Energias Pi Aroma Ti Cos

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2413Organic and Biological ChemistryHuckel Molecular Orbital Resonance Energies.The Benzenoid H ydrocarbons5. Andes Hess, Jr.,* and L. J. Schaad*Contribution fr om the Department of Chem istry, Vanderbilt Un iversity,NashviIle, Tennessee 37203. Received October 9 , 1970

Abstract: The HMO esonance energy per x electron (REPE) has been calculated for 40 benzenoid hydrocarbons.Compounds with an REPE of greater than 0.050/3 are found to be extremely stable. Compounds with an REPEof less than 0.050p are found to be of increasing reactivity (e ,g . ,in their ability to undergo additionreactions) as theREPE decreases, An excellent correlation is found between the REPE and the p band of the 40 ompounds.

e have recently shown that the well-knownfailure of Huckel calculations to predict arom aticor antiarom atic character in hydro carbons is due not toa fault of the Huckel wave functions, but instead to anerroneous identification of various delocalizationenergies with aromaticity. If resonance energy per z-electron (REPE) is defined as the difference betweenthe Hiickel T energy and the x energy of a localizedstructure obtained in an additive manner using theempirical x bond energies listed in Table I, divided byTable I.Double and Single BondsEmpirical T Bond Energies of Carbon-Carbon

C H F C HC H = C HC H F CC H = Cc=cCH-CHCH-Cc-c

23 2.oooo22 2.069922 2.oooo21 2.108320 2.171612 0.466011 0.436210 0.4358

the number of T electrons, a quantity is obtained thatcorrelate s well with experim ental stability. We pre-sent here the application of this method to a widevariety of totally benzenoid h ydrocarbons.Results and Discussion

I t is known that the linear annelation of unsaturatedsix-membered rings (the polyacenes) yields a series ofhydrocarbons that show decreasing s tability as thenumber of rings is increased.2 Benzene is an extraor-dinarily stable compound, whereas pentacene is veryreactive. On the other han d, angular annelation ofunsaturated six-membered rings leads to hydrocarbonswhich are much more s table than their l inear analogs;e .g . , picene ( 20 ) is considerably less reactive thanpentacene (15). The RE PE for the f irst eleven membersof the polyacene series and nine members of the phen-

(1) B . A . Hess, Jr., and L. J. Schaad, J . Amer. Chem. Soc., 93,305(2) E. lar, Polycyclic Hydrocarbons, Academic Press, New York,(1971).N. Y.,964.

anthrene, chrysene, picene series is plotted against thenumber of rings in Figure 1. The R EPE of the linearpolyacenes falls off quite sharply initially, whereas theTable 11. Hiickel MO Data for Compounds 1-40

REPE 8 x Dewars energy perx 103 io-*,- homo REPE,b A electronDeloc

Compd ( p ) cm-1 (P I eV (P I12345678910111213141516171819202122232425262128293031323334353637383940

655 56047555142505353564853493845515149535252514545454953414246514748434238444740

480351400267342300212278313317352230302231722212862852743043123042582321819923029182181238266246225165151171189212157

1.0000.6180.7040.4140.6050.4450.2950.4520.5200.5680.6840.3470.4970.3710.2200.3270.4730.4920.4050.5020.5500.5350.4390.2910.3030.2650.3510.5390.1990.2440.3480.4470.2960.2850.1940.1770.1280.2690,3940.194

0.1450.1320.1420.1140.1380.1310.1010.1270.1380.1380.1470.1310.1420.1290 0910.1340.1340,1400.1400.1400.1420.121

0.1470.112

0.3330.3680.3650.3800.3890.4070.3850.3940.4000.3990.4040.4120.4170.4110.3880.3910.4040.4040.4020.4060.4060 4060.4280.4210.4110.4130.4170.4410.4080.3980.4030.4100.4250.4270.4140.4310.4070.4050.4080.409

From ref 2. From M. J. S. Dewar and C. de Llano, J . Amer.Chem. Soc., 91, 89 (1969); C. R. e Llano, Ph.D. Thesis, Uni-versity of Texas, 1968.Hem, Schaad 1 Benzenoid Hydrocarbo ns


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O O O O Ou4 6 8 1 0number of ringsFigure 1 . R E P E ( p ) US. the number of six-membered rings inpolyacenes (0 ) and in the series phenanthrene, chrysene, picene,, (A).4 50 .

3 5 L200 - 300 4003 (sm-1) x 10-2Figure 2, REPE (8) VS , p band frequency (cm-1) for compounds1-40, The least squares line has standard deviation 20 x 10*cm-'.

REPE of the angular series decreases to a much lesserextent with increase in the number of rings which isin agreement with the above observations regardingtheir stability.The REPE along with addit ional data (see below) isgiven in Table I1 fo r 40 benzenoid hydrocarbons.There i s an excellent correlation between the reactivityof these hydrocarbons and their resonance energies.Compo unds wi th an R EP E grea te r than O.OSOp, e.g.,benzene, naphthalene, phenanthrene, and triphenylene,generally do not undergo addition reactions withmaleic anhydride and d o not readily undergo ph oto-oxida t ion. Those compounds wi th an R EP E lessthan 0.050/3 appear to undergo ad dit ion reactionsand photooxidation with increasing ease as the REPEdecreases. 1,2-Benzanthracene (8) ha s a n RE PE of0.050p and undergoes addit ion with maleic anhydrideonly with great difficulty.2 Zeth rene with an RE PEof 0.041p reacts with maleic anhydride immediately atroom temperature. *One might wonder why pentacene is so reactivealthough i t st i l l appears to have substantial REPE(0.038p). Its reactivity is easily explained when oneconsiders that i t undergoes addit ion reactions at the 6and 13 posit ions, e . g . , its addition reaction with maleicanhydride, to yield a 6,13-dihydropentacene derivativewhich now contains two naphthalen e moieties. Th eformation of two new cr bonds in addi t ion to the in-

n0r50

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.40

0.2 0.4 0.6I.8 !I1.0h,moFigure 3 . R E P E (0) us. energy of th e HOMO ( p ) for compounds1-40. Th e least squares line is shown.

I I I J0 020 0 - 300 400g(cm-1) x

Figure 4, SC F M O resonance energy per P electron (e") us .p band frequency (cm-*). The least squares line has standard de-viation 47 x 1 0 8 cm-'.creased REPE (0.055p) of the remaining IT electrons ismore than enough to offset the loss of tw o a bonds .Clar has noted that the mo re highly colored a benze-noid hy dro carb on, the less stable it generally is.* Heascribes this relationship to a bathochromic shift of th ep ba nd as the stability decreases. We therefore plottedR E P E us . the p band of compounds 1-40 (Figure 2) .A good linear relation is found . Th e p band is due toan electronic transition from the highest occupiedmolecular orbital (HOMO) to the lowest empty mo-lecular orbital (LEMO). For a l te rnant hydrocarbonsthe energy of the HOMO is the negative of that of th eL E M 0. 3 T he f re quency of the p band and thereforethe RE PE should then be propor t iona l to the energy ofth e HOMO. Figure 3 shows that this expected relationdoes hold. We do not totally understand why thereshould be this connection between the REPE andHOMO (and therefore the REPE-p band relationship).W ork is currently under way to determine th e basis forthe relationship.We have also examined Dewar's semiempirical SC FMO resonance energies computed by the Pariser-Parrmethod to see whether they correlate with stabilityas well as do the Hiickel REPE. A plot of Dewar'sresonance energy per a electron us. p band frequencywas made for a number of benzenoid hy drocarbo ns forw hic h da t a w er e a ~ a i l a b l e . ~t is apparent f rom Figure

(3) C.A. Coulson and G. S . Rushbrooke, Proc. Cambridge Phil.SOC.,36. 193 (1940).-- ,-(4) (a) M. J. S. Dewar and C. de Llano, J . Am er . Ch em . S O ~ . ,1,789 (1969); (b ) see Table 11, footnote b .Journal of the A merican Chem icalSociety / 93 :IO / M ay 19,1971


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2415

26 27 28

4 that the correlation is not as good as the HM OREPE-p band correlation. In light of the failure ofth e SCF M O resonance energies to give a good cor re-

12 131

14 15 n

23 24 25

290 41 32@@&3 34 35E&6 37

38 39

40lation with the p band of the benzenoid hydrocarbonsand the very low SC F M O resonance energy for thenonalternate hydrocarb on azulene, we feel that theeasily obtained HMO resonance energies appear to bemore satisfactory than d o Dewar 's SC F M O resonanceenergies.Finally, the delocalization energy of compounds1-40 was computed in th e usual way as E , - 2np, wheren is the numbe r of do uble bo nds in th e localized struc-ture. Plotting delocalization energy per ?r electronus. p band frequency (Figure 5 ) shows again that de-localization energy is not useful in predicting therelative stability of benzenoid hyd roca rbon s.In summary, we believe that HMO R E P E of ben-zenoid hydrocarbons has a def inite quanti tat ive corre-

Hess, Schaad 1 Benzenoid Hydrocarbo ns


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2416 46 t 034t 0 1

200 - 300 4003 (1 x IO-Figure 5 .band frequeiicy (cm-l) for compoun ds 1-40.H M O delocalization energy per T electron ( p ) us . p

lation with the stability of these compounds. Theformer treatment of HM O results (Le., delocalizationenergies) did not allow either qualitative or quantitativecorrelations of the types discussed above,Computational Details, H M O resonance energiesper P electron were obtained as previously described.In each case, the additive ?r energy used in th e resonanceenergy calculation was an average of individual additiveP energies of all possible resonance forms, For thelarger molecules the determination of all resonanceform s proved t o be a difficult and tedious ta sk. Acomputer program was written which, when given theordinary H M O matrix, allowed the determination ofnot only all possible resonance forms, but also of thedifferent kinds of bonds in each resonance form.In no case were the additive energies of resonancestructures of the sam e com pou nd significantly different.For example, coronene has 20 resonance s tructureswhich range from a low of 33.2986 to a high of 33.311/3in additive ?r energy. These values corre spon d toREPEs respectively of 0.053078 and 0.05258,Description of Resonance Form Computer Program.Embodied in the HMO matrix is the informationneeded to determine all resonance forms as well as thenumber of each type of bond in each resonance struc-ture. Eac h nonzero off-diagonal element (ij) repre-sents a carbon-carbon bon d. For a given resonancestructure some of these elements will represent doublebonds a nd the remainder s ingle bonds. A second ma-trix was constructed f or each resonance struct ure by re-placing each nonzero off-diagonal element in the orig-inal HM O matrix by either a 1 to indicate a single bo ndor a 2 for a double. To determine all resonance struc-tures one has merely to determine all possible ways ofconstructing this matrix. Thi s may be done in asystematic manner by assigning the first nonzero off-diagonal element in the first row to a double bond.The symmetrically placed element in the first column

which corresponds to this bond is also noted as adouble bond. One then proceeds to the next row andin a s imilar m anner begins to the r ight of the diago nalin search of a bond (a non zero element). If this rowalready contains a bond that has been assigned a doublebond ( i . e . , to the left of the diagonal), one proceeds tothe next ro w (again beginning to the right of thediagonal) , as each carbon at om may have only onedou ble bond . Furth erm ore, if a nonzero element isfound which is in a column that already has a doublebond, it is left as a single bond and one proceeds insearc h of the next nonze ro element.If a bond is assigned as a double bond which cannotbe a double bond, fo r example, the central bond ofbutadiene, a point will be reached in the matrix wherea readily recognizable impossibility arises. Fo r ex-ample, a row which contains no double bonds will befound (every carbon atom must have one and only onedou ble bond in a conjugated system). If this happens,one proceeds in a reverse manner through the matrixuntil this error is found (see below). If one has notassigned an y double bonds incorrectly, one c an proceedas above to the last row and obtain a matrix repre-senting on e possible resonance structure. To obtainanother possible resonance structure, one starts in thepenultimate row of the above matrix (with the doublebonds previously noted) at the r ight hand side andproceeds to the left along the row (only to th e diagonal)in search of a previously noted double bond (if none isfound in a row t o the r ight of the diagonal, one goes tothe row above). When a double bond is found it ischanged to a single bond (along with the correspondingelement in the lower left triangle) and another bond issearched for to the right of this bond on the same row.If one is found, then it is assigned a double bond (ifpossible) and one proceeds to finish the matrix asabove and obtain anot her resonance structure. If noother bonds are found on that row, then one proceedsto the far r ight of the row above and searches to theleft (only up to the diagonal) for a double bond. Whenon e is found, the procedure is the same as above,One continues this reverse process after each reso-nance s tructure is found until eventually all matricescorresponding to all resonance structures are found.All have been found when one reaches in the reverseprocess the top row and finds that there are no moreelements in that row which can be assigned doublebonds.One uses these matrices to determine the number ofeach type of bond , Th e number of carbon atomsbonded to carbon atom i of the ij bond can be found bydetermining the number of nonzero elements in the ithrow excluding the one representing the ij bond. Sim-ilarly, the number of carbon atoms attached to thecarbon j of the i j bond is found by looking at co lum nj.With the T bond energies in Table I one may then obtainthe additive bond energy.

Journal of the American ChemicalSociety 1 93 :IO May 19,1971

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Energias Pi Aroma Ti Cos