Edward A. Waltersl University of Minnesota Minneapolis
Models for the Double Bond
A s experimental data accumulate and theoretical concepts are refined, early explanations of natural phenomena are often rejected as too naive. I n the light of even more empirical evidence and clearer insight, however, it is found that many of these original models contain more than a mere modicum of truth. The case in point in this paper is the chemical double bond. The first construct was that of two atoms held together by "bent" single bonds and the later model is the u,?r description based on a quantum mechanical argument. Here the "benbbond" picture of the double bond will be discussed with particular emphasis on recent results obtained by studying detailed structure of molecules. I n this way the merits of the older model can be demonstrated and, since current texe books, with very few exceptions ( I ) , discuss the nature of the double hond in the language of the u , a approach, the value of including the Baeyer description as an alternative model can be emphasized. At this point let us reconsider some of the experimental evidence that was available a t the time the first model of the double hond was proposed. The simplest homologous series of hydrocarbons has the general formula C,&. + and is characterized by being chemically unreactive. These compounds are pictured as a chain of carbon atoms each surrounded tetrahedrally by four pairs of electrons, each pair shared more or less equally with an adjacent carbon atom or proton. There is another series of hydrocarbons with the general formula C,Hz,; one of the two possible ways of imagining this group is to eliminate the terminal hydrogens from the alkanes and to join these ends in a cyclic arrangement,
initiated by attack of an electrophilic species on the nnsaturated site; this suggests that the unsaturation may be physically represented as a region of high electron density localized between two adjacent carbon atoms at some definite point in the chain. I n its ability to undergo addition reactions the chemical reactivity of the double bond is related to that of the cycloalkaues as can be seen from a comparison of the ease of hydrogenation of the compounds in Table 1. The fact that butened exists in two geometrically isomeric forms, cis and trans, whereas n-butane, the saturated analog, exhibits no such isomerism, indicates that rotation about the unsaturated site is severely hindered, in fact, by some 40 to 46 kcal mole-' (8) as compared with 3 to 7 kcal mole-' for the internal rotation of alkanes.
Table 1.
A
Reactivity of Cycloalkanes to Hydrogen Reaction Temperature
H,, Pd
-----+ CH,CH2CHs
80'
Boeyer Model
The second model for this series is also a chain-like progression of carbon atoms, judging from a comparison of melting and boiling points alone (9). The primary distinguishing chemical feature of the second set is its ability to undergo addition reactions. For example, one mole of hydrogen may he added to these compounds under suitable prerequisites of pressure and catalysis to give the corresponding alkane, and this new product will accept no more hydrogen under normal hydrogenation conditions. Since the C,H,. sequence, the alkenes, is amenable to addition of certain reagents, it is given the term "unsaturated." It is known that the process of addition is frequently
' American Oil Foundation Fellow, 1964-65. 134
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With even this limited evidence it is now possible to suggest answers to the question of how this rigid region of high electron density can be physically represented in keeping with current bonding theories. Noting that the carbon atom is generally tetravalent and employing the ideas of van't Hoff and Le Bel, Baeyer (4) stated that the valencies of carbon are directed toward the vertices of a regular tetrahedron making an angle of 109" 28'. Saturated bonds are formed by joining two tetrahedra by their vertices and double bonds by two carbon atoms sharing a tetrahedral edge. If bonds were to be represented by wire springs, the unsaturated bond would be formed by bending two springs to join the carbon atoms:
This picture satisfactorily accounts for the observed electron dense region between the carbon atoms as well as the rigidity of the double bond as seen in the geometricalisomen. Baeyer pointed out that this model also explains the similaritv he had noticed between the chemical reactivity of ethylene and the lower cycloalkanes. The relative reactivities could be rationalized by assuming that the preferred bond angles are all 109' 28', but this angle cannot be accommodated in planar cycloall~anes, so the honds are bent from the tetrahedral angles. The farther the bond is bent, the more "strain energy" it has, and the more reactive it is. The relation is expressedby
where n = number of carbou atoms in the ring, and = angle strain. The results are:
A
By about 1950 organic chemists had accepted, virtually unanimously, a second model for the double bond, this one based on a symmetry argument in which a linear combination of hybridized s- and p- atomic orbitals produce a- and a-molecular orbitals. This a,a description has proven very convenient for illustrating resonance, another phenomenon associated with double honds, as well as for incorporating the stereochemical rquirements. Using the a, r description unsaturated molecules can be studied in a semi-quantitative way by the Hiickel Approximation, a simplified molecular orbital treatment which assumes that the molecule can be factored into sets of a-bonds and sets of a-bonds. The a-orbitals are regarded as products of two-center molecular orbitals, and are thus localized between two carbon atoms, while the a-orbitals are approximated as a product of molecular orbitals. This highly simplifying procedure carmot be applied to Baeyer's picture of the double bond, so the a, a model seemed to give a more accurate description of the actual situation. The consensus at this stage was expressed in the statement (5): "Organic chemists will note also that the idea. of the 'strained valency bond' which was introduced by von Bt~eyerto explain the regular increase in chemical reactivity of the cycloparaffins, CaHl0,C4Hs CaHs is no longer directly relevant to olefins themselves, though it is still cogent for pictorially explaining the hybridization of the bond orbitals in cyclopropane and cyclobutane." A hit of nostalgia remained, however, for "in an older theory of the C=C link the two C-C honds were regarded as both of the same nature, and the 'anomalies' in the properties of ethylene (relative to the paraffins) were attributed to the strain due to the dktortion of the bonds from the tetrahedral directions. While that theory held it is expected that cyclapropane should show some unsaturation character, for any two carbon atoms in it can he regarded as joined by two curved lines. The \\ / , quantum mechanical description of C=C, in discarding the /
\
older theory, has led to much progress in understanding the
\
/
/ ,
\
properties of C=C [particularly (a) spectroscopic properties of
,
eonjugt~tionand ( b ) properties of valences external to C=C, e.g.,
HCH], hut has destroyed the 'naturalness' of the unsaturation of cyclapropane" ( 6 ) .
A few years later Pople discussed (7a) a point originally made by Lennard-Jones (7b) that the same sort of process could be applied to the a- and =-orbitals m had been used to obtain them, without any loss of generality. That is the a- and s-orbitals, (Fig. I), can be combined in a linear fashion to produce two new equivalent orbitals
which may be pictured, as in Figure 2. These equivalent orbitals correspond to two bent honds. Each carbon participates in four bonds that are approximately tetrahedral; two are bent back toward the other carbon. Pauling (8) prefers to think of the double bond in this way; he includes a small amount of d- and &character in the bond-forming orbitals, however, in order to concentrate bond orbitals in a region close to the bond axis. Figure 1. The diagrom rhowr o common method of picturing the oand r-molecular orbitals in ethyltne; the lines reprerent approxt m ~ t e i y90% electron density contours of the wove functions. The o-moiecular orbital, shaded area, is superposed on the r o r b i t a l rystern. The signs I+ and -) indicate bonding ond ontibonding componenk of the T-molecular orbital wove function.
Utility of the Bent-Bond Method
This treatment described above adjusts both of the models to theoretical equivalence. However a number of examples can be cited which illustrate the utility of the bent-bond model and which are not adequately explained by the a, = representation.
Figure 2. A linear combination of wove functions for the o and r molecular orbitdr in Figure 1 results in two new (a r ) and X% equivalent orbitals, X , = ll/fil = 111lc TI, whore representototions are seen in this illustrotion. Lines joining carbon atoms ore included only to show the bond axis. Boundovies of the equivalent orbitals are approximately 90y0 eiectron density contours of the new wove function%,XI and x2.
-
+
If a tetrahedral arrangement of electrons exists about the carbon atoms in a double bond environment, it can be expected that the neighboring elements in the first row of the Periodic Table will show a similar tetrahedral distribution of electron pairs in a variety of situations. Oxygen compounds (9) appear to have the electrons arranged in this pattern, and it has been suggested as a result of nuclear magnetic resonance studies that nitrogen in ammonia is spahybridized (10). Volume 43, Number 3, March 1966
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Detailed study of the conformation of olefins has shown that, for example, the equilibrium conformation of propylene is I rather than I1 (Fig. 3) (11). Conformer I1 may have been expected to be more stable by ca. 0.5 kcal mole-', but I is found to be favored by 1.98 kcal mole-'. I n the light of Baeyer's interpretation of the double bond, however, this finding is perfectly acceptable (Fig. 4).
Figure 3. The equilibrium conformmtion of propylene i s presented in d i . grams lo and lb. la ir o conrontionol drawing in which all atoms except Hz ond Hqie in the plane of the paper. The projection diagram of propylene, Ib, is obtained b y looking down the C-C single bond axis or indicated by the dotted line in lo; HL ond CH1 eclipse one another. Conformotion I1 would be expected from conrideration%of Valence Shell Electron Pair Repuhion Theory whish rays "multiple-bond orbitair repel other orbitolr more strongly than single bond orbitals,' IGILLESPIE, R. J., J. Chem. Ed., vr.
On the basis of infrared spectral line separation this is more stable than the trans conformerZ by 1.15 kcal mole-'. The reason for this can be seen from the bent-bond drawing (Fig. 5), where the shaded orbitals represent the positions of the lone electrons on spa hybridized oxygen. The conformation of vinyl formate, a planar molecule (13), is interpreted just as easily with this model, as is the fine structure of isobutylene (14). Baeyer originally found the relationship between ethylene and the cycloalkanes useful, as mentioned earlier, in constructing a model for the double bond. Other instances of relations between alkenes and the cycloalkanes, with particular emphasis on the double bond character of cyclopropane can also be considered. The nucleophilic displacements of cycloalkyl derivatives have been examined (15), see Table 2,. to give the reactivity sequence.
Solvolysis rates of cycloalkyl halides in aqueous ethanol are in the same order (16). Table 2.
H"
-
Figure 4. Prolection diagram lb, Figuro 3, may be redrawn using an equivalent orbitol representation (bent-bond) of the double bond to illurtrote the convenience of vitvolizing the double bond as a re1of single bonds curved back on themrelver and terminating on a common atom. From this it can be seen thot an equivolentorbital repretentotion olropermitsoscurote prediction of the most stable conformotion of propyiene.
Figure 5. The equilibrium conformation methyl vinyl ether is given obove in term. of the bent-bond model; the shaded orbitolr represent the position, of the lone electron pairs on spa hybridized oxygen and R=CH, The molecule is viewed in Newman proiection diogrom from the oxygen atom dong the bond to the rp2 carbon otom odjocenf to it. A comporison with Figure 4 will show thot hydrogen atoms HZ m d Ha have been replaced by the lone electron p a i n of oxygen and HL by R=CHa.
Nucleophilic Displacement for
-
Cycloalkyl H a l i d e s RBr KI RI KBr
+
40, 295 11 9631.
1~
Rates of
+
R
k (bimolecular rate constant)
vinyl oyclo ropyl cycloEutyl cyelopentyl cyclohexyl
no reaction no reaction 0.0110 0.0437 0.0077
The seemingly anomalous position of cyclohexyl compounds has been explained in terms of the "I-strain" concept (17) which has more recently been resolved into torsional and bond angle strains (18). These concepts emphasize that in cycloalkyl compounds bond distortions may strongly influence the rate of reaction, and because undistorted bond angles of 109' 28' may be accommodated only in cyclohexyl compounds their chemical reactivity should be, and is, similar to that of acyclic alkyl halides. Another similarity can be observed in the rapid ringopening rearrangement undergone by cyclopropanols at
relatively low temperatures (19) as compared with their analogs in the olefin series, the well-known keto-en01 tautomerization 0
Again, the most stable conformer of methyl vinyl ether has been determined (It)to be the s-cis form:
/""
II
CHI-4-H t
99.9%
CH2=CH 0.1%
% I nthe trans configuration, electron pairs are eclipsed, so a gauche or skewed arrangement of bonds would be anticipated.
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Journal o f Chemical Education
Though cyclopropane reacts with strong acids five times as fast as propene the kinetics are very similar for both gases (20); the rate law for both reactions is given by
tary description to the ir, a approach in an introductory course in organic chemistry.
Rate = k[CaHel[acid]"
The author wishes to express his thanks and appreciation to Professors M. M. Kreevoy and H. A. Bent for their assistance during the preparation of this paper and t ~ )Professor C. D. Anderson for helpful comments and suggestions.
where n is a parameter dependent upon the particular acid used and its strength. The exact degree to which cyclopropyl groups can conjugate with another unsaturated site is somewhat in question, but a variety of spectral studies indicates that they can transmit resonance, though not as efficiently as a double bond (6,21). hIicrowave examination (22) of the structure of cyanocyclopmpane produces an HCH hond angle of 114" 36'. This value is very similar to the average of 113" 10' Wilson (23) noted for single-single bond angles on a trigonally (spz) hybridized carbon atom in general.
Finally, a linear function has been found to relate the lac-H nuclear spin-spin coupling constant J (in cycles per second) and the fractional &character (pH) of the carbon atomic orbital from which the C-H bond is formed (24) : So, as the coupling constant increases, the fractional s-character increases in direct proportion. The 13C-H coupling constants for the cycloalkanes follow the usual sequence, but the results are a measure of the s-character of the C-H hond (2.5), Table 3. Table 3.
Coupling Constants far Cycloalkanes
cyeloalkane
JI~,~(CPS)
Conclusion
Although the dat,a presented here have stressed the utility of the hent-bond model for the chemical double bond, neither this nor the a, a description give an ideal representation of the actual bonding arrangement. Both models have their advantages: the a, a picture is especially convenient for discussing resonance and for the application of the Hiickel Approximation, while the bent-bond model incorporates the double hond character of the cycloalkanes and permits prediction of the most stable conformational relationship of groups adjacent to the unsalurated link. Both models satisfy the requirements of structural rigidity at the site of uusaturation, yet the bond angles encountered in molecules (23) are closer to 109' 28', predicted by Baeyer's model than they are to 120°, expected in the a, a case. Therefore it is felt that the bent-bond model has sufficient merit, and the a, a model sufficient lack of uniqueness, for the former to beincluded as a complemen-
Acknowledgmenl
Literature Cited (1) Far example, I~OBERTS, J . D.,
AND CASERIO, M. C., "Basic Principles of Organic Chemistry," W. A. Benjamin, Inc., New York, 1964, p. 137. (2) FmsEn, L. F., A N D FIESER,M., "Advanced Organic Chemistry," Reinhald Publishing Gorp., New York, 1961, p.
12.6 A--.
(3) See BENSON, S. W., "Foundations of Chemical Kinetics," McGraw-Hill Book Ca., Inc., New York, 1960, pp. 254257. (4) BAEYER, A., Chem. Ber., 18, 2269 (1885). (5) WATERS, W. A,, "Physical Aspects of Organic Chemistry," 4th ed., D. van Nostrand Co., Inc., New York, 1950, p. 1R. (6) WALGH, A. D., Trans. Farad. Soe., 45, 179 (1949). (7s) POPLE,J. A,, Quart. Reus., 11, 273 (1957). (7h) HALL, G. G., AND LENNARD-JONES, J., Proc. Roy. Soc., 205A, 357 (1951). (8) PAULING,L., in "Theoretical Organic Chemistry, The
Kekule Svmuosium." Butterworths Soientilic Public* tions, 1959, i p . 2-4.' (9) BURNELLE, L., AND COULSON, C. A,, Tram. Farad. Soc., 53, 403 (1957); DUNCAN, A. B. F., AND POPLE,J . A., Trans. Famd. Soe., 49, 217 (1953); HEATH,D. F., AND L I N N E ~ , J . W., Trans. Farad Soe., 44, 556 (1948). (10) BISCH,G., LAMBERT, J. B., ROBERTS, B. W., AND ROBERTS, J. D., J. Am. Chem. Soc., 86, 5564 (1964). (11) HERSCHBACH, D. R., AND KRISRER,L. C., J. Chem. Phys., 28, 728 (1958); LIDE, D. R., AND CHRISTENSEN, D., J . Chem. Phys., 35, 1374 (1961). N.. Proe. Chem. Soc.. 264 (12), OWEN.N. L.. A N D SHEPPARD. (1963); ~ r d n sFarad. . Soe., 60, 634 (1964). (13) RAO,V. M., AND CURL,R. F., J. Chem. Phys., 40, 3688
.
(1964). (14) LAURIE, V. W., J. Chem. Phys., 34, 1516 (1961). (15) RO~ERTS, J. D., AND CHAMBERS, V. C., J . Am. C h m . Sac., 73, 5034 (1951). (16) Cox, E. F., CASERIO, M. C., SILVER,M. S., AND ROBERTS, J. D., J. Am. Chem. Soc., 83, 2719 (1961). (17) H. C.. A N D GERSTEIN. M.. J . Am. Chem. Sac.. 72. , , BROWN. 2926 ' (1950 j; BROWN,H. 'FLETCHER, R. AND JOHANNESEN, R. B., J. Am. Chem. Soe., 73, 212 (1951); BROWN, H. C., A N D BORKOWSKI, M., J . Am. Chem. Soc., 74, 1894 (1952). (18) GARBI~CH, E. W., JR., J . Am. Chem. Soe., 87, 505 (1965); GARBISCR, E. W., JR., in press. (19) DEPUY,C., D:\PPEN,G. M., A N D HAUSER,J. W., J. Am. Chem. Soc., 83, 3156 (1961). (20) LAWRENCE, C. D., I N D TIPPER,C. F. H., J . Chem. SOC.,713 (1955). ,, (21) KOSOWER, E. M., A N D ITO,M., P70C C h m . Soe.,25 (1962); GOODMAN, A. L., A N D EASTMAN, R. H., J. Am. Chem. Soe., 86, YO8 (1964); BELLMY,L. J., "The Infrared Spectra of Complex Molecules," Methuen and Co., Ltd., London, 1958, p. 17. (22) FRIEND,J . P., AND DAILEY,B. P., J. Chem. Phys., 29, 577 (1958). (23) WILSON,E. B., JR., Tetmhedron, 17, 191 (1961). (24) MULLER,N., AND PRITCHARD, D. E., J. Chem. Phys., 31, 768, 1471 (1959); SEOOLERY, J. N., J . Chem. Phys., 36, 350 (1962), JAUN,C., A N D GUTOWSKY, H. S., J. Chem. Phys., 37, 2198 (1962). (25) BURKE, J . J., AND L~UTERBUR, P. C., J . Am. Chem. See., 86, 1870 (1964).
'c.,
s.,
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