The Arithmetic of Aromaticity Christopher Glidewell and Dovglas Lloyd University of St. Andrews. St. Andrews, Fife KY16 SST. Scotland, Great Britain The Amhmetlc cd ArornailcHy*
The Hiickel (4n+2) rule concerning the n electrons in aromatic comnounds has long been a cornerstone of organic chemical theiry. More gener&ly, cyclic conjugated systems containing (4n+2) n electrons have been regarded as possessing some intrinsic electronic stabilization, called aromaticity, while those containing 4n n electrons have been considered to he corresnondinelv destabilized. and so are antiaromatic. ~uantita'tivem&sures of the' stabilization or destabilization of a eiven cvclic svstem as comnared with an appropriate acyclic reference system have been calculated using molecular orbital methods (I),VB methods (2),and chemical graph theory (3). In the original derivation of the (4n+2) rule, some very stringent a&roximations were made (4): not only was thk coniugated system assumed to be strictly planar with equal C-c tnmd lengths throughout, but the ;onjugation wasrequired to be restricted to a single closed loop. Although the tiuckel 14n+2) rule is not stricrlv. a~olicableto condensed polycyclic hydrocarbons, there are nonetheless many such systems in which some, a t least, of the canonical forms represent single conjugated loops spanning more than one ring. Azulene ( I ) and biphenylene (2) provide simple samples; in such canonical forms the cross-ring bonds are of o type only.
Eq~lvalence 2+2 2+4 2+6 2+8
--
P4
+
6 6 10
Example
7 8 9
10
.A
+
6+4+2+2 14 22 Thelable showsthe extent to which 2 r and 6 s and, to a lesser extent. 10s clrc~itoare slabillzing and 4 s and 877 circuits are destablllzlng, regardless of me total number of s electrons. 8
In this article we explore an aspect of such conjugated systems that has hitherto received little attention, namely the extent to which, in polycyclic hydrocarbons, the total r electron population tends to form small (4n+2) groups and to avoid the formation of 4n groups. Readers wishing to consult a more detailed account are referred to another publication by the present authors (5). We can define (5),on the basis of semi-empirical SCF-MO calculations, and often on the basis of experimental molecular geometries also, the conditions under which two or more conjugated loops in a molecule either interact to form a single Hiickel loop with enhanced stability or else interact repulsively, maintaining their individuality in small isolated a systems connected by long, weak bonds. Estimates of resonance energy per r electron, used as an index of aromaticity, established by comparison of the com-
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pounds in question with carefully formulated reference structures ( l b , 6 ) ,have shown that for the planar annulenes C,H, the systems having n = 4p are destabilized and those having n = 4p+2 are stabilized but that the magnitude of either the stabilization or the destabilization decreases rapidly as the value of n increases. Such procedures are open to a number of criticisms, especially when based upon primitive methods for calculating energies; in addition assumptions, often unjustified, have been made about the geometries of both the annulenes and the reference structures. Nevertheless, the conclusions are in reasonable accord with oualitative exverimental evidence in findine a maior destadi~izinge f f e i i n a 4r system, and a lessersuch Lffect in a planar 8n system, while there are corresponding stabilizing
effects in nlanar 6a and 10a svstems: when n 2 12. the effect upon stability of the a electrons is minor. In the nresent discussion we base our conclusions (5) unon a combination of experimental structural data and hond orders calculated from high-quality geometry optimizations made using semi-empirical SCF-MO methods. Our results often allow the descriotion of the electronic structures in terms of single bond-structures; our conclusions concerning the interaction or ntheru,ise of small groups of a dectnms to form larger cycles are summarized in-the table Blcyclic Systems When hicyclic systems consist of two fused rings, which have one carhon-carbon hond common to hoth rings, there are two different types possihle, depending upon whether or not hoth rings have an even numher of ring atoms. When hoth rings consist of an evennumber of atoms it is possihle to draw a structure made up of alternate single and douhle honds in such a way that the hond common to hoth rings is either a single or douhle hond, as, for example, in the case of naphthalene or hiphenylene (2). For compounds with odd numbers of atoms in the rings, e.g., azulene (I), it is not possihle to draw structures with alternate single and douhle honds unless the hond common to hoth rings is a single hond. In azulene (1) . . there is extensive delocalization. and ab initio calculations ( i )including electron corre~ariv~find the structure to have C2 symmetry with peripheral bond deloralization. X-ray data (81 on uulenea are incunclusi\~e,hoth hecauseofdisorder in thestructure ofazuleneitself (5,;) and because of the possibility (9)that crystal forces can perturb the small energy difference between localized and delocalized forms. In the homologous pentalene (3) and heptalene (4) there is almost complete hond fixation.
For azulene, alternative structures could he contemplated. wherein. in similar fashion to hinhenvlene (2). . . . . which is best represented as two 6a electron systems connected by two honds of vervlow order (10).. seoarate 4 a and 6 s svstems . are found, viz. 1: and lb.
In fact a delocalized l0a-electron system is preferred; hence we may write 4+6 3 10, expressing the conclusion that the 4 s and 6a fragments will interact to form a 10a cycle. For pentalene (3) there is no gain to the molecule either in adopting two delocalized 4a-electron systems as in 3a, or a 2a- and a 6a-electron system as in 3b, or in taking up a peripheral 8a-electron delocalized structure; the compound is a tetra-alkene (3).
which might alternatively he represented as 5a, shows peripheral delocalization of its 10a electrons, i.e., 4+6 =+ 10, hut the anion 6, which is isoelectronic with heptalene, contains two 6a systems which are mutually repulsive, heing separated by long weak honds, so that 6+6 =b12.
In cyclohutadiene (7) it appears that the two 2 s fragments are separated by long weak bonds (11) with no electronic delocalization, and we may write 2+2 + 4. In the hicyclic system butalene (81, there are six a electrons delocalized essentially as in benzene, although of course perturbed somewhat by the cross-ring a hond, so that hutalene should he best represented as 8a. In this case we may write 2+4 6.
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Continuing the hicyclic series from hutalene are the compounds 9 and 10.
Only highly substituted derivatives of 9 have been described; although there is considerable hond fixation, the 2a and the 6a fragments are separated by long weak honds (12). In 10 there is a weakly delocalized 10a system (13) and an Xray structure of a diphenyl derivative shows that this is sufficient to force planarity on the whole skeleton (14). (Contrast cyclo-octatetraene (15) and its di-anion (161.) The bridging hond is very long, longer than, for example, the bridging hond in azulene, and is of a type only. Here we may 10. write, for 9 and 10, respectively, 2+6 + 8, and 2+8 Trlcycllc Systems The series of four-membered ring compounds that begins with cyclohutadiene (7)and hutalene (8) continues with tricyclic system 11.
This representation of this compound is entirely consistent with the computed hond orders and minimizes the numher of distinct cyclohutadiene-type rings present; the valence isomers l l a and l l b hoth contain two such rings, and l l c contains three. There is no evidence of delocalization to form a single 8 r loop: we may write for this example, 4+4 P 8, hut rather 4+4 =, 2+4+2. Homolom of 11 are 12 and 13 with the a-carbon skeletons as shown, Laving 10 and 12 a electrons, respectively.
Heptalene could take up a (6+6)a-electron structure, as in 48, hut any gain from delocalization is probably offset by less
satisfactory steric factors. In any event, there is no gain in such systems combining to provide a delocalized 12a-electron system, so we write 6+6 ti 12. The cation 5, which is isoelectronic with azulene and
The computed hond orders indicate that the structures should he represented as 12a and 13a, respectively. Volume 63 Number 4
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12a
13a
13b
In 12. there is no interaction between the 6 a svstem of the large ring and the cyciol)utadiene fragment. The framework reauiresthnt there be at leait onecvclohutadienoid rinr. - and form 12a minimizes the number of such interactions; any 10a periphery must also include such a ring, and it is the relatively greater stabilization of a 6n system that dominates the electronic structure. Thus, in contrast to the cation 5, in the case of 12,4+6 9 10. This contrast between these examples must derive from other factors. It is possibly partly connected with the fact that by delocalizing all 10 electrons in 5 the charge is also delocalized as far as nossible. whereas. in the case of 12, there is no dispersion of ckarge to'encourage extended delocalization. Furthermore. in the case of 5. there is no adverse complication arising from concomitant development of cyclohutadienoid character. In 13 there is little delocalization in the 12a periphery; the electronic structure again minimizes the numher of cyclobualthough there is very strong bond tadienoid rings. fixation in the eight-membered ring, there is some delocalization of the 6 r system in bonds (a-d); this fragment is somewhat analogous to hutalene (8). In 13, again 6+6 + 12; nor is the alternative 4+8 system (13b) of consequence. In both 10 and 13 annelation of an unsaturated fourmembered rine issufficent to oromote ~lanaritvofthe eightmembered ring. MIND013 calculations ( 1 7 j have shown that annelation of either three-membered or saturated fourmembered rings is also sufficient to enforce planarity on the cyclo-octatetraene skeleton. In hiphenylene (2) and its charged analogs 14 and 15,
ow ever,
the two rings are connected by long bonds of low bond order, so for each system it is again found that 6+6 =b12. This is confirmed by experimental evidence (18). In the anionic analog of 15 having a total of 1 4 s electrons, once again there is no delocalization across the four-membered rings (16), so here 6+8 + 14.
The destabilizing effect of eight a electrons is small, and the stabilizing effect of 14 a electrons is minimal, so the dominating influence on the electronic structure is the 6 a group of thesix-membered ring. Delocalization of the a ele&o& in the seven-membered ring of 16 does not occur, since this would lead to a local 8 a electron system. In the 10 a electron dication derived from s-indacene (17), the bond orders indicate the structure (18) containing a 6n system in the central rings with two allylic 2a fragments connected by bonds of low order; thus 2+6+2 a 10, and there is no delocalized 10s periphery.
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Journal of Chemical Education
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In the dianion 19, however, the bond orders indicate a delocalized peripheral 14a system with two weak cross-ring 14; there is experimental evidence honds. Here 4+6+4 (19) for this type of electronic structure. In the dication, the dominant stabilizing effect of the 6 a system outweighs the weak contribution from a 10a loop hut in the dianion the overwhelmingly destabilizing influence of two 4a groups outweighs the stabilizing effect of the 6 a group, giving a very weakly stabilized 1 4 r loop. Also assisting may be the dispersal of the two "extra" electrons over as many sites as possible. Bifurcated and Condensed Systems
In contrast to the delocalized 14a system in s-indacene dianion, there is appreciable localization in phenanthrene (20), where the two 6 s systems are dominant; 6+2+6 =+ 14.
Phenanthrene is the first representative of the bifurcated benzenoid series, and in bifurcated systems containing a mixture of four- and six-membered rings, several general rules appear to hold: ( I ) the numher of closed 6 a loops is maximized, and the numher of 4a loops is minimized; (2) where these requirements are strongly contradictory there is very marked bond fixation throughout; (3)delocalized loops greater than 67 electrons are of negligible importance. These generalizations are illustrated by compounds 21-24.
In 21 and 22 there are no delocalized a loops while in 23 and 24 there are two and three 6a loops, respectively; there is no indication from the calculated molecular and electronic structures of 21-24 of 12a, 14a, 16a, or 18a peripheries, regardless of whether the total numher of a electrons is 4n or (4n+2). When only six-membered rings are present, simple examples of these rules are found in phenanthrene (20) and anthracene (25) (5);there are very many others.
For condensed hydrocarbons, Hiickel's (4n+2) rule is not generally applicable, since the electronic structure cannot usually be regarded as composed of simple loops. However, we note that compounds of this type exist in which a single peripheral loop is effectively isolated from an interior a system. Thus in 26 (20) the weakly delocalized peripheral 14a system surrounds an electronically isolated central ethene fragment.
In conclusion it may be noted that similar consideration of the arithmeticof aromaticity mav alsoeffect reaction paths. Kinetically controlled ele&oihilic substitution onnaphthalene provides the l-substituted product preferentially to the 2-isomer. Consideration of the two intermediates 27 and 28 shows that the former may be regarded as a 6+2 system, havinga stabilized benzene ring and an allylic cation (cf. la), whereas the latter, although having a benzenoid system, can have no supporting allylic system.
. .
. .
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ti& ~.~hi&.~~.-; vdagchemie: ~ & i n ,1938. (51 Glidewell, C.; Lloyd, D. Telmhedron 1984,10,4455. 161 Dewar, M.J.S.: de Llano, C. J. Amor. Chem. Soe. 1969,91,789: He-, B.A.: Schead, L.J. J. Amor. Chem. Sac. 1971,93,305; Tetrohedmn Lett. 1972,5113. (7) Haddon, R.C.; Raghsvsehsri. K. J. Amer Chern. Sm. 1982.104;35L6. (8) R o b e r u m J.M.: Shearer, H.M.M.;Sim, G.A.; Watson, D.G. A d o Cryat. 1962,15.1: Ammon.H.L.;Sundarslingam.M. J. Amer.Chem. Soc. 1366.88.4794. (91 Farnel1.L.; Kao, J.; Radom,L;SchaeAr, H.F. J.Am-r. Chem.Soc. 1981,103,2147. (101 Fsweett. J.K.; Trotter. J. Acta Crysf. 1966.20.87; Yokoleki. A,: Wileox. C.F.: Sam.. S.H. J.Amer. Chem. Soe. 1974.96,1025: Glidewell. C.: LloydD. TefrohodranLelf.
(E = e l e c t r o p h i l e ) 27
28
Generation of this 6+2 svstem in 27 ex~lainsthe ready activity of naphthalene in electrophilic substitution reactions; the same sort of picture has been drawn to explain the ready susceptibility of azulene to both electrophilic and nucleo~hilicattack and the sites at which reactions preferentialiy take place. Similarlv attack at the 9-position of anthracene or phenanthrene provides two benknoid systems in the interimediate; this is not achieved by attack at other sites. ~
~~~~~~
~
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Llterature Cited (11 See, inter aha la1 D-ar, M.J.S. "The M o l ~ u l aOrbital r Theory of Organic Chcmiatry"; MeOmw-Hill: New York. 1969; Pvro Appl. Chem. 1975.44, 767; Goldstein, MJ.: Hoffman,R. J.Amer.Chem.Soe. 1971,93,6193;IblSchaad,L.J.;Hess,B.A. J. Chem. Educ. 1974,51, MO. 121 interalia. Herndon. W.C.: Ellzev. M.L. J. Ampr. Chem. Soc. 1974.D6.6631: Harndon. . lS?i.96,7605: J. Chem.Edue. 1974.k. io;G&dlsr,w: w . C . 2 A ~ Wthem, 2.Chom. 1986,20,391.
see.
(12) Winter, W.; Svaub, H. Angelo. Chem. 1978,80,142; ~ $ a w . Chem. Inl. Ed. End. 1978.17, 127. (13) Ode. M.: Oikaws, H. Tetrahedron Laff. 1980.107. (141 Kahufo. C: Oda, M. Tmohadron Lett 1986,103. 1151 Bastianaen, 0.; Hedberg, L.: Hedbarg, K. J. Cham. P h w 1957,27.1311. 1161 Kstz, T.J. J. Amer. Chom. Sac. 1966, 82. 3784, 3785: Fritz, HE.: Keller, H. 2. Noturlorseh. 1961, 166,231; Chem. Ber. 1962.95, 158: Goldberg, S.Z.: Raymond, K.N.;Harmon. C.A.:Templeton, O.H. J.Amm Chsm.Sm. 1914.96.1348. IL71 Wong. H.N.C.;Li. W.-K. J. Cham.Rea. 1984. IS1 302. (I81 Lombsrdo,L.; Wege, E.Austro1. J. Chem. 1978,31,1569. (19) Edlund, U.:Eli-n. B.; Kowalewski, J.: fiogen,L. J. Cham. Soc., Perkin T a n s . 11 198L,1260. (201 Vogel, E.: Wie1and.H.; Schm&teig,L.: La,J. Angeu. Chom. 1984,D6,717;Angalli. Chem. Int.Ed.Eng1. 1384.23.717.
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