University of Newcastle N e w South Wales, Australia
Discussions on activation and orientation of substitution in aromatic systems generally use the concepts of valence bond theory ( I ) . This appears almost invariably the case in elementary qualitative treatments (2). I t may, therefore, be of interest to r e port on the use of the molecular orbital theory in a qualitative approach which we have offered to our students in their second year chemistry course. The nature of a- and s-bonds, as well as the general behavior of electrophilic and nucleophilic reagents are well known by then. Fundamental concepts of the transition state theory have also been introduced in the physical chemistry course. To start with we compare the initial stages of olefinic addition and of electrophilic aromatic substitution and a typical example chosen is that of bromination. There is an essential similarity between the intermediate cations obtained in both reactions. Because of its high electron density the olefinic Tbond is able to polarize the approaching halogen molecule which dissociates to give the intermediate cation. This intermediate, following Dewar, is often called a T-complex (3). The bromide ion, as a nucleophil, combines with the T-complex to give l,Pdibromoethane, which completes the addition. CHz
+
11
CHs
Br-Br
CH2 +
r,
Br-Br
tr
CHz
-+
I n butadiene the 2p,orbitals of carbon do not overlap to form two localized (i.e., separate) olefinic T-bonds, hut instead overlap to give T-molecular orbitals extending over the entire carbon skeleton with a resulting gain in the stability of butadiene of 3.5 kcal/mole (delocalization energy) (4). CH2=CH-CH=CHI is represented better by ................................. CH2-CH-CH-CH, where the dashes indicate the extent of x-bonding. Attack of electrophilic reagents occurs a t the ends of the delocalized system, for only in this way will the resulting ion maintain maximum delocalization. The electrophil, Br+, requires two electrons to form a a-bond. These two electrons are derived from the x-electron system of butadiene, leaving thus two electrons to be spread over three carbon nuclei in the intermediate carbonium ion. ..........
CH-CH-CH-CH* 4 7 electrons
. @ .-.................... + CH*-CH--CH-CH~:B~
+~r:"
2 ?i electrons
+ 2 c electrons
The nucleophilic Br- now attacks the carbonium ion 138
/
Journal of Chemical Education
intermediate giving a mixture of 1,4dibromo-2-butene and 3,4-dibromo-1-butene. If the reaction medium favors ionization of the active (allylie) bromides, the thermodynamically more stable 1,4-dibromo compound will ultimately predominate.
Now let us consider the action of bromine on benzene. According to the molecular orbital theory the six carbon atoms of benzene are in a state of spzhybridization and the Zp,orbitals of these atoms overlap with their neighbors to form six T-molecular orbitals extending over the entire ring. This makes the molecule flat and the carbon-carbon bonds are equal. Because of this high degree of symmetry benzene gains enormously in stability as shown by its delocalization energy due to T-bonding of 37 kcal/mole (4). The over-all electron density of benzene is lower than that of a simple or of a conjugated double bond system. Benzene is, therefore, not in a position to polarize a bromine molecule sufficiently for ionization to occur. So a Lewis acid catalyst (e.g., AIBrs) is necessary to generate a more reactive electrophilic reagent.
As in the case of the olefins discussed above, the attack of Br+ results in the formation of an intermediate cation in which Br is held by a newly formed r-bond. The two electrons necessary for this a-bond have been supplied from the pool of six T-electrons. The carbon atom holding the electrophil is now tetrahedral (spa), so the remaining four s-electrons are spread over five carbon nuclei. This form of intermediate cation was first suggested by Wheland (5) and is commonly r e ferred to as a a-complex.
There are now two possible ways in which the reaction can proceed. Either (by analogy with olefins) the nucleophil (Br-) may attach itself to one of the ends of the s-system to generate a cyclohexadiene with a stabilization energy of about 4 kcal/mole, or it may remove a proton from the tetrahedral carbon atom of the a-complex and give a substituted benzene, via., bromobenzene. I t is actually the latter reaction which
is favored, for the stabilization achieved by reestahlishing the 6 a-electron system of benzene more than compensates for the energy necessary to break the C-H bond. I n addition there is the gain in HBr bond energy. Therefore, aromatic hydrocarbons react by substitution, where olefins would react by addition.
The intermediate state (IS) is reached when the E-C bond becomes a true a-bond. I S is slightly more stable than TSI and so has a lower energy. According to Hammond's postulate (7), it is quite justifiable to consider TSI structurally similar to I S as the free energies are very close.
The activation energy (AG~:) varies directly with the electron density on the benzene ring. Activation
The common substitution reactions of benzene, such as halogenation, nitration, sulphonation, etc., are all electrophilic. This has been known for a long time, for it was observed quite early that negative charges near the henzene ring greatly increased the rate of reaction, whereas positive charges had the opposite effect. A negative charge increases the electron density of the benzene ring. Using the phenoxide ion as an example we would say, in molecular orbital language, that the electrons of the -0- were being spread over the benzene ring by overlap of the 2prorbital of oxygen with the r-bonds of the benzene ring. I n fact any atom with non-bonding electrons in suitable orbitals (e.g., nitrogen in -NHz) may, by sharing these electrons with the benzene ring, increase the reactivity of the substituted benzene towards electrophilic reagents. Elements of the first short period are generally capable of effective orbital overlap with the a-orbitals of the benzene ring. The release of electrons does, however, also depend on the electronegativity of the element concerned, and halogens do not readily share their electrons. A less effective way of charge transmission is by polarization of the 0-bond joining an atom or group to the benzene ring. The only groups releasing electrons in this way and so favoring attack by electrophilic reagents are alkyl groups. Electron-attracting groups, such as -NOz, -CN, -COOR, -C1, -Br, -I, lower the electron density of the a-orbitals below that of benzene and so substitution becomes very slow indeed. Orientation
Substituents have been divided into two groups depending on whether they direct an entering group suhstantially into an ortholpara or a meta position. The molecular orbital theory very nicely explains these facts in answer to two questions concerning the cationic intermediate. First, horn easily is the intermediate state (IS) reached, and second, how stable is it? Activation Energy. To discuss these questions, a somewhat simplified picture of the transition state theory will be used (6). As the electrophilic reagent E + approaches benzene, it polarizes the benzene molecule and forms a partial bond with the most negative carbon atom. This requires energy (activation energy) and leads to the first transition state (TSI).
AG$ determines the rate of the reaction and the ease with which the intermediate state is reached. AGv on the other hand, refers to a small energy hump, easily passed to give the reaction product. The plot of the energy of the system under reaction against the socalled reaction coordinate (amoleculardistancefunction) is the energy profile and illustrates the changes of energy as the reaction progresses.
Stabilitu of the Intermediate Slate. When a substituent i"s already present in the benzene ring, the energy of activation, AG~:, will no longer he the same for all unsubstituted ring carbon atoms. It will be least for carbon atoms, when the intermediate cation (IS) has maximum stability. Such an enhancement of stability is possible if the substituent can disperse the charge by electron release. This would be helped by increased delocalization through effective orbital overlap. Before going further, it is necessary to introduce the concept of alternant hydrocarbons (8). These are planar conjugated hydrocarbons; any carbon atom labeled by a star (starred atom) will have only unstarred neighbors. Examples are butadiene, henzene, and napht,halene.
As these have an even number of carbons they are Volume 43, Number 3, March 1966
/
139
representatives of even alternant hydrocarbons. Odd alternant hydrocarbons are radicals, e.g., pentadienyl and benzyl.
*
*
a*
The starred atoms exceed the unstarred by one. It can he shown that the number of molecular orhitals formed by overlap of Bpcorhitals equals the number of overlapping atomic orhitals. These n~olecularorbitals are symmetrically placed about the energy levels (a) of isolated 2p,-orbitals. Those more stable than or are bonding molecular orbitals and those less stable are antibonding molecular orhitals. In filling these orhitals with available electrons one proceeds in the same manner as with atomic orbitals. The most stable orbitals are filled first (Aufbau Principle). Pauli's exclusion principle and Hund's rule apply, as illustrated by hutadiene and benzene. I t will be noted that the number of velectrons just suffices to fill the bonding molecular orbitals, which accounts
for the stability of these structures. Next consider the case of pentadienyl. One of the orbitals has energy w. It is a non-bonding orhital. The energy diagrams for the cation, radical, and anion are shown,
cation
radical
anion
and we notice that adding one electron to the radical or taking one away affectsonly the non-bonding orbital. Returning now to aromatic substitution, we see that the Wheland intermediate (IS) is analogous to the pentadienyl cation.
The problem is to discover on which carbon atom (2 to 6) an electron-releasing group might best he able to stabilize the cation. I n other words on which carbon atom is maximum overlap of the group orhital and the non-bonding orbital possihle. So it is necessary to find the shape of the non-bonding n~olecularorbital. This shape is determined by the orbital coefficients (c,) which indicate the contribution of each atomic orhital (xi)to the non-bonding orbital. A pentadienyl molecular orbital (#) is of the type and it can be shown that for the non-bonding molecular orbital the sum of the coefficients around any atom equals zero. If we place c on the first carhon atom and apply the rule, we get the relative values of the coefficients.
0
c
0
c
c
3c2= 1 cx=
$
3
electron density
0
0
I
3
3
The sum of the square of the coefficients equals me (normalization) and c2 is a measure of the electron density of the orhital or its shape at any carbon atom.
The second and fourth carbon atoms have zero coefficients which indicate orhital nodes at these points. Applying these results to the cationic intermediate it will he seen that carbon atoms 2,4, and 6 carry a charge of one-third with no charge at 3 and 5. Also overlap of a suhstituent group is possible only at positions 2, 4, and 6.
From this it follows that electron-releasing groups stabilize a positively charged intermediate state (or transition state) if the tetrahedral carhon is ortho or para to themselves; or in other words, such groups Conversely bring about ortho-para-substitution. electron-attracting groups in positions 2, 4, or 6 may completely destabilize the transition state, but would affect it least, when the transition carbon is meta to the substituent, i.e., meta-substitution is brought about by the presence of electron-attracting groups. The above argument is easily extended to nucleophilic substitution. Following the principle of dispersal of the negative charge of the intermediate state by increased delocalization, we can easily see that electronattracting groups would be most effectivein positions 2, 4 and 6. This is shown most convincingly in the activating influence of nitro groups on halogen.
Literature Cited (1) WHELAND, G. W., "Resonance in Organic Chemistry," John Wiley & Sons, Inc., New York, 1955, p. 4i6. R. T., AND BOYD,R. N., "Orgainic Chernis(2) ~.~.:,MoRKIsoN, try, Allyn and Bacon, Inc., Boston, 1959, Chpt. 10 and
ROBERTS, J . D., AND CASERIO,M. C., "Basic Principles of Organic Chemistry," W. A. Benjamin, Ine., 1964, Chpt. 22. (3) DEWAR,M. J. S., "The Electronic Theory of Organic Chemistry," Oxford Univ. Press, 1949, p. 18. (4) PATILING,L., "The Nature of the Chemical Bond," 3rd. Ed., Cornell Univ. Press, 1960, p. 195. (5) WHELAND, G. W., J. Am. Chem. Soc., 64, 900 (1942). A,, (6) A more detailed account can be found in STREITWIESER, JR., "Molecular Orhital Theory for Organic Chemists," John Wiley &Sons, h e . , New York, 1961, p. 307. (7) IIAMMOND, G. S., J. Am. Chm. Soe., 77, 334 (1955). C. A., AND LONGUET-HIGGINS, 13. C., P70c. ROY. (8) COULSON, Soc., A192, 16 (1947).
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,a 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 texb books, with very few exceptions ( I ) , discuss the nature of the double bond 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 bond was proposed. The simplest homologous series of hydrocarbons has the general formula C,H2. + 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,H2,; 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 lccal mole-' (3) as compared with 3 to 7 kcal mole-' for the internal rotation of alkanes.
Table 1.
Reactivity of Cycloalkanes to Hydrogen
Reaction
A
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
/
Journal of Chemical Education
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 cycloalkanes, 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 bonds, as well as for incorporating the stereochemical requirements. 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 simplifyiug procedure cannot 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,C4H8,CaHs is no longer directly relevant to olefins themselves, though it is still cogent for piotorially 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 cyclopropane 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 oyclaprapane" ( 6 ) .
A few years later Pople discussed (7a) a point originally made by Lennard-Jones (7b) that the same sort of process could he applied to the a- and =-orbitals a 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 diagram rhowr o common method of picturing the oand r-molecular orbitals in ethyltne; the lines represent opproxt m ~ t e i y90% eledron density contours of the wove functionr. The o-moiecular orbital, shaded area, is superposed on the r o r b i t a l ryrtem. 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, T representation.
Figure 2. A linear combinotion of wove functions for the o and r molecular orbitmlr in Figure 1 results in two new (a r ) and ~1 equivalent orbitals, X , = 11/fil = 111In TI, whore reprerentdotions 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 electron density contours of the new wove functions, 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
/
135
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 he more stable by ca. 0.5 kcal mole-', hut I is found to be favored by 1.98 kcal mole-'. In 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 10 and lb. la ir o conrontionol drawing in which all atoms except Hz ond HSliein the plane of the paper. The projection diagram of propyiene, Ib, is obtained b y looking down the C-C single bond axis or indicated by the dotted line in la; HL ond CH1 eclipse one another. Conformation I1 would be expected from conrideration= of Valence Shell Electron Pair Repuhion Theory whish rays "multiple-bond orbitair repel other orbitals more strongly thon single bond orbitals." IGILLESPIE, R. J., J. Chem. Ed., ve.
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.
H3
-
Figure 4. Prolection diagram lb, Figuro 3, may be redrawn using an equivalent orbitol representation (benhbond) of the double bond to illurtrote the convenience of vitvoiizing the double bond as a set of single bonds curved back on themrelver and terminating on a common atom. From this it can be seen thot an equivolentorbital repretentotion olro permits occurote prediction of the most stable conformotion of propylene.
Figure 5. The equilibrium conformation methyl vinyl ether is given obove in terms of the bent-bond model; the shaded orbitals represent the po& tion, of the lone electron pairs on spa hybridized oxygen and R=CH, The molecule ir viewed in Newman proiection diogrom from the oxygen atom dong the bond to the rp2 carbon otom odjocent 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 (1 9631.
1-
Rates of
+
R
k (bimolecular rate constant)
vinyl cyclo ropy1 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 (18)to be the s-cis form:
/""
II
CH84-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.
136
/
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,, Trans. 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
.
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