a
REPRESENTATION OF POLYCYCLIC AROMATIC COMPOUNDS THEODORE I. BIEBER The University of Mississippi, University, Mississippi
IN1918 Robert Robinson called attention to the importance of the aromatic sextet (l),and in 1925he andArmit represented benzene, pyridine, pyrrole, and thiazole by (I), (11), (111), and (IV) respectively, where the
circle symbolizes a sextet of =-electrons (9). The sextet principle has since then received a theoretical explanation (1, $, 4) and further experimental support (5,6,7). The circle as a symbol of the sextet has also been used in the representation of polycyclic aromatic compounds. Numerous instances from the chemical literature could be cited, but the reader is referred, instead, to the chapter by Wilson Baker in "Perspectives of Organic Cbemistry" (8). Naphthalene may thus be represented as (V) where the meaning of the circle is now modified
to represent a sextet of =-electrons which may in part be shared with an adjacent sextet (or sextets). Since naphthalene possesses only 10 u-electrons, it is clear that two =-electrons are shared. The extension of this symbolism to polycyclic compounds must not be interpreted as signifying in a strict sense that each ring in the ring system constitutes an autonomous aromatic unit and as such obeys the sextet principle. There is undoubtedly some over-simplification involved here. But it is interesting to note that in azulene there is an unmistakable tendency for each ring, the five-membered One as as the seven-membered one, to possess a sextet of T-electrons, two u-electrons again being shared. This tendency finds expression in the dipole moment of azulene (9)and in the fact that electrophilic attack occurs on the five-membered ring (10-15) and nucleophilic attack on the seven-membered ring (16). One may therefore write (VI) as an extreme structure for azulene.
(W The purpose of the present article is to inject more precision into the matter of =-electron sharing by adjacent sextets. It is proposed a t the outset that in ring VOLUME 35, NO. 5, MAY, 1958
systems where no atom is common to more than two aromatic rings a line joining adjacent circles representing sextets be used to denote the sharing of two =-electrons. With the use of this device the total number of =-electrons becomes more readily apparent. Thus naphthalene (VII) has (2 X 6) - (1 X 2 ) = 10 u-electrons. Antbracene (VIII) and phenanthrene (IX) each have (3 X 6) - (2 X 2) = 14 u-electrons.
Azulene may now be represented by (X). This is, of course, an extreme structure. One way in which the symbolism may be refined i n order to approximate the true situation is shown by (XI). The introduction of the arrowhead, placed for convenience on the line joining the circles, indicates a slight redistribution of the =-electron population in the direction shown, taking the extreme structure (X) as a basis. Obviously this redistribution causes a reduction in the charge separation.
w -+
(XI
-
G s
u6+ S(XI)
The sharing of =-electrons by neighboring sextets is a greater problem in more highly condensed ringsystems. The arguments lead to results that are very easy to apply. It will be assumed as a n approximation that the Telectron population of an atom involved in the fusion of aromatic rings is me. I n general, the =-electron population of any atom participating in an aromatic system may slightly exceed me or fall slightly short of me, the deviation from unity being always small because the over-all number of rr-electrons in the system is similarto and frequently equal t o the number of atoms composing it, Inequalities in the distribution of the cloud are never sufficiently drastic t o cause the 7-electron population of a ring atom to approximate an integral number other than me. A distinction must he made between an atom of ring fusion common to two aromatic rings and an atom of ring fusion common t o three aromatic rings. The first type will be referred t o as a n atom of simple fusion because it is involved in the fusion of but one pair of rings. The second type will be referred to as an atom of triple 235
fusion because it is involved in the fusion of three mutual pairs of rings. An atom of simple fusion has its R-electron population of one shared by two sextets. An atom of triple fusion has its R-electron population of one shared by three sextets. If completely unshared sextets were assigned t o all the rings of a polycyclic aromatic system, then there would be one electron too many for every atom of simple fusion and two electrons too many for every atom of triple fusion. This excess of electrons must obviously be subtracted. For every atom of simple fusion a subtraction of one is required. Since only one pair of sextets is involved, the subtraction of one is to be carried out in full when the relationship between these two sextets is considered. For every atom of triple fusion a subtraction of two is required. Since three mutual pairs of sextets are involved, it seems most logical t o subtract 2/3 when each of these pairs is considered. The follcwing rules are then readily derived: Case I: When a pair of sextets is present in rings fused by means of two atoms of simple fusion, then a subtraction of 1 1 = 2 r-electrons must be made. Let this subtraction of two be symbolized by a simple line connecting the pair of circles representing the sextets in question. (This rule is equivalent t o the suggestion made earlier.) Case 2: When a pair of sextets is present in rings fused by means of one atom of simple fusion and one atom of triple fusion, a subtraction of 1 2/3 = 5/3 T-electrons must be made. Let this subtraction of 5/3 be symbolized by a wavy line connecting the pair of circles representing the sextets in question. Case 3: When a pair of sextets is present in rings fused by means of two atoms of triple fusion, a subtraction of 2/3 2/3 = 4/3 ?r-electrons must be made. Let this subtraction of 4/3 be symbolized by a broken line connecting the pair of circles representing the sextets in question.
+
The sextet formulatic n applies equally well to heterocyclic compounds. Examples are quinoline (XXI), indole (XXII), isoindole (XXIII), authranil (XXIV), benzfurazau (XXV), thiophthene (XXVI), the ''anhydronium bases" (2) (XXVI1)-(XXX) and condensed "mesoionic" compounds (21) like benzosydnoue (XXXI), not yet prepared. Curved arrows, as in (XXX) and (XXXI), signify mesomeric adjustments. More highly condensed polycycles with heteroatoms are, of course, representable in similar fashion as (XI1)(XIX).
+
+
Total number of n-electrons contained by sextets = (number of circles X 6) (number of simple connecting lines X 2) (number of wavy connecting lines X 5/31 (number of broken connecting lines X 4/3)
The method is illustrated by pyrene (XII), perylene (XIII), coronene (XIV), pyranthrene (XV), zethrenr (17) (XVI), acepleyadylene (18) (XVII), the perinaphthy1 radical (19, 20) (XVIII), perinaphthenone (1Hbenzouaphthen-l-one) (XIX) and 1,5-naphthoquinone (XX). The arrowheads in (XVII) for acepleyadylene have the same significance as has the arrowhead in (XI) for azulene. It will be noted that the number of r-electrons in the perinaphthyl radical (XVIII) is 13. Perinaphthenone (XIX) has a total of 14 R-electrons and is, of course, not a free radical. Similarly 1,5naphthoquinone (XX) with a total of 12 R-electrons is not a free radical. It is worth pointing out that any quinone is representable by a formula resembling (XX).
(XXIX)
Sldh
(XXXI)
Those fully conjugated polycyclic structures for which sextet formulations cannot be written are of special interest. As has been pointed out previously (8), neither pentalene (XXXII) nor heptalene (XXXIII) can be provided with sextets. (Only a t the sacrifice of making the two fused rings non-equivalent would it be possible to provide one of them with a sextet.) Attempts t o prepare pentalene or heptalene have not JOURNAL OF CHEMICAL EDUCATION
yet been successful and it appears unlikely that they would be endowed with appreciable aromatic stability (8). I n contrast thereto stands awlene, which, superficially, appears closely related to both pentalene and heptalene, but which is representable by the sextet formulation and is, in actual fact, clearly aromatic. It is also interesting that pleiadiene (XXXIV), whose seven-membered ring cannot be provided with a sextet, shows considerably less aromatic stability than acepleyadylene (XVII) (18). Furthermore, let it be noted that structures related to pentalene, such as s-indacene (XXXV), have still not been prepared (22, 93). (Here again one of the five-membered rings could be provided with a sextet only a t the sacrifice of making the two fivemembered rings non-equivalent.) The fact that a yet unknown polycyclic structure is not expressible or only partly expressible by the sextet formulation is, however, no reason for lack of vigor in the pursuit of its synthesis.
(XXXII)
(XXXIII)
(XXXIV)
compounds. It is not obvious from this formulation whether the ground state of a molecule representing a continuous aromatic =-electron system with an even number of =-electrons is diamagnetic (all electronic spins being coupled) or paramagnetic (biradical). From theoretical considerations it has been concluded that the number of unpaired electrons present in the ground state of any unsaturated hydrocarbon is a t least as great as the number of carbon atoms (if any) having a deficiency of valence bonds in any principal resonance structure (classical valence structure) (24). For example, while the sextet formulation of triangulene (XXXVI) appears perfectly normal, every one of its classical valence structures exhibits two carbon atoms with a deficiency of valence bonds (if one does not write bonds between non-adjacent atoms). I t is thus very likely that triangulene is a biradical in the ground state; this circumstance mayaccount for the factthat attempts to prepare triangulene have not yet been successful (24,251.
(XXXV)
This discussion cannot be complete without mentioning a shortcoming of the sestet formulation for aromatic
(XXXVI)
LITERATURE CITED (1) See COUL~ON, C. A., J. Chem. Soc., 1955,2076. J . Chem. Soc., 1925, 1604. (2) ARMIT,J. W., AND R. ROBINSON, E., L, (3) HBCKEL,E., 2.Physik, 70,204 (1931); see also H ~ ~ C K E "Gnm&.~imdw Tlworit, unges.t~~igtm und arwn~tt:sclwr Vwlindungm," V w I w C'hmie, lhrlin, 1938, pp. 71-8:. "The Structurr of \ I u r t r r , " I, I , RII:,:. t'. i).A\I, E. TELLER. .John Wiley & Sons, Inc., ~ e York, w 1949, pp. 104-11: W. YON E., AND L. H. KNOX,J . Am. Chem. Soc., (5) DOERINQ, 76. .. ,3202 --. .(1954) ....,. (6) LINDER,M. S., E. I. BECRER,AND P. E. SPEOREI,J . Am. Chem. Soe., 75, 5972 (1953). (7) BECKER,E. I., Abstr. of Am. Chem. Soc. Meeting, Sept. 12-17, 1954, p. 9. (Div. of Organic Chem.) (8) TODD,A. (editor), "Perspectives in Organic Chemistry," Interscience Publishers. h e . . New Yark. 1956. cha~terbv oft the'con&t i f WILSONBARERon he ~ e v e l a ~ m e n Aromaticity, pp. 28-67. (9) WHEMND,G. W., AND D . E. MANN,J . Chem. Phys., 17,264 (1444) ,A"-",. (10) ANDERSON, A. G., JR.,AND A. J. NELSON, J . Am. Chem. Soc., 72, 3824 (1950). (11) ANDERSON, A. G., JR., A. J. NELSONAND J. J. TAZUMA, J . Am. Chem. Soc., 75, 4980 (1953).
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(12) ANDERSON, A. G., JR., E. J. COWLES, J. J. TAZUMA, AND J. A . NELSON, J. Am. Chem. Soc., 77, 6321 (1955). W. L., D. H. REID, AND W. H. STANFORD, (13) GALLOWAY, Chem. & Ind., 1954, 724. P. A,, E. HEILBRONNER, AND S. WEBER,Helo. (14) PLATTNER, Chim. Acta, 35, 1036 (1952). E.. AND M. SIMONETTA. H e b . Chim. Acta. 35.. (151. HEIIBRONNER. 1049 (1952): ' (16) HAPNER, K., AND H. WELDES, Angew. Chem., 67,302 (1955). Chem. B ~ T . , (17) CLAR,E., K. F. LANQ,AND H. SCHULZ-KIESOW, 88, 1520 (1955). V., AND G. K. VICK,J . Am. Chem. Sac., 78, (18) BOEKELHEIDE, 653 (1956). (19) REID,D. H., Chem. & Ind., 1956, 1504. P. B., M. N A R A Z A AND K ~ M.CALVIN, J . Chem. Phys., (20) SOGO, 26, 1343 (1957). 1211 See BAKER.W.. AND W. D. OLLIS.Chem. & Ind.. 1955.910: . , d m BIEBER,'T. I., Chem. & ~ n d . 1955, , 1055: R. D., J. Chem. Soe., 1951, 2391. (22) BROWN, (23) CRAIG,D . P., J. Chem. Soe., 1951, 3175. H. C., J . Chem. Phys., 18, 265 (1950). (24) LONQUET-HlOQrNs, J. Am. Chem. Soc., 75,2667 (25) CLAR,E., AND D . G . STEWART,
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