Armin Wilson ond David Goldhamer Bristol Myers Product Division
Hillside, New Jersey
I
I
Cytlobuttme Chemistry 7.
Structure a n d strain energy
The planar character of the skeletal carbon atoms of the cyclobutane ring has been accepted as a fact by organic chemists for many years (1). Modern textbooks of organic chemistry still continue to promote this idea, despite the existence of a variety of physical evidence that tends to restrict the catholicity of this concept (8). While the evidence for a "bent" or "folded" cyclobutane ring is neither as extensive nor as definitive as in the cyclohexane series, the data obtained during the last decade has nonetheless consistently tended to establish a warped skeleton for many of the simpler derivatives. Since the chemistry per se of these small rings has recently become both voluminous and, more important, fascinating, these conformational commentaries should properly be incorporated into the teaching of cyclobutane chemistry. Physical Approaches to Structure
We shall review briefly some possible limiting factors in the physical studies of structure before we consider in detail the various conformations that have been proposed for particular four-membered rings. One central fact ahout these small alicyclic rings should he borne in mind: They are dynamic systems with finite conformational possibilities. This fact is often forgotten in considerations employing graphic formulas or molecular models (3). At best these are a frozen photograph of our conception of the real molecule and not, unfortunately, a moving picture film of conformational events in the molecule. Instrumental probing for the molecular parameten on which we base our ideas of physical structure is likewise limited. One should hear carefully in mind that different techniques convey to us different kinds of raw information (4). Infrared and Raman measurements tell us essentially all that we need to know about the structure of a molecule even with their existing powers of resolution. Unfortunately, we can decipher this message fully only for very simple two- or threeatom molecules. By comparison, X-ray and electron diffraction techniqnes are only rough estimates. However, these latter techniques do allow us to locate relatively all the atoms except hydrogen even in fantastically complex structures (the hydrogen locale is presently accessible by NMR and neutron diffraction techniques). Hence we will find on occasion that infrared or Raman techniques will suggest one conformer while X-ray or electron diffraction will suggest another. To some extent our difficulties in reaching a wholly satisfactory decision are based on the instrumental A second article which will appear next month will discuss the reactions and mechanisms in cyclobutrtne chemistry.
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difficulties outlined above. There are also deeper underlying philosophical reasons. Pitzer cites an instance in his work with cyclopentane in which certain investigators felt unable to accept his "rippling" set of conformers for the cyclopentane molecule because of the "structural uncertainty" imposed by this concept (5). A remark made by Bertrand Russell some yean ago is apropos in this connection: "There has been a great deal of speculation in traditional philosophy [read: chemistry] which might have been avoided if the importance of structure, and the difficulty of getting behind it, had been realized (67." We are all familiar with the ancient proverb that "A thing is what it is and what it is becoming." We are further familiar with a specific application of the proverb; that is, the particle-wave duality of the electron. Such duality becomes manifest when we impose a "signal" on an electron and obtain a readable signal in return. The quality of the electronic state suggested by the signal, that is, particle or wave, depends on the particular type of perturbation. This uncertainty extends also to the molecule, which is considered to be a collection of electrons in orbitals that bear to each other and to the particular nuclei involved a most complicated set of quanta1 interrelationships. The echo of the principle of indeterminacy can still be heard then within the larger confines of molecular architecture. Therefore we can readily perceive that information fed back to us by instrumental interference with the processes that give "life" to the molecule is apt to consist in a multiplicity of answers rather than a yes or no answer concerning a "pet" conformation imagined by some one investigator. The immense complexity of problems of molecular symmetry is indicated by recent developments in conformational work on the cyclohexane molecule, especially the machinecomputationsof Hendrickson (7). We see here that the simple Chairl-Chair* relationship is no longer a sufficient basis for explaining all of the structural aspects, properties, and reactions of cyclohexane. We appear to he confronted also in the cyclobutanes with the problem of dealing with a molecule that presents itself in various shapes, our knowledge of which is dependent both on the technique used to gather the structural parameters and probably to an even greater extent on our primitive understanding of the nature of the motions of the atoms attached to the quantized chemical bond. Structural studies, though fraught with dangers inherent in the interpretation of instrumental data, are nevertheless of overwhelming importance for the chemistry of cyclohutane. There is no doubt that such studies will involve more precise application of the older techniques and that newer, more incisive tech-
niques will be added. This growth and refinement of techniques is absolutely essential, since we shall have to know what the relatively-relaxed molecule, disturbed only by its surrounding twins, 'looks like" before we can make a reasonably sound estimate of the particular shape of the transition state for a given reaction of this molecule. Since the chemistry of cyclopropane and cyclobutane together forms a class that might properly be dubbed "the chemistry of the abnormal or pathological C-C bond," we shall need as full an energetic and geometrical description of these moIecules as possible. Such finely-detailed structural studies are mandatory to the unraveling of this truly delightful chemistry. There are three cyclobutane conformations which have received the greatest attention as structural candidates in X-ray and electron diffraction studies. These include the Dl,, planar, Dz6 planar and the Dzn nonplanar (Fig. 1). Simple cyclobutanes tend in general to display a folded ring of symmetry Ds6. The dihedral angle theta formed between the tu-o intersecting planes of the ring has an average observed value of about 20" for most of these compounds (8). However, Bastiansien has recently reported a dihedml angle of 35' for the parent hydrocarbon (8). The tendency toward ring-warping across the diagonal is, logically enough, thwarted by fusion of other rings with the cyclobutane skeletal carbon atoms. Biphenylene (I) for example, contains a captive cyclo-
butane ring in the center of the molecule and has been found by X-ray analysis to be perfectly flat. Afurther
comment on the structure of this molecule is to be found in the chemical reactivity: the substitution reactions of biphenylene tend to be those of a ringfused cyclobutane rather than those of a similarlyconstituted cyclobutane or cyclobutadiene (9). X-ray analysis also indicates a flat cyclobutane ring and centrosymmetry in the isomer of 1,2,3,4,-tetraphenylcyclobutene (11) in which the consecutive pairs
of phenyl substituents are alternately cis and lrans around the ring (10). The carbon skeleton in the molecule is rectangularly disposed, reflecting possible contributions of cis repulsions of the phenyl groups to the lengthening of the &ernate skeletal bonds. Horuever, Meredith and Wright have suggested on the basis of measurements of the dipole moment that this isomer is neither flat nor rigid (3). The cis phenyl groups of the model are not free to rotate completely but are confined to an oscillatory motion about the C-phenyl to C-cyclobutane bond (11). The role of crystal forces in determining the "flatness" of this particular cyclobutane ring is not known. With the limited data a t our disposal, uae can make only a gross estimate of the factors that fundamentally determine whether or not a cyclobutane with a given set of suhstituents d l have a warped or a planar ring.
Figure I. The D (dihedral) clam of molecular point groups to which there three conformers belong, is chomcterired by a vertical principal axis, i, and two-fold rubridiory oxer perpendicular to the principal one. lhe descriptbn is completed b y consideration d voriow plones d symmetry that mmy b e Jther vtrticol or horirontd. Thus, the D4hplanor form has o four-fold principol oxis, i, (therefore DJ and a horizonhi plane of symmetry (therefore D a dto which the vertical planes of 3ymmetry k, k'; I, 1'; m, m', n, n' are subsidiary. (Vertical ploner indicated b y their liner of intersection with the horizonto1 plane of the ring.) Did wn-planal has a two-fold principal axis, j, (therefore 41 and two diagonoi (vertical) ploner of symmetry (therefore Dpdor sometimes Val, o, 0 ' ; p, p' thot bisect the angles between the two rub4diary two-bid axesq, q'; r, r'. The i d t e r 3ymmetry elements also hold for the D2dplanar form.
Dihedral angle, 8 , is the angle between p l m e
A, A', containing carbon ohms CL,C*, and Cd and plane ~
.
~
'
,
~Cs,G ~ tand~ Cc i ~
i
~
~
Volume 40, Number 10, October 1963
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505
The observed entropy of the parent hydrocarbon is, for example, too large to be accounted for by a simple planar form of Dl* symmetry alone. Therefore the structural order of this substance is greater than one, and a mixture of conformers must be present. There are also too many bands in the infrared absorption spectra a t room temperature to be accounted for on the basis of the allowed frequencies of the Dqhplanar form. Rathjens and Freeman have on the basis of these measurements put forward the suggestion that an inversion occurs which encompasses the two possible DX nonplanar conformations as the extreme structures and the D,, planar form as the mid-structure of the process (12) (Fig. 2). The barrier hindering this inversion is very low; as the temperature increases, the population of the planar form will increase rapidly at the expense of the bent or staggered forms.
J -30.
0'
lo.
Dihedral Angle (very approxim.,k)
Figure 2.
The introduction of simple suhstituents into the cyclobutane ring leads to a similar picture. Electron diffraction and X-ray studies on octafluorocyclobutane, methylcyclobutane, and other monocyclic cyclobutanes are suggestive also of Dzd nonplanar conformations. A third possible conformation, Dz, planar (Fig. I), was ruled out in the electron diffraction study of octofluorocyclobutane (IS). Recent work concerned with physicochemical properties of the cyclobutanes also points to possible ringfolded conformers. Brewster has suggested that a diagonally-folded (DZdsymmetry) cyclobutane ring would best explain the similarity of the observed and calculated values of the optical rotation of the caryophyllenic acid stereoisomen (14). Roberts' group has, moreover, used a buckled-ring model to explain an unusual magnetic spin-spin coupling between the proton and a fluorine nucleus separated by five consecutive saturated bonds in 1,l-difluoro-2,2-dichloro3-plienyl-3 methylcyclobutane (15). On the negative side, Hollis has run high and low temperature NMR studies on a group of substituted cyclobutanes and has found no perceptible change in the spectra over the range from approximately -70 to +90°C (16). Therefore, if these protons are subjected to an averaged environment from dynamic ring buckling, the onset of the ring buckling occurs well below -70°C. (The other, less attractive alternative is that the ring is frozen in one position and remains locked in that position throughout the given temperature range.) This latter finding is in contrast to the work of Jensen on cyclohexane (17). He observed a definite splitting of the ring proton signal in cyclohexane as the tem506 / Journal o f Chemical Education
perature of the sample was lowered. One source of all these difficulties in structural determination in addition to the two mentioned above is possibly to be found in the fact that the cyclobutanes are one of those strange transition structures lying between highlystrained, small cyclic structures such as cyclopropane and spiropentane, and the larger, relatively strain-free alicyclic hydrocarbons, cyclopentane, and cyclohexane. As such, cyclobutane partakes somewhat of the characteristics of each class. Strain Energy of Small Rings
Molecular strain, like the more general term molecular stability, assumes various meanings for the chemist (18). The organic chemist who is faced with the problem of rationalizing the "go" or "no-go" of a small-ring reaction will look upon strain as a bond property that affects the rate or over-all result of the reaction in a special way. If the ring breaks open under exceptionally gentle circumstances, strain is thought of as the property of the bond that is responsible for facile cleavage. The bond at which cleavage occurs is thus considered weaker than normal. If the solvolysis of a small ring halide is unusually slow, strain is invoked as the property of the transition state which forestalls its production in sufficient quantities to permit a normal rate (19). On the other hand, the chemical physicist is generally not concen~ed with the consequences of strain in reactions but is concerned instead with strain as something which contributes to abnormal physical properties in the "resting" or ground state molecule (20). The concrete expression of strain for the latter may be an unusual value of the dipole moment @I), an "off-value" of a thermodynamic function that points to an unusual conformational population, or a bond force constant that is smaller than usual. Thus a working definition of molecular strain which is satisfactory for all schools is not easily set down. We could consider strain in a limited sense to be the departure of the intraring spa carbon orbitals from their normal tetrahedral mode, as found in cyclohexane. A bond maladjustment of this type is usually considered to raise the total bond energy and thus make the molecule less stable. Hol~ever,strain is not, as we shall see, solely a destructive force tending to tear the molecule apart under any and all circumstances (2Z). Further, strain imparts to a ring a complex set of motions over and above the normal ones (3). Hence, the origin of strain in molecules and its ultimate effect on the physical and chemical properties of a given molecule are still phenomena that elude comprehensive definitions. We shall therefore merely review below certain aspects of strain energy of concern to the operating chemist and attempt to point out some of the less well-known features of the problem. Kaarsemaker and Coops have determined calorimetrically a value of 26 kcal per mole for the strain energy of cyclobutane or 6.5 kcal per methylene group (25). This observed value demonstrates that the ring is indeed strained but does not permit a clearer interpretation of the nature of this strain. Several semi-empirical calculations have led to the same or somewhat higher values than the one observed (20,24, 25). These latter calculations are not surprising since
any calculation today involving an atomic network as large as cyclobutane necessarily involves very broad estimat,es and considerable guesswork (80). I n addition, the uncertainties in conformational assignments noted in the last section indicate that we lack a secure model on which to base calculations of the physical parameters of bond strain, such as bond force constants, the degree of departure of bond angles from their normal values, torsional effects (bond-twisting), and the effectof repulsive (or attractive) forces between the nonbonded atoms. The qualitative picture of strain that emerges from the reactions undergone by cyclobutane and its derivatives is likewise not very enlightening, although certain general tendencies can be observed which are reagentdependent. We have long been aware of a tendency of the ring C-C honds to sever under a variety of chemical circumstances.' Further, as Roberts and his students have found, the cyclohutane Eramen-ork is a flimsy, collapsible structure under conditions favoring carhonium ion formation a t the ring carbons (26). A remarkable equilibrium is established under these circumstances in which cyclobutyl fragments coexist with cyclopropyl carhinyl, open chain, and other forms which still defy adequate description. Nonetheless, there are many circumstances under which cyclobutane (and cyclopropane) rings maiutain their curious structure intact, in particular, when treated with certain oxidizing agents (27, 88). Hopefully, improvements in techniques of separating mixtures and in spectral techniques such as NMR, ESR, and mass spectrometry will enable small ring chemists in the next few years to unravel much of this confusion and, finally, to achieve a firm understanding of the "rules of order" for the strained bonds in these molecules. Although the gross structure of cyclohutane as a four-membered, "saturated" hydrocarbon ring has long been settled, the more arduous task of precisely defining the electronic and energetic composition of the C-C and C-H honds is still in the primitive stages. However, a monumental conceptual step forward was made by Coulson and Mofi.tt in 1949 (29). The manner in which they attemptrd to solve the problem of the unusual C-C hond character of these small rings is instructive even today for the organic chemist. The original paper is still, in our view, required reading for those engaged in research or in teaching about small rings. The fact that the junior author, William Moffitt, was 24 years old at the time this paper was published, forms an interesting eocial as well as scientific commentary. Their basic contribution was the full pursuit of the intuitive idea that the principle of maximum overlap of atomic orbitals was not inviolate. The consequent implication of a "straight-line" hond was therefore snhject to reconsideration. The approach of Coulson and Moffitt enables us to see clearly and generally that a tetrahedral C-C hond can under circumstances of strain depart from tetrahedral symmetry, T d ,to the lower symmetry, C2., in small rings (Fig. 3). Even under these conditions the carbon-carbon orhitals involved can still provide a bond of considerable strength. A grasp of the implications of this concept is essential to an understanding, not only of small ring chemistry Cf.part 2 of this paper to be published in THIVJOURNAI..
generally, but also of other related phenomena such as the Thorpe-Ingold effect (SO). They proceeded by selecting the "hybridization ratio"2 of the ring carbon orbitals as the variational parameter of the molecule and minimized the energy of the molecule in terms of this ratio. Their calculations show that in the minimum energy state of a small-ring molecule, the ring carbon orhitals in, for example, cyclopropane, are a t an angle of 106' to each other and not a t GO0, as m ~ u l dbe required by straight line bonds. Thus the orbitals are not in a condition of regular spa
vi* T d %,mn.t..,
Carbon do",
Lu.R=1=6
Cmbn .tom With C l " symmetry '-*A Ll=b
Figure 3.
Cyslobutme (top view)
Benqene (3ide view)
A$V : m e o
af rorban orbital werlop
Figure 4.
tetrahedral o-verlap but are actually bent outward from the hypothetical internuclear straight line. This effect, while not so pronounced in cyclobutane, is nonetheless still present to the extent of about 20% as compared to cyclopropane. This poor overlap engenders in turn a certain amount of electron delocalization (pi character) which contributes to the stability of these ring honds. These hent honds are thus seen to be made up of contrasting forces: Poor overlap of the orbitals, which are nominally sp3, tends to reduce the strength of the hond below that of a structurally comparable C-C bond in, for example, ethane or cyclohexane, while the consequent possibilities for electron delocalization contribute a stabilizing force. One should note carefully that this latent pi character of these bonds is oriented in the same plane as the ring carbons and not in two planes parallel to the ring as in benzene. These hent orbit,als can he depicted as shown in Figure 4 and the residual pi orbital overlap by the dotted lines. This unusual type of orbital with its dual character has important chemical and physical implications. The pi character inherent in this bent ring hond has been known empirically for many years. The facile ring-opening of cyclopropane with bromine and the more reluctant ring-opening that results on the catalytic hydrogenation of cyclopropane and cyclobutane with Raney nickel catalyst are well-known 2This term dictates how much "p-orbital character" shall be mixed with the 8-orbital to provide a.proper bonding orbital for a given symmetry. Volume
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examples of this ethylene-like behavior ($8). Subsequent developments have disclosed that both of these small rings, when appropriately substituted, can be cleaved readily with a wide variety of reagents. This array of chemical cleavages is thus indicative of a special property of these small ring bonds. This can be generally attributed to an availability of electrons of the ring bonds considerably above that of a normal sigma C-C bond. For the moment, super electron availability in these bondscan beascribed to "pi-likecharacter" as the handiest common coin of bond language.
Figure 5. Vinylcyclobutane. Dotted area indicates main pi orbitol conjugated with the ring. Slonted line oreo indicates sigma orbital overlapof ring carbons.
Thus one would expect conjugative powers for these small ring bonds similar to but considerably weaker than ethylene This has been demonstrated by Cromwell on the basis of the spectral properties of conjugated systems which incorporate a cyclopropane ring as a substitute for one of the ethylenic units (31). According to Cromwell, conjugation of a clear-cut pi+ltvtmn syztetn s1v.11a i a vinyl or rarbonyl proup e m occur with thcsc sn~xllri~rfiOIIIV I bent o r l h l s " ~ I I P I the of the small rings are in the same plane with the pi orbitals of the attached group (Fig. 5). While somewhat controversial, Cromwell's views are supported by his data which is part of a growing body of evidence indicating that cyclopropane, a t least, does possess conjugative powers similar to ethylene. The evidence for the cyclobutane ring is not as abundant or as definite but even here some conjugative ability appears possible (32). This ethylene-like character is curiously absent in reactions with oxidizing agents. Neither cyclopropane nor cyclobutane are known to be attacked by ozone (28). However, cyclohexane, which is certainly more strain-free and more "aliphatic" in character than these small rings, is largely converted on prolonged ozonization into a mixture of products of which cyclohexanone and adipic acid have been identified ($3). All of this work should probably be repeated under the control of a single investigator. In view of the known sensitivity of many cyclobutane derivatives to light, ozonization of this small ring in the presence of light might prove interesting. This stability to oxidizing agents may conceiwbly be rooted in the unusual pi characteristics of these bent ring bonds as indicated by the work of Coulson and Moffitt. While these bonds are characterized as bent away from the hypothetical straight l i e joining the ring carbon nuclei, they are a t the same time bent below the tetrahedral angle of They should thus be designated as a kind of super sp3or sp3+hybrid orbital. There is unfortunately no simple way of relating this hypothetical concept to the observed stability of small rings to oxidants. This is, however, not the usual ~
u
~
aCoulson and Goodwin (J. Chem. Sac., 1962, 2851), have recently carried through a. rough M.O. calculation of theae C-C bond angles: cyelopropane, 108' 48'' and cyclobutane, 111' 28'.
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stability of a closed pi system since such systems are fragmented by ozone. Here is an area in which, as Pauling has suggested, the pi-sigma concept of bonding meets a practical test of survival and from which such a concept may not emerge intact (34). However, with these reservations, the very valuable orbital details of these small rings given by Coulson and Moffitt enable us to "see" the bond-weakening affects of strain in these molecules at the level of the electron pathway as well as to understand the possibility of the existence of residual ghost pi orbitals that encircle a molecule and thus bind it together in spite of the strain. Further, Coulson observed that there is possibly an area of increased electron density in the center of the cyclopropane molecule. As Coulson himself has said in another connection, further theoretical progress in the area of orbital strain should properly await the amassing of definitive laboratory work (35). The theoretician may thus know more clearly that which he must describe in precise terms and enlarge upon predictively. A square planar model with local symmetry Cz. at each carbon atom was used by Coulson and Moffitt in their work on the disposition of ring orbitals in cyclobutane. As we have seen, evidence for the presence of crumpled conformations in cyclobutane has continued to accumulate since that paper was written. While the departure from planarity is considered to be small, relative to a molecule such as cyclohexane, renewed attempts a t a quantum mechanical description of this molecule should take these conformations into account. Since strain energy and conformations are intimately related, a qualitative review of certain conformational aspects of this molecule can be of assistance in our attempts to understand the sources and effectsof strain. There are many anomalies in small rings that are as yet begging for a clear explanation. One such problem arises from the fact that the ring bond of cyclopropane is slightly shorter (1.524 A) than a normal C-C single bond (1.540 A) whereas that of cyclobutane is somewhat longer (1.548 A). A strained bond, because of its increased tendency to undergo cleavage with the appropriate reagents, would be considered as weaker and, therefore, longer. Coulson and MoEtt explained the short bond in cyclopropane as follows: Since the bond is bent, the l i e of maximum electron density which corresponds to the actual bond will follow an arc which is of greater length than the hypothetical straight line joining the carbon nuclei. The actual bond is therefore said to be longer than one is led to helieve by, for example, electron diffraction studies, which locate only the relative position of the nuclei. However, the long bond of cyclobutane is clearly not explainable solely on the basis given for cyclopropane. I n our efforts to unravel such puzzling molecular features, we are forced to consider and weigh simultaneously the contributions of a multiplet of conformations. As we have noted before, one can no longer elaborate structural theory for these small rings on the basis of a rigid, inflexible nuclear framework. Even the smallest of the cyclic molecules, cyclopropane, probably undergoes a continual change of conformations similar to cyclopentance (36). This alleged change would be manifested by a torsional hydrogen staggering in
consequence of single carhon oscillation (Fig. 6). The conformational alterations in cyclobutane must become even more involved because of the additional methylene group. Dunitz and Schomaker have suggested that a prime cause of the long bond in cyclobutane might well be the cross-ring repulsion of the
Figure 6.
1,3 carbon atoms (37) (Fig. 7). This would not be possible in cyclopropane, since each carbon is bound to only two neighbors. Hence none of the carbons in this ring "looks at" a middleman carbon. I n support of this proposed repulsion in cyclohutane, they cite the fact that the 1,3 pair of carhon atoms is 0.3 A closer (2.2 A) together than the corresponding 1,3 carbon atoms in cyclohexane (2.5 A). Consequently, the repulsive forces between these diagonal pairs of carbon atoms in cyclobutane should be considerable.
Figure 7.
This proposal is a n attractive one conceptually and points to a possible explanation of a good part of the strain energy in cyclobutane. Herein may lie also an explanation of the bending of the ring. Let us assume that the molecule would either have to expand in one plane (breathing) or twist out of the plane with a coupled torsional motion in order to compensate for this repulsion. The latter seems more plausible, since rotation about a bond can normally be accomplished with a smaller expenditure of energy than bond-stretching. The twisting in cyclobutane would involve most logically a diagonal pair of carbon atoms or, rather, both pain simultaneously. This would appear to be a more economical route for a four-membered ring than the single carbon twist characteristic of cyclopentane. Using this assumption one can account for the many observations of the form of Dzd symmetry in electron diffraction and X-ray work. The only alternative is to insist that such cross-ring repulsion would tend to maintain the carbon nuclei in the same plane. The latter avoids certain conceptual weaknesses in the former argument but fails to explain the structural observations. Since the molecule does show a tendency to escape the planar conformation, we should examine all of the possible means of increasing the stability of the molecule in the bent form. For this purpose we should, of course, like to relate cyclobutane to a simpler model.
The barrier to free rotation of the two methyl groups comprising ethane is probably in the last analysis a very simple example of strain energy. We could imagim cyclobutane as a substituted ethane in which two vicinal protons are replaced by a dimethylene bridge. However, after 30 years of prodigious effort, even this simple manifestation of strain is still wrapped in friendly controversy (38). Another possible approach to cyclobutane, still largely empirical, is the recently proposed "principle of minimum bending of orbitals" under development by Eyring and his group (39). This principle is based on one of the most difficult areas of quantum mechanics,
H
Figure 8.
that of the kinetic energy of the bonding electron. However, this rule appears to us to be capable of considerable conceptual development and holds out the promise of lending assistance in problems such as this one. Re-examination of the problem of dihedral bending in cyclobutanes in the light of this principle yields a partial answer to the riddle of "Why the molecule bends a t all." Conceivably, the planar molecule could be pulled into the DM conformation by the opportunity for a trans electron delocalization involving the HI-CI-CZ-H2 nuclei (Fig. 8). The right side of this equilibrium would he terminated by a new set of growing forces that would tend in turn to push this conformational equilibrium toward the left. These new forces are the repulsive ones that would be increasing as carbon atoms 1 and 3 approach each other and the angles between the ring bonds decreased. This scheme would entail a loss of co-planarity as the molecule departs from the planar form. Hence, any stabilization resulting from electron delocalization in the plane of the ring would he sacrificed. However, as noted above, this effect is presumably not very large in cyclobutane. Some gain in stability would occur as a ~ result of an eightfold (or sixteen for the two D z forms) trans staggering of nonbonded H atoms.' We are thus able to explain the following observations: 1. There can be two coexistent conformations, Dmand Dl,,, in dynamic equilibrium. 2. The C-H bonds would be somewhat stronger than those in ethane because of increased delocalization of the C-C bonding electrons toward the C-H bonds in cyclobutane. This has been verified experimentally by the observation of an increased H-C-H angle to l l Z O (increased sp2 character). Some additional stabilization of the C-H bond may also be realized throughrelaxationof the nonbonded H-H repulsion (40). t nit her unique manifestation of strain energy in There are actually two sets of spatially nonequivslent ring hydrogens which come into being as the ring bends (see Fig. 1). The axial set achieves coplanarity with the associated carbon nuclei at a dihedral anele of about 60". The eauatorial set, of course, does not. ~~
-
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certain cyclobutanes is the ease with which they decompose to ethylenes. I n a manner of speaking, these four-membered rings appear to possess a built-in memory of their ethylenic origin. Thus cyclobutanes' in many instances can be neatly broken into their component ethylenes by thermal urging. Srinivasan and Kellner demonstrated in an elepnt study of the pyrolysis of cyclobutane 1,1,2,2-d4at low pressures that a unimolecular decomposition occurs as illustrated in Figure 9 (41). No CHICDl was observed in thermal splitting of mixtures of cyclobutane and cyclobutane ds, so we have reasonable assurance that the pyrolysis of cyclobutane is of the simplest possible type: a unimolecular C2-C2 split uncomplicated hy hydrogen
H
----+---
o
H
-
1 H,C
1
+ =
CH,
DIG f CD2
2 H,C=CD, H
a
Figure 9.
state of this cyclodimerization, if achieved a t all, must resemble two loosely-bonded molecules of monomer. We assume that under these circumstances very few degrees of internal freedom would be available. Consequently, there would be little probability of "concealing" any sizeable amount of additional molecular energy within the incipient bonds for any length of time. Nor would the similar electronegativities of carbon and hydrogen contribute to stability in this instance. All these factors argue against the existence of a stable (long-lived) excited state in sufficient population numbers to permit the reaction to move down the product side of the energy hump. Several related reactions which have been discovered recently offer some promise that the cyclodimerization of ethylene will eventually be achieved, although in a manner more elaborate thau the purely thermal. The reactions listed below are rough aualogues of this cyclodimerization in one way or another. However, in each instance some special assistance factor is present:
,
exchange. Keat fragmentation can also occur in the liquid phase. For example, Gundermann in his studies on the cyclodimerizationof8-mercaptoalkylacrylonitriles to the respective cyclohutanes has also observed quantitative splitting of the dimer into the monomer under the proper conditions (48). Reverse cyclodimerization has, of course, long been known to occur when cyclobutane photodimers are exposed to "short" ultraviolet light (45). The ready reversibility of some of these reactions present a possible opportunity for the study of strain energy in four-membered rings by the use of appropriate kinetic and thermodynamic techniques.
(1)
The photocyclization of myrcene to 8-pineoe (47).
Table 1
Ring size
Number of carbon atoms in rine 4 5 6 7
Boruhydride roduotion of monoketonem (k2 X 10' 1 mole-'
Two Unsolved Problems
The dimerization of ethylene to cyclobutane has not heen observed. The prospects of such an accomplishment are discouragingwhen viewed historically. Ethylene has indeed been exposed to an enormous variety of experimental conditions which were calculated to produce higher molecular weight hydrocarbons. In no instance has cyclohutane appeared in the products. However, much of this work was done before the advent of gas chromatography and hence trace amounts would probably have gone undetected. Infrared and Raman spectral measurements which have been done on the products of such work are open to question. Attempts to identify peaks definitely characteristic of a unique ring motion (skeletal vibrations) for cyclobutane in these spectral regions have not been successful (44). One thermochemical calculation showed a small (minus 25 kcal) hut favorable enthalpy change for this cyclodimerization (45). ]base analyzed the problem indirectly some years ago in a paper concerned with ethylene polymerization (46). He pointed out that a "quasi-molecule," CaHs, consisting of two activated ethylene molecules would have a vanishingly small lifetime. During this short time the sum of the activation energies of the two ethylene molecules would have to be jettisoned in a quantized fashion. Such energy dumping is therefore subject to the dictates of the uncertainty principle and the principle of the conservation of momentum. The transition 510
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Journal of Chemical Education
trans-dicarhox$ic acids (K,'/Ka2). ',BROWN,H. C., A N D ICHIKAWA, K., Tetrahedron, 1, 223 (1057): cj. also STREITWIESER, A., Chem. Rev., 56,667 (1956). KIEFER.E. F.. A N D ROBERTS. J. D.. J . Am. Chent. Sot.. 84. 786 (1962);'the original article shbuld h; consulted for struriure~ of the particular hr&ides. C. D., A N I ) SMITH,T. D., J . Anr C h s n ~ Sor., . 82, *GUTSCHE, 4070 11960). d i l ; i d . , fbntnote za. -MARFA,F., ROCEK,J., A N D SICHER,J., Coll. Czech. (:hem. Cornm., 26,2362(1961). GERO,A., J . Org. Chem., 26,3157(1961). U BROWN, H. C., ET AL., in "Determination of Organic Strur-
'
'
tures by Physical Methods," BRAUDE,E. C., AND NACHOD, F. C., eds., Academic Press, New York, 1955, Vol. 1, p. 6'25; cf. Gourn, E. 8 , "Mechanism and Structure in Organic Chemistry," Hdt, Rinehart and Winston, New York,l959, p. 242.
(2) The cross cyclodimeriaation of ethylene and tetrafluoroethylene (48).
(3) The dimerization of ethylene to linear hutenes in the presence of weak Lewis acids (49). 2 H2C = CH? -r CH, - CH
=
CH - CH, CH! = CH
+
- CHICH1
Some years ago Roberts and Chambers made a thorough study of the properties of alicyclic ring compounds (50). In general, they found that a number of properties would indeed change in a more or less regular fashion as one ascends the series. However, in the course of preparing this review, we observed a curious alternation of properties which was particularly marked for the subset, cyclobutane, cyclopentane, cyclohexane, and cycloheptane. These are tabulated helow for the C&I hydrocarbon derivatives. We cauuot possibly judge whether the similarity of properties between cyclohutane and cyclohexane derivatives is indeed indicative of the participation of a "bent" conformer of cyclobutane. To do so a t this stage would be tantamount to invoking the "Rule of Selective Inattention to Data.'I5 However, one group of investigators is attempting to locate the "axial" and "equatorial" groups in cyclohutanes by means of microwave spectroscopy (61). This investigation and the others cited previously proves, we believe, our general contention: namely, that cyclohutanes "in the real and in the round" are far less symmetrical than the graphitic flat square would imply. If this be so, then chemical evidence for this will begin to occur "at the bench." We can only conclude, with A. M. Whitehead, that "Panic of error is the death of progress (5t)."
(12) RATHJENS,G. W., JR.,FREEMAN, N. I
