia J. H. Potgieter PPC Technical Services, P.O. Box 40073, Cleveland, 2022, Johannesburg, Republic of South Africa
Benzene, CsHs, is the simplest and best-known representative of aromatic hydrocarbons. I t was discovered by M. Faraday in 1825. Its most importH2C=CH-C=C-CH=CH2 HCIC-(CH,)rC-CH a n t structural feature, namely t h a t its carbon atoms form a six-membered ring, wa6 established 6 7 by A. Kekule 40 years later. The structure of the benzene molecule cannot be represented by a single classical structural formula. The reason for this is that not all of its chemical bonds (namely those formed by the so-called n-electrons) can be consid8 9 ered a s two-centric; i.e., a s being localized between two particular atoms. An often-used solution of this difficulty is to regard benzene as a resonance hybrid of two of its Kekul6 structures Ia and Ib (13). More details on the structure of benzene can be found in any textbook of organic chemistry For the purpose of this paper, i t is important to note that 10 11 12 t h e molecule of benzene consists of six carbon atoms and that a hydrogen atom is attached to Figure 2. Some known CsHs-speciesthat are not valence isomers of benzene. each carbon. In other words, benzene consists of six CH-moups, and its formula can, therefore, be writtenis (cH)~. one ring, a double and a triple bond (e. g., 12, Fig. 21, or Benzene is a colorless liquid with a relatively pleasant the compound is acyclic with four double bonds, or odor. Its melting point is 5.5 'C and its boiling point 80 'C. is acyclic with two double bonds and a triple bond (e. g., 6, Fig. I t is a very stable substance and has important applica21, or tions in the chemical industry. Benzene is claimed to be is acyclic with two triple bonds (e. g., 7, Fig. 2). carcinogenic. As can be seen from the above, there are several hundred Isomers and Valence Isomers of Benzene possible C&-isomers, some of which are well-known compounds; for instance, 1,5-hexadien-3-yne (or divinylThe formula C.H., .. ... imnlies that a narticular hvdrocarbon acetylene, 6)and 1,bhexadiyne (or dipropargyl, 7). The possesses r = ( 2 n 2 - nl I 2 rings andlor multiple bonds. In bicyclopropenyl compounds, 8 a n d 9, together with the r = 4, which means that a comthc case ofthc CcHc-soecics. - - . (CH)G-hydrocarbon5, were obtained i n 1989 by W. E. pound of the formula CfiHfieontains either: Billups a n d M. M. Haley (4). Some very u n u s u a l four rings and no multiple bonds (e. g., 4, Fig.11, or isobenzene compounds (10,11,and 12);i.e., six-membered three rings and a double bond (e. g., 3, Fig.11, or carbon rings with the same total number of hydrogen two rings and two double bonds (e. g., 2,5, S,9, Figs. 1and 21, atoms and double bonds a s benzene, have been syntheor sized recently (5,6).Figures 3 and 4 contain a few more t w o nngr and s tnple hnnd, or examples of CsHfi-isomers.A recent computer-aided proceone rinpand three double Lnnds ce. g., 10, 11, Fig. 21, or dure resulted in the construction of 217 distinct CEHs-isomers (7).
F 4
B-4
0 0 0
.
I n connection with Figure 4, the following historical cuOn 4 February 1867, a t riosity should be mentioned (8,9).
Figure 1. The known (CH)E-isomers:benzene ( I ) , Dewar ( Z ) , benzvalene (3),prismane (4), bicycioprop-2-enyi (5). 222
Journal of Chemical Education
benzene
Figure 3. The five possible acyclic benzene-isomers containing two triple bonds.
1989. After the lecture, a student asked how one could be sure that compounds 15 were the only possible (CHI -isomers. Because we had no immediate answer to this question, we decided to design a formal demonstration of the f a d that the (CH)fi-isomersdepicted in Figure 1 are the only possible ones. For this purpose, graph theory was chosen (14-18). When the language of graph theory is used, it can be seen that every valence isomer of benzene corresponds to a six-vertex connected cubic multigraph. It is relatively easy to enumerate and construct these H multigraphs (cf. Fig. 5). / \ H H I We briefly outline the construction of H-CC-H \ lH \ lH \ C-c the multigraphs 1-6. Avertex will be said C c=c to be saturated if three edges are incident II I I II II C c=c C-C to it. We may start with six isolated verti/ \ I I I I C,CXH ces v ~ , v ~ , v ~ , vand ~ , vvs ~ ,and analyze in H H H,C--CH, H&-CH, I how many ways they can be saturated so H t h a t the multigraph obtained i s connected. One should first observe that two vertiFtgure 4. Benzene-~somersconsidered by Dewar (1867);the compound marked by an asterces cannot be connected by a triple edge, ~skIS nowadays called Dewar benzene. for then they are immediately saturated and need not be connected to the remaina meeting of the Royal Society in Edinburgh, the British ing four vertices. Thus, only single and double edges may chemist James Dewar read a paper entitled "On the oxidaoccur. tion of phenyl alcohol and a mechanical arrangement Examine fint the case when a double edge is present; let adapted to illustrate structure in the non-saturated hydrothis edge connect the vertices vl and vz. Then one more carbons" (10). In his lecture, Dewar described a mechaniedge must be attached to both vl and vz in order to get cal device consisting of a series of bars and nuts, with saturation. The vertices vl and vz may be adjacent either which he could construct models of organic molecules. In (a)to a single vertex v3, formingthus a triangle, or order to illustrate the potential uses of his invention, he to two distinct vertices v3 and v4. constructed a model of the Kekul6 formula of benzene, as well as of six further CsHs-isomers (Fig. 4). Dewar never In case (a)the vertex v3 must be incident to one addiclaimed that any of these six models could serve as altertional single edge, whose other end is a vertex v4. In order to saturate v4 we must attach to it two more edges. Benative representations of benzene. cause two more vertices (v5 and vs) are available, this can Somewhat later the German chemist H. Wickelhaus (11) be done in a unique way, resulting in the multigraph 5. proposed a formula for benzene that coincided with one of In case (p) the vertices v3 and v4 are either Dewar's examples (marked by an asterisk in Fig. 4). Eventually, the chemical community started (erroneously) to (PI) not adjacent, or call it the Dewar benzene formula. I t was only in 1963that (P2) connected by a single edge. it became clear that KekulB's formula and that of Dewar They must not be connected by a double edge because correspond to two completely different compounds. then the saturation process would end before all the six Benzene-isomers with the formula (CHI are referred to vertices are included into the construction. as valence isomers of benzene. In other words, a C&-speIn case (P1) the remainingvertices vs and v6 can be either cies is said to be a valence isomer of benzene if it is composed of six CH-groups. In contrast to the tatal number of (P{) adjacent to both v3 and v4,forming thus two pentagons, C&-isomers, the number of possible valence isomers of or benzene is quite small. There are only four such compounds, which have been obtained experimentally, and their formulas (2-5) are depicted in Figure 1.Details of the chemistry of compounds 2-5 can be found in a recent artlcle published in thls Journal (12). Dewar benzene (2), benzvalene (31,and prismane (4) are colorless liquids that decompose relatively easily to benzene (1).They were discovered in 1963 (by E. E. van Tamelen and S. P. Pappas), 1967 (by K. E. Wilzbach et al.), and 1973 (by T. J. Katz and N. Acton), respectwely. When Billups and Haley ( 4 ) reported t h e synthesis of bicycloprop-2-enyl (5) in 1989, it was believed that all the valenceisomers of benzene had been discovered (13).
e
*
-
One More (CH)slsomer? In 1991, one of the authors (I. G . ) visited the King's School in Canterbury, England, and gave a lecture on benzene. In the lecture he mentioned that benzene had four valence isomers, the last of which had been synthesized in
Figure 5. Connected &vertex cubic multigraphs; the graphs 1-5correspond to the (CH)-isomers1-5 from Figure I ; the graph 6 would correspond to the hydrocarbon 13;these graphs were first reported by A. T. Balaban (19). Volume 71 Number 3 March 1994
223
(PI") each adjacent to one of the vertices v3 and v4,forming a hexagon. Subcases (Pi) a n d (P,")immediately lead to the multigraphs 3 a n d 1,respectively. By this t h e case (PI) is exhausted. Similar arguments show t h a t t h e only multigraph satisfying (Pz) i s 2. T h e examination of t h e connected cubic multigraphs without double edges i s analogous and results in 4 a n d 6. We, thus, establish that, i n addition to t h e five cubic multigraphs corresponding to (CH)risomers 1-5 from Figure 1,one more multimaph can be wnstructed t h a t would correspond to a hydro&&on species, 13.
valent (two-centric) bonds. that all carbon atoms are formally four-valent, and that a hydrogen atom is attached to each carbon. In other words. formula 13 reoresents a (CHIisomer obeying all t h e requirements of thcclassical t h e o j of chemical structure. The unusual feature of hydrocarbon 13 is i t s (clearly very long) C-C bond, which, of necessity, passes through a four-membered ring. If i t is possible for molecules of type 13 to exist at all, they will possess a n enormous steric strain and are expected to be extremely reactive moieties. Nevertheless, we wish to emphasize t h a t t h e set of ( C l l ~ ~ i s o m epresented rs in Figure 1 is not complete. It 1s possible to construct one more CH16-species that obeys the rules of classical structural chemistrv. Althoueh it is more ~~~t h a n likely t h a t a compound of the >ormula i 3 would be h i ~ b l yunstable and not a reasonable tareet of chemical synthesis, t h e possibility of its existence(perhaps a s a transient intermediate) should not be discounted. ~
~
Literature Cited 1. Wheland. G. WResomncp in Organic Chemistry; Wile?: New York,1955. 2. Pauling, L TheNolureoffha ChemimlBond; Cornell Univ Rees: Ithaca,New York, 1960.
A. T.Balaban seems to be t h e fust to point out this sixth v a l e n c e i s o m e r of b e n z e n e (19). H e d u b b e d i t "benzmobiusstripane". Eventually t h i s hypothetical hydrocarbon was considered by R. R. Karl and S. H. Bauer (20)and quite recently by S. D. Warren and B. M. Gimarc (21). . .
It i s by no means easy to deduce t h e actual form of t h e hydrocarbon 13. We depicted i t (somewhat arbitrarily) as a distorted octahedron. What we deem to be important i s t h a t all the atoms i n hydrocarbon 13 a r e wnnected by w -
12. Potgleter. J:H. J. Cham Educ. l'k1,68,28&281. 13. See; for instanstane,Angow C 6 m . Inf. Ed. Engl. 1889,28,1\2%9. 14. Seybold, P. 0.; May, M.; Bagal, U. A. J Chem. Educ. 1881,64,57.%581. 15. Balaban, A. T.; Kennedy,J. W: Buintas, L.V.J C 6 m Educ. 1988,66,304413. 16. Haneen,P J.; Jun, P. C. J. C6m.Edue. 1988.65.574-580, 17. Trhajstic, N. Chemical Gmph Theory. 2nd ed.: CRC Press: B- Raton, FL, 1992. 18. See the September 1992 issue of his Journal, that contains a series ofsmcles devoted to chemical applications ofgraphs: J Chem. Educ. 1992.69.690-718. 19. Balaban, A. T. Re". RoumoineChim. lW. 11, 1097-1116. 20. Kar1.R. R.;Bauer,S. H. J Mal. Sfrucl. 1975.25, 1-15. 21. Warren, D.S.; Gim8rc.B.M. J A m . Chm. Soc. 1982,114,5378-5385.
Research Associateship Opportunities The National Research Council announces the 1994Resident, Cwperative, and Postdoctoral Associateship Programs to he conducted on behalf of Federal agencies or research institutions whose 140 participating research laboratories are located throughout the United States. The programs provide opportunities for PhD scientists and engineers of unusual promise and ability to perform research on problems largely of their own chwsing yet compatible with the research interests of the sponsoring laboratory. Initiated in 1954,the Associateship programs have been awarded t o over 7000 scientists ranging from recent PhD recipients to distinguished senior scientists. Approximately 350 new full-time Associateships will he awarded this year in a broad spectrum of sciences including chemistry, earth and atmospheric sciences, and biological sciences. Most programs are open to hoth US and non-US nationals and to hoth recent PhD degree recipients and senior investigators. Awards are for one or two years, renewable to a maximum of three years. Senior applicants who have held the doctorate for at least five years may request a shorter period. Annual stipends for recent PbD's are in the $30,00045,000 range, with appropriate adjustment for senior Associates. Applications submitted directly to the National Research Council are accepted on a continuous basis. Those postmarked no later than April 15 will be reviewed in June with announcements made in July; those received by August 15 will be reviewed in October and recipients will be announced in November. Information an specific opportunites and participating laboratories, as well as application materials, may he ohtained from: Assaeiateship Programs (TJ2094iD31,National Research Council,2101 Constitution Avenue, N.W., Wasbiogtan, DC 20418.FAX: (202)334-2759,
224
Journal of Chemical Education
