George Vogel
Boston College Chestnut Hill, Mossochusetts
An Aid to Visualizing Fused Ring Systems
In
studying the important and interesting subject of conformation and stability in systems of fused cyclohexane rings, it is frequently difficult to visualize the shape of the molecule and to determine the nonbonded interactions from which the relative stabilities of the various geometrical isomers can be estimated.' It is not always convenient to build models, and even when this has been done, the interactions may still he difficult to find and count. The problem is greatly simplified when one keeps in mind that any system of fused cyclohexane chairs in fart represents a portion of the diamond lattice, and that each bond (we are concerned only with bonds directly associated with the ring carbon atoms) must therefore have one of four directions in space, represented by the four bonds around any one of the carbou at,oms. It is thus possible to label these bonds according to their direction, e.g., a, b, c, and d, conveniently reserving a for the axial bonds in the cyclohexane chair from which one starts, and then assigning b, c, and d to the ring bonds, starting with any bond and proceeding in any direction, provided the sequence is repeated twice. For example, a carbon taking part in the ring t.hrough a c and a d bond will have a b bond as the equatorial bond, as shown in Figure 1, from which it is seen clearly that all bonds with the same letter are parallel to one a n ~ t , h e r . When ~ this is kept in mind, it is easy to draw even rather complex systems. In trans-decalin, on the left of Figure 2, we have first labeled the right-hand ring. Since the fusion to the other ring is tl.ans, it must be diequatorial, and the bonds involved must he c and b as shown. The resulting sequence cdb is repeated once more in the new ring. The perspective view on the right of Figure 2 is t,he result of considering which bonds in the new ring are parallel to those of the old one (Fieser's "Chemist's Triangle" is a useful device for drawing cyclohexane chairs"). In cis-decalin (Figs. 3a and 3b), the fusion must be equatorial-axial. Of the two equivalent forms, the former is more readily drawn and visualized, but even the lat,ter presents no difficulty when one realizes which bonds are parallel in space; shading also is helpful with rings viewed head-on. Before proceeding to more complex systems, let us (a) DAUBEN, W. G., AND PITZER, K. S., in NEWMAN, M. S., Editor, "Steric Effects in Organic Chemistry," John Wiley and Sons, Ino., New York, 1956, pp. 23-35. ( b )ELIEI.,E. L., "Stereochemistry of Carbon Compounds," McGraw-Hill Book Co., Inc., New York, 1962, Chapters 8 and 10. % Asimple check of formulas in various books will show how often bonds which are in fact parallel are not so represented. Distributed by Reillhold Publishing Carp., New York.
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note how t,he "skew butane" interactions present in systems of this type can be detected and counted. I t is obvious t,hat one such interaction will be present in any C-C-C-C sequence unless the first and third bonds are anti to each other; in this latter case, they are parallel and therefore identified by the same letter. I t is thus readily seen that trans-decalin has no skew int,erartions (other than those confined to the same ring, which are present in any ease and need not be counted): all of the six butane units extending over bot,h riugs are anti (bcb, cbc, etc.). By contrast, three skew butane interact,ions are found in cis-decalin (adc, abc, and abc in Fig. 3b). This result is obtained more readily in this manner than by examining models, let alone sketches. When a 9-methyl group is introduced into transand cis-deralin (Figs. 4 and 5), four skew interactions
FIG. I
FIG. 30
FIG. 4
FIG. 5
FIG. 6 b
are int,roduced int,o the trans isomer but only two additional ones into the cis isomer, bringing them closer together in energy. The reader should have no difficulty in finding that both cis- and trans-9,lOdimethyldecalin have the same number of skew interactions (eight).
As a final example, one of the various perhydrophenanthrenes, the cis,anti,cis isomer, may be examined. The left-hand half of Figure 6a shows the result of first, labeling the center ring, and then the two outer rings, keeping in mind the proper steric relationships between the bonds. Seven skew interactions are readily found. On the right of Figure 6a, after drawing the center chair, the two others have been drawn in, remembering that bonds with the same letter will be parallel. This gives a good idea of the shape of the molecule. Now, since both fusions are cis, the entire system can "flip," axial bonds turning into equatorial and vice versa. The result is shown on the left of Figure 6b, and it is readily seen that now only six skew interactions are present, and this conformation should therefore be more stable than that of Figure 6a. A perspective view of this molecule is shown on the right. I t is not easily drawn by other methods. I t may be left to the reader to verify the interactions in other perhydrophenanthrenes and perhydroanthracenes,'" and to convince himself that the method here described also makes it easy to find whether a bond is equatorial or axial to a ring (e.g., the b bond linking the two outer rings in Figure 6a is axial to both, because b is not among the letters labeling these rings). I t also makes it simple, for example, to detect the energetically very unfavorable 1,3-diaxial interactions (as in cis,syn,cis-perhydrophenanthrene) or to predict the existence of boat conformations (as in the trans, syn,trans isomer) when an all-chair conformation is ruled out by the inlpossibility of a diaxial 1,2-fusion.
Volume 42 Number 5, May 1965
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