The Stevens rearrangement: an antiaromatic pericyclic reaction?

摘要

1974 1839The Stevens Rearrangement : an Antiaromatic Pericyclic Reaction ?By Michael J. S. Dewar and Christopher A. Ramsden, Department of Chemistry, The University of Texasa t Austin, Austin, Texas 7871 2, U.S.A.The possibility that the Woodward-Hoffmann rules may break down quite generally for very exothermic reactions isdiscussed. MIND0/3 Calculations for a pericyclic mechanism for the Stevens rearrangement support this possi-bility. Although a concerted mechanism for the Stevens rearrangement is formally ‘ forbidden ’ according to theWoodward-Hoffmann rules, the calculated activation energy is extremely small (1 7 kJ mol-l). The calculatedstructure of a benzoyl-stabilized nitrogen ylide is reported and the electrostatic energy of the ylide is estimated.IN the classic article by Woodward and Hoffmann 1 onpericyclic reactions, the section headed ‘ Violations ’ intermediates.begins with the sentence ‘ There are none! ’.Wood-ward and Hoffmann suggest that reactions in whichorbital symmetry is not conserved cannot take placeterms of alternative mechanisms involving biradicalIn an alternative theory of pericyclic reactions whichwas first proposed by Evans,2 the facility of the re-actions depends on the resonance stabilization of thevia a concerted pericyclic mechanism and they explainin 2 (a) M. G. Evans and E. Warhurst, Tram. Favaday Soc.,1938, 34, 614; ( b ) M. G. Evans, ibid., 1939, 35, 824; (c) M. J . S. apparent Of ‘ forbidden ’R. B. Woodward and R. Hoffmann, ‘ The Conservation of Dewar, Chem. s’oc.Special Publ., No. 21, The Chemical Sosety,London, 1967; (d) Angew. Chew. Internat. Edn., 1971, 10. 761. Orbital Symmetry,’ Academic Press, New York, 19701840 J.C.S. Perkin Icorresponding transition states. Reactions which followthe Woodward-Hoffmann rules have transition stateswhich are aromatic while reactions which violate therules have antiaromatic transition states. Reactions ofthe latter kind should have correspondingly highactivation energies and so occur correspondingly lessreadily; nevertheless they should be feasible and shouldindeed occur in cases where no better alternatives exist.This seems to be so in the ' forbidden ' electrocyclicconversion of Dewar benzene (1) into benzene (2) and ofthe bicyclopentene (3) into cyclopentadiene (4).Ineach case rearrangement via an intermediate biradical isruled out by steric considerations and MINDO/3calculations strongly suggest that both these reactions(I) ---t (2) and (3) + (4) do indeed involve con-certed antiaromatic pericyclic proce~ses.~The purpose of this paper is to point out an alternativeway in which the effects of antiaromaticity may beevaded, thus leading to the possibility of true pericyclicreactions violating the Woodward-Hoff mann rules.A pericyclic reaction involves a cyclic permutation ofbonds around a ring of atoms, the process being analogousto the conversion of one Kekul6 structure for a cyclicpolyene into the other, i.e. :The intermediate phases of such a reaction can thus berepresented by superpositions or hybrids of the initialand final structures.The resulting resonance energywill then be positive or negative, depending on whetherthe system in question is aromatic or antiaromatic, andthe magnitude of this resonance energy will be greater,the more evenly the structures are mixed. The effectsof aromaticity or antiaromaticity will therefore begreatest at a point midway between reactant andproduct.Now according to the Bell-Evans-Polanyi (BEP)P r i n ~ i p l e , ~ ~ the more exothermic a reaction, the lowerin general will be its activation energy and the nearerthe transition state will be to the reactants in structure.In the case of a very exothermic pericyclic reaction, theeffects of aromaticity and antiaromaticity on theAT.J . S. Dewar and S. Kirschner, unpublished work.See M. J. S. Dewar, 'The Molecular Orbital Theory of5 G. S. Hammond, J . Amer. Chern. SOC., 1956, 77, 334.M. J. S. Dewar, Discuss. Faraday SOC., 1947, 2, 261. ' (a) T. S. Stevens, Progr. Org. Chem., 1968, 7 , 48; (b) A. R.Lepley and A. G. Giumanini, ' Mechanisms of Molecular Migra-tions,' ed. B. S. Thyagarajan, Wiley, New York, 1971, vol. 3,p. 297.Organic Chemistry,' McGraw-Hill, New York, 1969.transition state should then be small because it will haveonly a small contribution from the product structure.The distinction between aromatic and antiaromaticpericyclic reactions should therefore diminish as thereactions become increasingly exothermic. Since, more-over, a very exothermic reaction should, according tothe BEP principle, have a correspondingly low activationenergy, one might expect very exothermic antiaromaticpericyclic reactions to occur quite readily.This thenwould represent an area where the Woodward-Hoffmannrules might break down quite generally.An interesting possible example of this kind is pro-vided by the Stevens rearrangement of nitrogen ylides(9) to tertiary amines (lo).' This reaction violates theWoodward-Hoffmann rules and if it were concerted,the corresponding pericyclic transition state (1 1) wouldbe isoconjugate with the cyclopropenyl anion (12) andso be antiaromatic. The reaction should also be veryexothermic because it involves a large decrease incharge separation and a corresponding large decreaseR R RA * Rqc -y- Me3N + - - CH,Me2N - C H2Me(15)in coulombic energy.Moreover, a reasonable alter-native non-concerted reaction path is available, byfission to a pair of radicals (13) which can recombine to(ll), and a number of experimental studies have beenrecently reported in which attempts were made todistinguish between these two mechanisms.Until recently no theoretical procedures were availablethat could give meaningful predictions for such a re-action. Ab ivtitio SCF MO methods, apart from doubtsconcerning their accuracy, would be far too expensivewhile all the available semiempirical methods wouldhave been suspect due to their tendency to overestimatethe stabilities of small rings. Recently, however, animproved version (MIND0/3) * of the MIND0 semi-empirical SCF MO method has been developed in theselaboratories which seems to avoid the systematic errorsinherent in MIND0/2 and MIND0/2'.1° Here wereport its application to the simplest known Stevensrearrangement, that of trimethylammonium methylide(14) to dimethylethylamine (15).In view of the current8 R. C. Bingham, I. J. S. Dewar, and D. H. Lo, unpublishedwork.S (a) M. J . S. Dewar and E. Haselbach, J . Amer. Chem. Soc.,1970, 92, 590; (b) N. Bodor, M. J. S. Dewar, A. Harget, and E.Haselbach, ibid., p. 3854.10 N. Bodor, M. J. S. Dewar, and D. H. Lo, J . Amer. Chem.SOC., 1972, 94, 53031974interest in ylides, we have also carried out calculationsfor a benzoyl derivative of (14).HL-C A w C! kH7 HeReaction co-ordinate : 8Symmetry conditions during optimization1 7 = 1 82 9 = 2 1 010 11 = 10 12 = 10 13 = 9 14 = 9 15 = 9 162 1 8 = 2 1 79 2 1 = 102 111 10 2 = 12 10 2 = 13 1 0 2 = 14 9 2 = 15 9 2 = 16 9 2- - - - - - - 7FIGURE 1 Reaction co-ordinate and symmetry conditions forthe Stevens rearrangement of trimethylammonium methylideto ethyldimethylamineTheoretical Procedztre.-The calculations were carriedout by the MINDO/3 procedure,8 details of which areStructure(a) Trimethylammonium methylideHC(b) Dimethylethylamine,H5HtC3-H6I1841the same value for an atom in a molecule as for thecorresponding free atom but rather is treated as aparameter and different values are used for 2s and 29AO’s.The 2 ’ s appear only in the calculations ofoverlap integrals, used in the Mulliken approximationfor the one-electron core resonance integrals.The geometries were calculated in all cases by mini-mizing the total energy, using the SIMPLEX method.In order to reduce the amount of computation in thecase of (14), symmetry conditions were assumed asindicated in Figure 1. The conversion of (14) into (15)was studied by using the H,C-N-CH, angle 8 (seeFigure 1) as reaction co-ordinate. For each value of 8 ,the energy was minimized with respect to all the otherco-ordinates, subject to the assumed symmetry con-ditions.RESULTSThe calculated geometries and heats of formation of (14)and (15) are shown in Figures 2a and b. The reaction ispredicted to be very exothermic (AH -363 kJ mol-l).Figure 3 shows a plot of the energy as a function of thereaction co-ordinate 0 (see Figure 1).This should corre-spond to the concerted conversion of (14) into (15) since thesingle determinant description used in MINDO/3 greatlyoverestimates bond dissociation energies and so cannot beBond length (A)- 12 = 1.471; B = 1.47934 = 1.115; 35 = 1-116B = 1-115; 17 =18 = 1.133T9 = T O = 1.499-AHf, 415.0 kJ mol-1- - 12 = 1.435; 13 = 1.49917 -18 = 1.130- 34 = 1.112; = 1.11236 = 1.112;29 = T O = 1.415cIAH,, 52.2 kJ mol-l- 12 = 1.452; 2 = 1.50334 = 1.138: 35 = 1.119 -Bond angles (”) Dihedral angles (”) *- - 1234 = 179.01235 = 59-11236 = 298.93218 = ‘ZB = 126.5 ZFZ = 10213 = 119.0- 123 = 105.1234 = 114.2EE = 113.1236 = 113.1217 = 218 = 109.8E 9 = 121O = 113.8-- 213 = 118.8134 = 117.0135 = 112.6- - - 136 = 112.6217 = 218 = 109.81T= 121O= 119.6123 = 80.0234 = 105.2 - - - ZE = 1.119; 235 = 119.029 = 310 = 1.489 236 = 119.717 = 18 = 1.128 - - - - 217 = 218 = 114.1129 = T E O = 117.1 -- - 1234 = 178.91235 = 67-4 - 1236 = 290.33218 = 7123 = 122-5 - - - 3129 = 10213 = 115.4(c) Transition state* Dihedral angle ijkl is defined as the angular displacement of the distance relative to the one measured anticlockwise alongthe direction j __t k .FIGURE 2 Calculated geometries (a) of (14); (b) of (15); and (c) of the pericyclic transition state for conversion of (14) into (15).being published elsewhere. This differs from the used to follow such processes e.g.(14) + Me,NCH,* +original version of MIND0/2 9 only in two respects. The reaction was followed in both directions, the C-H,.First, the one-centre integrals are estimated by aeffective nuclear charge (2) is no longer assumed to have11 (a) L. Oleari, L. Di Sipio, and G. De Michelis, Mol. Phys.,modification Of Oleari” method; l1 the 1966, 10, 97; (b) M. J. S. Dewar and D. H. Lo, J . Amer. Chem.SOC., 1972, 94, 52961842 J.C.S. Perkin Iforward and backward paths being identical. This suggeststhat 8 is a satisfactory reaction co-ordinate.12 The con-version of (14) into (15) is predicted to have a very lowactivation energy (17 kJ mol-l); the structure of thetransition state is shown in Figure 2c.1300 -cI E2 200-a100 -OllO d o 9b sb 70 6b 5b Lo 3b 20eldegreesFIGURE 3 Plot of the calculated heat of formation (AH) againstthe reaction co-ordinate 8 (Figure 1) for the pericyclic conver-sion of (14) into (15)5.04 ~ 0n' j 3 c Ed0 P6- 2.01 cc-- Transition state I l l0 100 90 80 70 60 50 40 30 20a /degreesFIGURE 4 Plot of the calculated dipole moment (p) us.0 for theThe arrow indicates the pericyclic conversion of (14) into (1 5).position of the transition stateFigure 4 shows the variation of dipole moment (p) duringthe reaction as a function of the reaction co-ordinate 0.The arrow indicates the position of the transition state.l2 M. J. S. Dewar and S. Kirschner, J . Amev. Chem.SOC., 1971,93, 4290, 4291, 4292.l3 U. Schollkopf, U. Ludwig, G. Ostermann, and 31. Patsch,Tetrahedron Letters, 1969, 3415.DISCUSSIOXThe results reported above obviously provide strongsupport for the suggestion that antiaromatic pericyclicreactions may occur very readily if they are sufficientlyexothermic. The calculated activation energy for con-version of (14) into (15) in the gas phase is extremelysmall (17 kJ mol-l) although this is an antiaromaticprocess violating the Woodward-Hoffmann rules.l7hile the Stevens rearrangement was chosen simplyas a convenient example of an extremely exothermicreaction that could take place by an antiaromaticpericyclic pathway, it is also of interest in view ofcurrent controversy concerning its mechanism.Theobservation of the CIDNP effect during a number ofStevens rearrangements has led to the suggestion thatthe reactions may not in fact be pericyclic but takeplace by fission to an intermediate pair of radicals(S) (13) which then recombine inside a solventcage.13914 This evidence certainly shows that at leastsome of the product must have been formed by re-combination of radicals but does not establish this asthe main reaction path. The CIDNP effect is sosensitive that large signals can be obtained in caseswhere only a few percent of product are formed viaradicals.The calculations reported here suggest that theStevens rearrangement may very well take place by aconcerted pericyclic path but does not allow a distinctionbetween this and the radical pair mechanism.In thecase of (14), MINDO/3 predicts dissociation to radicals(Me,NCH,* + CH,) to be exothermic (AH, - 42 kJmol-l). In the gas phase (14) should then dissociatewithout activation. In practice, however, the Stevensrearrangement is carried out in polar solvents where theheat of solvation of the zwitterionic ylide may well be125-175 kJ mol-l. Most of this solvation energy willbe lost on forming the pair of weakly polar rzdicals andthe energy required for their formation will be corre-spondingly increased. On the other hand the transitionstate for the pericyclic reaction, while less polar than theylide, should still be strongly polar since it should benearer to the reactant ylide than to the product instructure.The increase in activation energy on passingfrom the gas phase to a polar solvent should then bemuch less than that for fission to radicals. Our calcu-lations do indeed indicate that the transition state forthe conversion of (14) into (15) (see Figure 2) is muchcloser to (14) than to (15) in structure and Figure 4shows that its calculated dipole moment (2-5 D), whileless than that of (14) (4.0 D), is still large. The peri-cyclic path could therefore very well be favoured for thereaction of (14) in polar solvents.Little is known concerning the conversion of (14)into (15). Wittig and Polster reported the preparationof (14) by treating tetramethylammonium bromide withphenyl-1ithi~m.l~ The product was, however, isolated14 R.W. Jemison, S. Mageswaran, W. D. Ollis, S. E. Potter,A. J . Pretty, I. 0. Sutherland, and Y. Thebtaranonth, Chem.Comm., 1970, 1201.15 G. Wittig and R. Polster, Anitale??, 1956, 599, 1 1974 1843as a complex with lithium bromide and may have beenan alkyl-lithium derivative, LiCH,NMe,Br-. When amixture of phenyl-lithium and phenylsodium was used,the ylide decomposed giving (15) in 49 yield.l6 In astudy of the decomposition of tetramethylammoniumfluoride by potassium amide, Musker found that (15) wasformed in 5-10 yie1d.l'The majorit!. of Stevens rearrangements reported inthe literature have involved ylides stabilized by +Esubstituents, usually acyl. We have not studied such aprocess because the molecules in question are ratherlarge and the cost of following their rearrangements bythe SIMPLEX method would be excessive.It has beenreported that Stevens rearrangement of the ylide (16)to (17) in chloroform takes place with 95 retention ofconfiguration.18 The high degree of stereospecificitycertainly seems to suggest that at least a large part ofthe reaction may have taken place by the pericyclicroute.+H Ph I + IMe Me2N- CH - COPhPh - C- N Me2- CH COPh Me- C- HI I(16) (17)'CH co P h ' c HCOPh( 1 8 ) (19)The bonding in nitrogen ylides is of interest in view ofthe large separation of charge in them and because thestructures of the stable ylides (l8) and (19) haverecently been determined by X-ray crysta110graphy.l~For comparison we have calculated the structure of thebenzoyl derivative (20) of (14).The calculated structureis shown in Figure 5 together with the measured lengthsof corresponding bonds in (18) and (19). In order toreduce the amount of computation, the benzene ring in(20) was assumed to have the structure calculated(MIND0/3) for benzene. Note that the predictedlength of the CH-CO bond in (20) is much greater, andthat of the C-0 bond much less, than the measuredlength of corresponding bonds in (18) or (19). Evidentlythe negative charge is much more strongly localized onthe ylide CH in our calculated structure than in (18)or (19), the latter approximating closely to enolates(EN-CH=C-0). Likewise we predict the N-C bond tobe shorter in (20) than the corresponding bonds in (18)or (19), as would be expected if the carbon atom carries+.I - f -l6 G. Wittig and D. Krauss, Annale?z, 1964, 679, 34.l7 W. I<. Musker, J . Org. Chem., 1967, 32, 3189.l8 J. H. Brcwster and 31. W. Kline, J . Amer. Chem. SOC., 1952,74, 5179.a large negative charge. Our calculations of courserefer to an isolated molecule in the gas phase where theE? = 1.467 (1.48; 1.47)23 = 1.417 (1.36; 1.34)S = 1.234 (1.27; 1.30) = 1.543 (1.52; 1-51)-25 = 1.109- 123 = 129.2 (119.0; 123.0)234 - = 123.0523 = 121.5 - 1234 = 0.15234 = 180.0 -FIGURE 5 Calculated bond lengths (z) (A) and bond angles ( r 7 )(") in (20). The first value in parentheses is the observed valuefor the corresponding bond or angle in (18), the second for thatin (19)energy of the enolate structure would be increased bythe large separation of charge in it (cf.EN-CH- with=N-CH=C-0). The ylide molecules in a crystal of ylideare in a highly polar environment where the effect ofcharge separation must be much less than in the gasphase.A rough estimate of the electrostatic energy due tocharge separation can be made by considering thechange in energy when an ylide is formed by union of anammonium ion with an anion :f -- + I -- f - -H + H-C< + -N-C< + H,The change in energy (AE) can be written in terms ofbond energies (EX=) and the electrostatic energy (E+) :(1)AE = E N H + ECH - ECN - E H H + E+- ( 2 )If bond energies followed an arithmetic mean rule, thebond energy of an XY bond being the mean of the bondenergies of XX and YY, the bond energy term ( E N H +EcH - E O N - E m ) in equation (2) would vanish.Itsactual value can therefore be estimated by usingPauling's rule 2o for deviations from the arithmeticmean, i.e.E~~ = o . ~ ( E ~ ~ +- E ~ ~ ) + (ax - ap)2 (3)where ax and ap are the electronegativities of X and Y.Using the electronegativity values suggested by Jolly,21we estimate the value of the bond energy term inequation (2) to be cn. 0.25 eV.l9 N. A. Bailey, S. E. Hull, G. F. Kersting, and J . Morrison,2o L. Pauling, ' The Nature of the Chemical Bond,' 3rd edn.21 W. L. Jolly, J . -4mer. Chem. SOG., 1970, 92, 3260.Chem. Comm., 1971, 1429.Cornell University Press, Ithaca, New York, 19601844 J.C.S. Perkin IThe Table shows total energies for the various speciesUsing these and equations calculated using MIND0/3.Total energies of various species calculated by MINDO/3Species +Me,N-HCH,-PhCOCH,H 2Me,N-CH+ -Electronicenergy (eV)- 712.87- 168.59- 1427.87- 31.72- 858.01Me,HCOPh -2115.11(2) and (3) we arrive at the following estimates of theelectrostatic energies E+- in (14) and (20) : (14) E+- =8-0 eV (770 kJ mol-l), (20) E+- = 6.1 eV (590 kJ mol-l).The electrostatic energies are both very large and thatfor (20) is significantly less than that for (14). Onewould of course expect the electrostatic energies to belarge since both compounds, according to simple valencetheory, are zwitterionic. One would also expect theelectrostatic energy to be less for (20) than for (14)because in (20) the negative charge is dispersed over theenolate system. The mean distance between thepositive and negative charges is consequently greaterthan it is in (14) and the electrostatic energy (-e2/r)correspondingly less.This work was supported by the Air Force Office ofScientific Research and by the Robert A. Welch Foundation.3/1671 Received, 7th August, 1973