A molecular orbital theory of organic chemistry—VIII

Tetrahedron,

SuppI. 8,

Part I,

pp. 7542.

A MOLECULAR

l%rgamon Pms Ltd. Printed in Great Britain

ORBITAL THEORY OF ORGANIC CHEMISTRY-VIII’

AROMATICITY

AND ELECTROCYCLIC

REACTIONS*

M. J. S. DEWAR Department

of Chemistry, The University of Texas, Austin, Texas 78712, U.S.A. (Received 1 June 1966)

Abstract-The perturbational MO (PMO) method described in earlier papers of this series is used to develop a simple and general theory of aromaticity, which seems to account well for the availaMe evidence and to be in accord with recent SCF MO calculations. This treatment also provides a very simple interpretation of both thermal and photochemical electrocyclic reactions. following the general rule that such reactions seem always to take place via aromatic transition states. INTRODUCfION THE problem

of aromaticity has long been a major preoccupation of organic chemists, having served as a touchstone for chemical theory for many years. Currently much of this effort has centered on attempts to check the HMO method by testing its predictions concerning aromaticity; however it has become increasingly evident that the HMO method is not a reliable guide in this connection, and a great deal of time has been wasted on the synthesis of otherwise uninteresting molecules solely because the HMO method had erroneously predicted them to be aromatic. The Hiickel method, in its original form, was a very crude approximation in which a number of wholly unjustifiable assumptions were made at the outset. Nevertheless it seemed to work well in practice, for a variety of chemical problems, and so it became accepted as a legitimate tool on purely pragmatic grounds. We now know, however, that this early success was coincidental. Most of the early applications were to the r-systems of altemant aromatic hydrocarbons; here a series of fortuitous cancellations of errors enables the HMO method to give good results.2 Consequently the fact that the method works in this particular case cannot be taken as a justification for extrapolating it to compounds of other types; its extensions to non-altemant systems, to molecules containing heteroatoms, or to conjugated systems where there is marked bond alternation, is not only unjustified in principle but leads in practice to results which are unreliable even in a qualitative sense. Recently a satisfactory solution of the problem has been found in terms of a more refined approach, based on a semi-empirical SCF MO treatment ;3 this has so far given * This work was supportedby a grant from The Robert A. Welch Foundation. 1PartVII: M. J.S.DewarandR. Pettit. J. ChemSoc. 1625(1954). 2 See M. J. S. Dewar, Rev. Mod. Phys. 35,586 (1963). 3a A. L. H. Chung and M. J. S. Dewar, 1. Chem. Phys. 42,756 (1965); 6 M. J. S. Dewarand G. J. Gleicher. J. Amer. Chem. Sot. 87.685 (1965); ’ eid., Ibid. 87,692 (1%5); eid., Tetrahedron 21, 1817, 3423 (1965); Tetrahedron L&rem4503 (1965). 75

76

M. J. S. DEWAR

good results when applied to a very wide range of conjugated molecules. However calculations of this kind require the use of a large digital computer, and it would therefore be useful if they could be supplemented by some simpler approach. Most chemists seem to be under the impression that resonance theory alone meets this need ; yet a much superior and equally simple treatment has been available for the last fourteen years.4 This treatment, which is based on the use of perturbation theory applied to the HMO method, has the following advantages. Firstly, it is an objective treatment where there is no scope for post facto manipulation; it is always possible to “explain” anything in terms of resonance theory, once one knows from experiment the answer that one has to reach. Secondly, it presents predictions of stability, reactivity, etc. in a quantitative form; the predictions of resonance theory are at best qualitative. Thirdly, it is much more reliable in practice than resonance theory, or even the HMO method. And GnalIy, it can be applied with no more difficulty than resonance theory, any “calculations” involved being carried out in seconds with pencil and paper. Unfortunately the papers4 describing this treatment, while complete, are somewhat condensed, and no general account has as yet appeared in print. Here we will illustrate the potentialities of the method in two ways; firstly, by a general discussion of aromaticity; secondly, by applying it to electrocyclic reactions. Some applications of this kind were outlined in the original papers,4 and all the essential principles will be found there; the general treatment given here has not as yet been published. This topic seems especially appropriate in the present connection; for Sir Robert Robinson was one of the founders of modern theoretical organic chemistry and his concept of the aromatic sextets provided the first coherent account of aromaticity. It should be added that the potentialities of his electronic theory5 have at times been underestimated; it is perhaps not generally appreciated that the resonance theory, so far from representing a theoretical advance, was in fact but a translation of the earlier theory into a new and less convenient symbolism. Definition of aromaticity

The term “aromatic” was originally introduced by organic chemists to describe certain cyclic conjugated molecules whose chemical behaviour indicated a stability higher than that expected from analogy with similar open chain systems. In recent years the term has been used in a number of other connections, to describe molecules where the +electrons are “delocalized” or where NMR spectroscopy indicates the presence of a “ring current”. These alternative definitions depend, however, on specific theoretical treatments of possibly dubious chemical significance, whereas the original definition rested on an unambiguous experimental distinction, independent of any theoretical interpretation. Similar considerations apply to terms such as “bond localization” and “resonance energy”. It is an experimental fact that many molecules behave, in certain connections at least, as if the bonds in them were localized; thus the heats of formation w M. J. S.Dewar, J. Amer. Chem. Soc.74.3341,3345,3350.3353,3355,3357(1952); b for reviews see M. J. S. Dewar, Science Progress 40,604 (1952); Progress in Organic Chemistry 2,l (1953). 5 J. W. Armit and R Robinson, J. Chem. Sot. 127,1604(1925); see R. Robinson, Outlineofan Electrochemical (Electronic) Theory of the Course of Organic Reactions, Institute of Chemistry, London (1932).

A molecular orbital theory of organic chemistry-VIII

17

of such molecules can be well represented by additive sums of bond energies of the individual bonds in them. Certain molecules, in particular those of aromatic compounds such as benzene, deviate from this additivity relationship; the term “resonance energy” can then be used in an experimental sense as a measure of this deviation. In this sense the resonance energy of benzene would be equated to the difference between its measured heat of formation and the heat of formation calculated for 1,3,5-cyclohexatriene on the assumption that the bonds in it are similar to those in an open chain polyene. Used in this way, the terms “bond localization” and “resonance energy” assume an unambiguous significance, independent of any theory.6 Most of the present confusion has been caused by the HMO prediction, that the bonds in classical7 polyenes should be “delocalized”. This prediction now seems definitely incorrect, being a consequence of the tendency of the HMO method to underestimate bond alternation in such systems.2 Calculations3c1d by the SCF MO method suggest very strongly that the bonds in classical polyenes are in fact “localized” in the empirical sense of the previous paragraph, and the available chemical and physical evidence strongly supports this conclusion. If so, there is no need to depart from the “classical” definition of resonance, as a measure of the deviation from “localization” shown by a given system, localization being defined by reference to a real classical molecule rather than some theoretical abstraction with “pure single” and “pure double” bonds. In this sense, an aromatic compound is defined as a cyclic conjugated molecule whose collective6 properties cannot be represented in terms of localized bonds, and its resonance energy is defined as the difference between its observed heat of formation and that calculated for a corresponding classical isomer. PM0

Theory of aromaticity

In the PM0 method,4 the energies of two very similar systems are compared by a perturbational approach, based on the HMO method. It may at first sight seem surprising that such a treatment could give better results than the method to which it is apparently a first approximation; that it in fact does so is due to its very nature. In a perturbational approach we calculate small energy differences between related systems directly, rather than by difference; for a given degree of overall accuracy, we can tolerate much inferior wave functions in the former case. Thus if the energy difference we are calculating is 1 ‘Aof the total energy of the unperturbed system, and if we wish to calculate it to within 10 %, we can tolerate a 10 % error in our perturbational treatment, but only a 0.05 % error in each of the absolute energies if the difference is to be found from them by subtracting one from the other. Naturally we use the usual Hiickel (0 : n) approximation; for our purpose it will also be sufficient to ignore differences in u-energy between the systems we are comparing, due to changes in the lengths of o-bonds; for these changes should cancel, to a first approximation. In the original papers4 the PM0 method was presented in a series of seventy-four theorems; these will be referred to by number below. It should be added that the terminology used there4 followed conventions current at the time; thus 6 For a detailed discussion see M. J. S. Dewar, C&E News 43.86 (1%5); Press, New York, N.Y., 1962; Tel&e&on Suppl. 19, (2) 89 (1963). 7

Hyperconjugution

Ronald

A classical molecule is defined as one for which only a single classical structure (“unexcited resonance structure”) can be written.

78

hi. J. S. DEWAR

“resonance energy” was defined by reference to idealized structures with pure single and double bonds. The modifications needed to adapt it to the ddinitions used hcre6 are, however, self evident. Our object is to compare the heat of formation of a cyclic conjugated molecule with that of a corresponding classical structure; with the simplifying assumptions made here, this is equivalent to a comparison of the corresponding total n-bond energies. The difference between these can be found most simply by comparing the total r-bond energy of the cyclic compound with that of an open chain analogue. To do this, we introduce the concept of union. Union of two conjugated systems R, S through atoms t in R and s in S consists of a linkage of atoms r, s by a u-bond so that the two corresponding 7r-systems can interact. Thus union of two benzyl radicals through the methylene carbon atoms gives stilbene, in which the two sevencarbon a-systems of the benzyl groups are linked into a single fourteen-carbon nsystem. Union will be represented by the symbol : WI-+; e.g. PhCHztu+&H2Ph

+

PhCH=CHPh

(1)

Union can also take place between two atoms in the same molecule; e.g.

HC “‘CH

c! AI, kI.9

HZ

H ’

r

‘CH F; HC-

(2)

In our discussion of aromaticity we need consider only conjugated hydrocarbons; for it is easily shown (Theorem4 9) that the resonance energy of a conjugated molecule containing heteroatoms is approximately the same as that of the isoconjugate4 hydrocarbon. Since our object here is to discuss aromaticity in general terms, rather than to calculate resonance energies, etc., quantitatively, we should be able to rely on this parallel. First let us consider union of two altemant hydrocarbons (AH) R,S to form a single hydrocarbon RS,union being through atom r in R to atom s in S. In Part I,4 it was shown that the union leads to no first order change in n-energy (RR& and that the corresponding second order change is given (equation (41) of Part 14) by (3) Using the fact that R,Sand RS are all AH’s, (4) Since RRSis in any case relatively small, being a second order effect, and since E,,,, F,, being energies of bonding MO’s in even AH’s, will not vary greatly from some mean value E, we can replace (Em+F,,) on equation (4) by 2E; thus:

A molecular orbital theory of orLpnic chemistry-VIII

79

last result following since the charge density of any atom in an even AH is unity.4 Thus the n-energy of union has a value, /32/2E, regardless of the nature of R or S. Consider now two classical polyenes R, S, and a longer polyene RS formed by their union. During union we break two CH bonds in order to form the C-C bond linking R to S in RS. If the heats of formation of R,S, and RS are AH,, AHs, and AHRs respectively, then The

AHRs=AH,+AHs+2EcH-EccfRRs

(6)

where EcH, Ecc are the bond energies of the CH and CC bonds.8 The argument given above shows that we can write this in the form: AHRs=AHR+AHs+2&H-&

(7)

E&=&+/2E

(8)

when Now Eq. 7 would hold if the bonds in polyenes were localized in our empirical sense,” and if E& were the bond energy of a “single” bond in a polyene. This argument therefore provides a simple alternative derivation of the rule” that bonds in classical polyenes are locahzed. Moreover since fl-20 kcal/mole in the Hiickel treatment, and since E will be somewhat greater than 8, RRSshould be somewhat less than 10 kcal/mole in good agreement with the value (8 kcal/mole) given by the SCF MO treatment. In the case considered above, union led to no first order change in n-energy. First order effects appear in two cases. Firstly, in intramolecular union between two different atoms r,s in the same conjugated system, leading to formation of a new ring; the corresponding first order change in p-energy (AE,,,J is given2 by: A ET,,3= ?P~S

(9)

where prr is the bond order between atoms r and 3 in the original system. The second case arises in union between two odd AH radicals R, S. The unpaired electron in such a radical occupies a NBMO (non-bonding MW) in our approximation, the energy of which is supposed to be equal to that of a carbon 2pAO. The total energy of the bonding electrons in R and S is unchanged to a first approximation by union; however there is a Brst order interaction between the two NBMO’s (Fig. 1) which leads to a decrease in total energy, since the two non-bonding electrons in R, S occupy a lower energy bonding MO in RS.

R

Rs

S

Fro. 1. Interaction of NBMO’s of two odd AH radicals, R, S on union to RS. * The confusing signs in Eq. 6 arise from the convention that bond energies are treated as poslrive quantities, while the heat of formation of a molecule is defined BSminusthe heat evolved when it is formed.

M. J. S. DWAR

80

The splitting (SE) of the two new levels in RS is symmetrical (Fig. l), being given (Eq. 42 of Part 14)by: 6E= aor bosB

(10)

where a,,, b,, are the NBMO coefficients of the AO’s of atom r in R,and of atoms in S, respectively. The first order change in r-energy, RRS,due to union of R with S is thus given (Theorem 134) by: ~~s=%,b.s~

(11)

This result can be immediately extended to cases where R is linked to S through more than one bond; in this case (Theorem 204);

where the sum is over all pairs of atoms r, s through which R is united with Sin RS. Let us now consider an even cyclic AH I whose aromaticity we wish to investigate. Consider one atom 1, linked to two adjacent atoms r, s. Removal of atom t would leave an odd AH (II). Union of II with methyl through atoms r or s would give either of two even AH’s, III, IV, each differing from I in that the ring containing atoms r,s,t has been opened, while union of II with methyl through both atom r and atoms would regenerate I. -C-CH-Cr

t

I

s

--CH r

HCs

SH2 r

HCs

t

III

II

--cH r

H#Z===C

t

s

IV

Thus all these n-systems I, III, IV can be derived by union of the same two fragments, II and methyl. Now methyl can be regarded4 as the simplest possible odd AH, its “NBMO” being a single carbon 2pAO; consequently we can treat union of an odd AH to methyl by setting the corresponding coefficient (bos) in Eq. 12 equal to unity. The three r-energies (SE,,) of union of II with methyl to form I, III, or IV are thus given by: I : 8E, = 2/3(a,, + a,) (13) a,,,

III:

8E,=28

IV:

SE,=2/Ia,,

(14) 0%

If then the coefficients a,,, a,, have similar signs, I will be more stable than either of the structures III, IV in which the ring containing atoms r,s,t has been opened; the ring in question will then be aromatic. Conversely if a,, and a,, have opposite signs, I will be less stable than one or other of the open chain structures; in that case the ring in question will be antiaromatic. NBMO coefficients can be calculated extremely simply by a method due to LonguetHigginss. 9 H. C. Longuet-Higgins, J. Chem. Phys. 18,265 (1950).

A molecular orbital theory of organic chemistry-VIII

81

If we star4 an odd AH in such a way that the starred set is the more numerous, the NBMO is confined to the starred atoms; and if atom i is unstarred, Te/%=o

(16)

where the sum is over starred atomsj that are directly linked to atom i. In the case of a symmetrical odd AH, when all the /?‘s are the same, this reduces to : (17) Thus the NBMO coefficients in a symmetrical linear odd AH, with (h-1) atoms, are as follows :

where a=n-i/2

(1%

Thus the n-energy differences (6E.J between such an odd AH, and a linear or cyclic polyene formed from it by union with methyl through the two terminal atoms, are given by: linear:

SE,=2u/3

(20)

cyclic:

SE, = q(afa)

(21)

If n is odd, the sign in Eq. 22 is positive; the cyclic polyene is then the more stable, i.e. aromatic. If n is even, the sign in Eq. 23 is negative; in this case the cyclic polyene is less stable than the open chain analogue-i.e. antiaromatic. Thus cyclic polyenes should be aromatic if, and only if, they contain (4k +2) atoms, k being an integer. It is amusing to note that this simple derivation remained until recently the only justification for Hilckel’s rule; thus the HMO method predicts’ that ah cyclic polyenes should be aromatic while neither resonance theory, nor VB theory, draws any clear distinction between the 4k- and (4k +2)-membered rings. The PM0 treatment has, however, now been supplemented by the SCF MO approach referred to above.3 The perturbation treatment can indeed be extended further in the case of the 4n-membered rings. If we calculate the NBMO coefficients for a linear odd AH, with (a-1) atoms and alternating “single” and “double” bonds, and if the ratio of the corresponding ,9’s is l (< l), then the NBMO coefficients are as follows : ae2 +aC-l--a2 &L=C...GC==C

(22)

The difference in n-energy between the cyclic and acyclic polyenes is now -a#?2; this will be less than the value (-a/3) for the symmetrical structure, and will rapidly decrease with increasing ring size. Bonds in a 4k-membered ring should therefore alternate in length, and the resonance energy3’, while negative, should diminish rapidly with increasing ring size. Both these conclusions agree with the results of SCF MO calculations.*o 10 M. J. S. Dewar and Carlos dellano, unpublished work ; the earlier calculations3 were for symmetrical structures with equal bond lengths. where the ground states will be triplets.

82

M. J. S. D~WAR

The resonance energy calculated for singlet cyclobutadiene is large and negative, for planar singlet cyclooctatetraene small and negative, and for the large rings virtually zero, while the bond lengths are very close to those calculated3’*ia for open chain polyenes. These conclusions rest on the usual assumption that all the resonance integrals @) have similar signs. In a normal 7r-system, the basis set AO’s can always be chosen to overlap in phase with one another, in which case all the /3’sare negative. This choice is ofcoursearbitrary ; however inversion of the phase of one A0 in such a system will invert the /?‘s of P-bonds to all the adjacent atoms; in the case of a single ring, this will lead to inversion of two of the /&-and it is easily seen that inversion of the signs of an even number of /3’sleaves the rules for aromaticity unchanged.

+___ + --+ -___ + --em - 88 88 B

-B

V

VI

VII

The PM0 derivation of Hilckel’s rule can be extended to polycyclic systems, using an argument due to Dewar and Longuet-Higgins.” If atoms r,s,t, in I form part of one ring in a polycyclic system, it can be shown that the signs of the NBMO coefficients a,,, a, are the same if the ring contains (4n +2) atoms, and opposite if it contains 4n. Htickel’s rule can therefore be extended to individual rings in such polycyclic systems. One would for example conclude that the terminal rings in biphenylene (VII) should be aromatic, and the central ring antiaromatic; this agrees with the results given by the SCF MO method, but not with those given by the HMO method. Thus the HMO method predicts that VII should have a larger resonance energy than biphenyl; using this value, Coulson and Moffitti2 deduced a value of 74 kcal/mole for the strain energy in the four-membered ring-which is clearly much too large. The heat of formation calculated for VII by the SCF MO method leads to an estimated strain energy of 29.5 kcal/mole, which is certainly of the right order of magnitude, judging by thermochemical data for other microcyclic compounds (cyclopropane, cyclobutane, cubane, etc.). The PM0 method can also be extended to cyclic conjugated systems containing just one odd-numbered ring. Such a system (VIII) can be derived from an odd AH (IX) by intramolecular fusion, which we may suppose to take place between atoms r and s. -CH r

HC-

s

VIII

IX

X

XI

Consider Grst the case where VIII is a neutral system, i.e. either an even system such as fulvene (X), or an odd radical such as cyclopentadienyl (XI). Since r, s are adjacent atoms in an odd-numbered ring in VIII, they must be atoms of like parity4 in the AH IX. Now it can be shown13 that the bond order between atoms of like parity in a neutral 11M. J. S. Dewar and H. C. Longuet-Higgins,

Proc. Roy. Sot. A 214,482 (1952). 12C. A. Coulson and W. E. Moffitt. Phil. Mug. 40.26 (1949). 13C. A. Coulson and G. S. Rushbrooke, Proc. Camb. Phil. Sot. 36,193 (1940).

A molecular orbital theory of organic chemistry-VIII

83

AH vanishes; it follows from Eq. 9 that VIII and IX have identical r-energies, to a first approximation, so that the odd numbered ring in IX is neither aromatic, nor antiaromatic, but simply non-aromatic. Thus if IX is a classical AH, VIII will also be classical, with local&d single and double bonds. Fulvene (X) is a good example of this. Its chemical properties show it to be non-aromatic, while the SCF MO method predicts3*10 that it should have zero resonance energy and locahzed bonds. Next let us consider the case where VIII is an odd system, i.e. a cation or anion. The corresponding odd AH ion IX will differ from the neutral radical by having one less, or one more, electron in the NBMO. Since the bond orderpN is zero for the corresponding radical, the bond orders of the ions will be determined solely by the contribution of this non-bonding electron; thus anion :

p,, = a,, a,,

(23)

cation : pN = - a,, aos

(24)

If a,,, aos have similar signs, pls will be positive for the anion, and negative for the cation. It follows from equation (9) that_the anion will then be aromatic, and the cation antiaromatic. Likewise if a, and a, have opposite signs, VIII will be aromatic as the cation and antiaromatic as the anion. In the case of monocyclic systems, rings with (4n + 1) atoms will then be aromatic as the anion, and antiaromatic as the cation; while rings with (4n +3) atoms will be aromatic as the cation and antiaromatic as the anion. In each case aromaticity is associated with the presence of (4n+2) rrelectrons; this completes our derivation of Htickel’s rule. Here again the argument can be extended (see above) to polycyclic systems; polycyclic systems with one odd numbered ring will be aromatic as the anion, but antiaromatic as the cation, if the odd ring contains (4n + 1) atoms, and aromatic as the cation, but antiaromatic as the anion, if the odd ring contains (4n +3) atoms. These results of course agree with experiment; thus indenylium (XII), and fluorenylium (XIII), give aromatic anions, while the various benzo derivatives of tropylium (e.g. XIV) are also aromatic.

00 03 XII

03 00

XIII

XIV

This treatment cannot in general be extended to systems containing two or more odd-numbered rings; it can, however, be applied4 to systems where two odd-numbered rings are present and are fused together. Thus azulene (XV) can be derived by union of the odd AH nonatetraenyl (XVI) with methyl :

xv

XVI

XVII

The P-energy of union (4&is greater than that (2&) for formation of an open chain decapentaene, so azulene should be (and of course is)aromatic. Note that #e NBMO coefficient vanishes at one point of union;:the energy of union of XVI with methyl to

84

M. J. S. DEWAR

form XV is therefore the same as it would be in forming the monocyclic system XVII, Azulene on this basis should be regarded as a slightly perturbed form of the Hiickel hydrocarbon [IO]-annulene, the central bond contributing little to the mesomeric stabilization; the resonance energy of azulene should be much less than that of naphthalene, where both rings are aromatic, and the central bond in axulene should be effectively single. Both these conclusions agree with the results of the SCF MO treatment3*r0 and with experiment. Likewise the PM0 method correctly predicts that pentalene (XVIII) and heptalene (XIX) should be antiaromatic, being perturbed forms of [8]-annulene and [12]-annulene respectively; this again agrees with experiment and with the SCF MO calculations. 3*10 The HMO method draws no clear distinction between XV, XVIII, and XIX, predicting all three to be aromatic hydrocarbons with large resonance energies; indeed XVIII and XIX were assigned trivial names in the expectation that they would prove to be aromatic.

m /’ .\

,‘/ 03

XIX

XVIII

In this first order treatment, no attention has been paid to the role of second order perturbations. However it can easily be shown that the second order contributions are approximately the same as for the union of two even AH’s, i.e. approximately equal to /32/2E (cf. Eq. 5). These contributions are automatically taken into account by using the empirical value Ei, (Eq. 8) for the bond energy of the new C-C u-bond. Anti-Hiickel systems The arguments of the previous section apply only to conjugated systems where all the /3’s have, or can have, similar signs; one can, however, envisage cases when this condition might not be fulfilled. Thus Craig14 has pointed out that replacement of one pA0 in a cyclic conjugated system by a d-A0 leads to a dislocation such that at least one pair of adjacent orbitals overlap out of phase (XX), while Heilbronnerls has pointed out that the same will be true of a normal cyclic n-system which, instead of being coplanar, has the topology of a Moebius strip.

-I$$-kByyP

@g-:8

a

a

-B

B xx

XXI

XXII

It is easily seen that the rules for aromaticity are inverted in the case of a ring where one /? has a different sign from the rest; thus if one p in pentadienyl is positive, the terminalNBM0coefficient.s haveoppositesigns(XXI), whereasifall the$s arenegative, as in a normal ?r-system, the terminal coefficients have similar signs (XXII). It follows that a benzene analogue, with one such dislocation in the ring, would be antiaromatic, D. P. Craig, J. Chem. Sot. 997 (1959). 15 E. Heilbronner, Tetrahedron Letters 1923 (1964). 14

A molecular orbital theory of organic chemistry-VIII

85

whereas the corresponding four- and eight-membered rings would be aromatic. Compounds of this type may be described as anti-Htickel systems. It seems unlikely that systems of this type will be found among normal compounds in their ground states. Thus “Moebius strip” molecules, even if they could be prepared, would be at best amusing curiosities, while P-systems involving d?rbonding seem not’6 to involve the kind of through-conjugation indicated in XX. However anti-Hiickel systems appear to play an important role in certain cyclic transition’states, as we shall now see. Thermal electrocyclic reactions Some thirty years ago Evans” pointed out that the course of the Diels-Alder reaction, in particular the preferential formation of six-membered rings, could be explained in terms of an “aromatic” transition state in which six electrons occupy cyclic MO’s analogous to those in benzene, being formed by mutual overlapping of six AO’s of the participating carbon atoms. Since that time many other reactions have been interpreted in terms of analogous cyclic transition states and this type of process can now be regarded as welI established. Recently Woodward and Hoffmann 1s have published several communications discussing reactions of this type (for which they propose the convenient generic term electrocyclic) in terms of the frontier orbital method; in particular they accounted in this way for the stereospecific course of reactions involving the f&ion of a single bond in an otherwise unsaturated carbocyclic ring. Longuet-Higgins,*9 and Hoffmann and Woodward,is have also discussed these reactions in terms of correlations between the MO’s of the reactants and products, arriving at similar conclusions, and recently Fukui*O and Zimmerman*1 have suggested alternative treatments based on the Hiickel MO method. The frontier orbital method is, however, open to criticism22 while the Hilckel method is known to be unreliable as a guide to the stability of cyclic conjugated systems,*3 and the use of orbital correlation diagrams involves a kind of argument that is still somewhat unfamiliar. We will now show that electrocyclic reactions can be interpreted in a much simpler and more general manner, using the model proposed by Evans,17 together with the PM0 theory of aromaticity that has been outlined above. All known reactions of this type conform to one simple rule. Thermal electrocyclic reactions take place preferentially via aromatic transition states (The aromaticity of a given transition state is of course defined by reference to the isoconjugate hydrocarbon, i.e. the cyclic or acyclic conjugated hydrocarbon whose n-system shows the same topology as the system of delocalized orbitals in the transition state.) 16M. J. S. Dewar, E. A. C. Lucken and M. A. Whitehead, J. C/tern.SOC.2423 (1960). 17 M. G. Evans, Trans. Faraday. Sot. 35,824(1939). I* R. B. Woodward and R. Hoffmann, J. Amer. Chum. Sot. 87,395.2511 (1965); R. Hoffmann and R. B. Wocdward, Ibid. 87,2046.4388,4389 (1965). 19 H. C. Longuet-Higgins and E. W. Abmhamso n, 1. Amer. Chem. Sot. 87.2045 (1965). 20 K. Fukui, Terrahtdon Letters 2009 (1965). 21 H. E. Zimmerman, 1. Amer. Chem. Sot. 88.1564 (1966). u See M. J. S. Dewar, Adwurces in Chunicol Physics 8,65 (1964). 23OA. L. H. Chung and M. J. S. Dewar. J. Cti. Phys. 42,756 (1965); b M. J. S. Dewar and G. J. Gleicher, J. Amer. Chem. Sot. 87,685 (1965).

M. J. S. DBWAR

86

Consider for example the Diels-Alder reaction (XXIII). This could take place in one step, via a cyclic transition state (XXIV), or in two steps via a stable intermediate (XXV), itself formed via an acyclic transition state (XXVI).

XXVI

The two position states are isoconjugate with benzene and hexatriene respectively; moreover XXIV is of Hiickel type since, as indicated, the phases of the orbitals can be chosen so that all pairs of adjacent orbitals overlap in phase. One would conclude that XXIV should be more stable than XXVI, i.e. that the one step electrocyclic mechanism should be preferred over the two step acyclic one. Analogous reactions are also known which lead to four- or eight-membered rings; for example the dimerization of butadiene to 4-vinylcyclohexene (XXVII) is accompanied by the formation of 1,2divinylcyclobutane (XXVIII) and l,S-cyclooctadiene (XXIX). Here one would expect the electrocyclic transition state to be antiaromatic, containing a four- or eight-membered ring; therefore a two-step reaction via an intermediate biradical should now be favored. Present evidence seems to suggest that these “abnormal” Diels-Alder reactions do in fact take place in steps via a stable biradical intermediate.

XXVII

XXVIII

XXIX

XXX

The dimerization of butadiene raises another interesting point. The diene component must of course react in a& form for the reaction to be sterically convenient; however Eisler and Wassermann24 have presented evidence strongly suggesting that both molecules react in the cis form in the “normal” reaction leading to XXVII. Now if both molecules are in the cti form, and if they approach in the manner indicated in XXX, the terminal atom of the “dienophile” can approach one of the central carbon atoms of the “diene”. The corresponding interaction between the two AO’s should lead to the introduction of an additional’&+membered ring into the delocalized system of the 24B. Eisler and A. Wassermann, J. C&em.Sot. 979 (1953).

81

A molecular orbital theory of organic cbcmistry-VIII

transition state; since the relevant orbitals are easily seen to overlap in phase, this additional interaction should then lower the total energy. No such interaction could occur in the combination of cis-butadiene with trans-butadiene; it is therefore understandable that the reaction takes place most easily between two molecules of the CL conformer. The necessary geometry (XXX) can moreover be attained only if addition takes place end0 cis; since similar arguments will apply to reactions where other unsaturated groups are attached to the double bond of the dienophile, we have provided a general explanation for the general prevalence of end0 cis addition in Diels-Alder reactions. Note that this picture of the transition state is entirely equivalent to that proposed by Woodward and Katz;*5 the present treatment provides a concrete interpretation of their “secondary attractive forces” and explains the way in which they lead to a stabilization of the transition state. Similar arguments can be applied to the majority of thermal electrocyclic reactions, e.g. the Cope rearrangement, 26 dipolar additions to multiple bonds,*7 or the Claisen rearrangement,*8 All these reactions involve transition states of Hiickel type with (4n +2) delocalized electrons (usually six, i.e. n = 1). The Cope rearrangement (XXXI) presents one interesting feature; here the transition state could have either a chair (XxX11) or a boat (XXXIII) configuration. In the latter, the orbitals of the two central carbon atoms overlap, adding a transannular bond to the delocalized system of the transition state. Now this extra interaction leads to the introduction of a four-membered ring; it should therefore raise the energy of the transition state, and we would therefore expect the favored geometry to be XXX11 rather than XXXIII. Doering and Roth*9 have shown that the stereochemical course of one such reaction does indeed indicate that the transition state must have had a chair of configuration.

c-3 xxx1

XXXII

X?CxIII

Woodward and Hoffman+ have drawn attention to one particularly interesting class of electrocyclic reactions, involving ring opelning by fission of a single bond between two saturated carbon atoms in an otherwise conjugated ring; the conversion of cyclobutene @XXIV) to 1,3-butadiene (XXXV), or of 1,3cyclohexadiene (XXXVI) to 1,3,5-hexatriene (XXXVII), are typical examples.

a--Q XXXIV

0-c xxxv

XXXVI

R. B. Woodward and T. J. Katz, Terruhedron 5.70 (1959). 26 See E. Vogel, Angew. Chem. (Internat. Edit.) 2,1 (1963). 27 See R. Huisgcn. Angew. Chem. (Internat. Edit.) 2,633 (1963). 28 See D. S. Tarbell, Org~ic Reactions 2,1(1944). 29 W. E. Doering and W. R. Roth, Tetruhedron 18,67 (1962). 25

XXXVII

88

M. J. S. DEWAR

Reactions of this type involve a rotation of the two carbon atoms forming the single bond, the transition state being one in which their two hybrid AO’s no longer he in the plane of the r-system and so can interact with the 2pAO’s of the adjacent carbon atoms. Two possible transition states of this type can be envisaged, depending on whether the carbon atoms rotate in the same (XXXVIII), or opposite @XXIX), directions; and if substituents are present, the two modes of reaction can be distinguished by comparing the geometries of the reactant and product. Woodward and Hoffmannis term reactions of the first type conroia~ory, of the second type disrotutory.

s

x

Y

XL

These interactions of the two hybrid orbitals with the orbitals of the adjacent conjugated system lead to the formation of typical electrocyclic structures, isoconjugate with the MO’s of a cyclic conjugated ring. Consider now the signs of the resonance integrals for interaction of the hybrid orbitals with 2p orbitals of the adjacent carbon atoms. Each hybrid orbital can be written (XL) as a combination of an s component (s), a vertical p-component (x), and a horizontal pcomponent (y). Since s and y are symmetric with respect to reflection in the nodal plane of the a-system, they do not interact with the adjacent 2p orbital; the sign of the relevant resonance integral is therefore determined solely by the relative phases of the 2p orbital, and of the vertical component x of the hybrid orbital. If then we choose the phases of the two hybrid orbitals in such a way as to make the resonance integral between them “normal”, the resonance integrals to the adjacent 2p orbitals will have opposite signs for the conrotatory transition state (XXXVIII), but similar signs for the disrotatory transition state (XxX1X). It follows that the delocalized system of the conrotatory transition state is of anti-Hiickel type, that of the disrotatory transition state of Htlckel type. The choice of reaction path should then be determined by the number of delocalized electrons. The conrotatory mode should be favored for 4n electrons, the disrotatory mode for (4n+2) electrons. This prediction agrees with experiment;18 thus cyclobutene derivatives (XXXIV) open by the conrotatory path, cyclohexadienes (XXXVI) by the disrotatory path.30 This treatment can of course be extended immediately to systems with oddnumbered rings; thus the conversion of the cyclopropyl cation (XLI) to ally1 cation (XLII) should be disrotatory, two electrons (i.e. (4n- 2) with n=O) being involved, whereas conversion of the corresponding anion (XLIII+XLIV) should be conrotatory. According to this treatment, the corresponding reactions of cyclic radicals 30

Zimmermanz* has discussed these reactions in terms of a Htickel treatment, based on the same idea that the conrotatory transition state is analogous to a dislocated x-system of Moebius strip type.

A molecular orbital theory of ormic

89

chemistry-VIII

should be non-stereospecific sinee cyclic odd radicals are non-aromatic. One would also predict that reactions of such radicals should be less facile than those of corresponding ions, the latter taking place through aromatic &ctrocyclic transition states.

XL1

XLIV

XLV

One can also apply the same technique to reactions involving polycyclic systems, using the extended forms of the Htiekel rule deduced earlier. Thus opening of the fourmembered ring in XLV should be conrotatory since a four-membered ring can be aromatic only if it contains one fl of inverted sign. All these conclusions agree with the available experimental data, and of course the same kind of approach can be applied with equal simplicity to other types of electrocyclic reaction. For example the thermal migration of allylic hydrogen atoms across conjugated systems should-and does-take place preferentially by l,S-shifts rather than 1,3-shifts,31 since reactions of the former type can take place by an electrocyclic reaction via a cyclic transition state which, being six-membered, will be aromatic, whereas a I&shift would involve an antiaromatic four-membered ring. Again, the rearrangement of vinylcyclopropene (XLVI) to cyclopentene (XLVII) should not be a concerted process since it would involve an antiaromatic four-membered electrocycle. This reaction seems indeed to take place in steps via an intermediate biradical.32 Under similar conditions, the homologous reaction of l-cyclopropylbutadiene (XLVIII) to ~clohep~diene (XLIX) might on the other hand take place in a concerted manner via a six-membered electrocyclic transition state.

The PM0 treatment can be extended, to a limited extent, to problems involving light absorption; photochemical electrocyclic reactions provide a good illustration of this. When an even AH (R) is constructed by union of an odd AH (5) with methyl, the bonding and antibonding MO’s of R are’, due to a first approximation, the same as those of S. However R contains an additional pair of MO’s, one bonding and one antibonding, arising from a first order interaction of the NBMO of S with the 2p orbital of methyl. The difference in r-energy between Sand II can be equated, as a first approximation, to the change in energy when two non-bonding electrons, originally in 31 See R. B. Woodward and R. Hoffmann, J. Amer. Chem. SOC.87,2511(1%5). 32See Doering and Roth, Anger. C&em.(Internat. Edit.) 5 115 (1963).

M. J. S. DEWAR

90

the NBMO of S and the methyl 2pA0, are transferred to the new bonding MO (Fig. 2a). This energy difference is greater, the greater the separation of the two perturbed MO’s; the PM0 treatment of aromaticity is based on a discussion of this separation.

+I S

R

--ICH3

(a)

s

R'

CM3

W

Ro. 2. MutuaI perturbation of the NBMO of S, and the 2pAO of methyl, on union to form R; (a) represents the situation in the ground state of R, (b) that in the first V-T* excited state.

Consider now the tist ?r-VT*excited state of R. In the PM0 approximation, this contains two unpaired electrons, occupying the two MO’s that arise from mutual interaction of the NBMO of S and the 2pAO of methyl. The corresponding excitation energy should then run parallel to the separation between these MO’s; a parallel of this type does indeed exist,33 suggesting that the PM0 method can Serve as a reasonable indication of the energies of such excited states. Now according to this picture, the total energy of the two relevant electrons (Fig. 2b) shouldbe thesameintheeven AH Rasin theinitialsystem(S+CH,); forthesplitting of the perturbed levels in R is symmetrical. On this basis the energy of union would be zero, and independent of the interaction between the NBMO of S and the methyl 2pAO. There would then be no distinction between aromatic and antiaromatic systems, all such excited states being non-aromatic. However this’ simple MO picture is known to be in error, in the sense that it grossly underestimates the antibondingness of antibonding MO’s. The energy of the excited state (Fig. 2b) should consequently be greater, the greater the orbital separation; this is exactly the reverse of the situation in ground states where the energy is lower, and the system consequently more stable, the more the two perturbed MO’s are separated in energy. If then one uses the terms aromatic and antiaromatic in an extended sense, to denote the energy of any cyclic system relative to that of an analogous open-chain structure, one must conclude that the first n-?r* excited state of an even aromatic AH is antiaromatic, and that of an antiaromatic AH is aromatic. Let us now consider a photochemical electrocyclic reaction, involving an evennumbered ring. If the reaction takes place adiabatically, it will do so through an excited form of the corresponding cyclic transition state. The arguments given above then indicate that the preferred transition states will be excited versions of antiaromatic structures; the rules governing such reactions should be exactly the opposite of those controlling the corresponding thermal reactions. 33M. J. S. Dewar, J. Chem. Sot. 3532,3544(1952).

91

A molecular orbital theory of organic chemistry-VIII

Next let us consider excited states of an odd AH ion or radical Q. The corresponding structures for a cation, radical, and anion, are indicated in Fig. 3a, b, c, respectively, where ZV,A, B denote respectively the NBMO, the lowest antibonding MO, and the highest bonding MO.

C~_c______C~C

I

i

.---. cl I

,.*-.., : __ cl

j

LIII

A

LIV

-

(a)

(b)

(c)

(d)

FIG. 3. Dia grammatic representation of the occupation of the NBMO (N), and adjacent bonding (B) and antibonding (A) MO’s, in excited states of an odd AH; (a) cation; (b) (c) radical; (d) anion.

Following the arguments outlined above, we can see that the energies (dE) of the corresponding excited states of an odd cyclic ion or radical (a), derived from L by intramolecular union, are given relative to that of L by: (cation)

dE= -.2pps

(radical)

dE=

2/?(pA-pN)

(anion)

dE=

2/3~~,,

or

2/3(pN-pB)

(25)

where pe, PN, pA are the partial bond orders in L between atoms i, j that hecome linked in U, from the MO’s B, N, and A respectively. If L is an open chain AH, its MO’s will be either symmetric (LI), or antisymmetric (LII), with respect to a plane (P) bisecting the chain. If union takes place through the two terminal atoms (e.g. LIII+LIV), then the partial bond order in L between these atoms will be positive for a symmetric MO, negative for an antisymmetric MO. Moreover the MO’s in a linear AH alternate in symmetry ; thus if the MO N is symmetric, A

92

M. J. S. DEWAR

and B will be antisymmetric, and conversely. These considerations lead immediately to the following rules for aromaticity in the corresponding transition states: NBMO symmetric; cation and radical (b) aromatic, anion antiaromatic. NBMO antisymmetric; anion and radical (a) aromatic, cation antiaromatic.

(26)

For the two ions, these rules are again the antithesis of those pertaining to the grofnd state; reactions of this type should likewise take place preferentially through excited forms of antiaromatic transition states. Radicals on the other hand should follow a different pattern. Here there are two alternative possible excited states, one of which is aromatic, the other antiaromatic; photochemical ring opening reactions of radicals should therefore be non-stereospecific, like the corresponding thermal reactions,*0 since each excited state favors a different mode of fission. There should, however, be a marked difference between the ease of the two types of reaction. Photochemical ringopening of cyclic radicals should take pla;cejvery easily indeed, the extra stabilization (equation 25) of the transition states being greater than for the corresponding ions. These calculations apply rigorously only to monocyclic reactions; in less symmetric situations, the orbitals A and B in Fig. 3 may or may not differ from N in symmetry. With this reservation we may sum up our conclusions in the following rules: Photochemical electrocyclic reactions of closed shell molecules should tend to take place via excitedforms of antiaromatic transition states. Analogous reactions of radicals should take place more readily than those of corresponding ions, but without electronic stereospecificity. The first part of this rule again agrees with conclusions reached previously and with experiment;t* thus the photochemical opening of cyclohexadienes to hexatrienes (XXXVI+XXXVII) takes place by the conrotatory path whereas the corresponding thermal reaction is disrotatory. Another striking example is provided by the DielsAlder reaction. The thermal electrocyclic Diels-Alder reaction gives exclusively sixmembered rings; analogous thermal reactions leading to four- or eight-membered rings take place in steps via intermediate biradicals. Under the influence of light, however, four-membered rings form very readily, a reaction which indeed has become of practical importance in organic synthesis. Since the electrocyclic transition states for formation of a four-membered ring by a thermal reaction is antiaromatic, the corresponding excited state should be aromatic and photochemical reactions involving it should therefore take place very readily.