Structure-Resonance Theory for Pericyclic Transition States William C. Herndon Universitv of Texas at El Paso. El Paso, TX 79968 Theoretical quantum mechanical principles are introduced advantageously in the organic chemistry curriculum during discussions of three topics. These are the concept of aromaticity, suhstitution reactions in aromatic compounds, and the stereochemistrv. of . oericvlic . reactions. Aromaticity and aromatic substitution have long been accorded an essential status in elementarv . oreanic chemistw texthooks, and more recently pericyclic reactions have come to be discussed as a separate fundamental class of organic transformations. The aromaticity concept is usually developed by reference to the stahilizing effect of resonance among valence hond structures (1-3). This concept can be extended and brought into better agreement with experimental facts if stahilizing nromatir resonance interactions are limited to those involvine ~~-~ cyclic conjugation of odd numbers of pairs of electrons ( 4 ) . Benzenoid systems possess conjugated circuits (5) of 4n + 2 (n integer) n orbitals, giving an odd number of electron pairs, and they are resonance stabilized. The cyclic conjugation of even numhers of pairs of electrons (e.g., the T system of cyclohutadiene) is destabilizing and leads to properties characterized by the term antiaromatic (6, 7). A strncture-resonance theow using these ideas has been tested ( 8 , 9 )and gives calculated rksonance energies that correlate precisely with the results of LCAO-MO-SCF calculations. The rates of aromatic substitution reactions also can be easily rationalized using structure-resonance theory. For examnle. - ~ - - ~ in electronhilic substitution. the reaction intermediate is assumed to be8. carbonium ion (the Wheland intermediate (10)) . .. for which several resonance structures can be drawn. The relative assigned stabilities of resonance hybrid intermediates are presumed to eovern relative rates of reaction. In support of this presump&n, one finds that calculated relativeresonance energies of Wheland-type intermediates generated from benzenoid polycyclic hydrocarbons are in excellent quantitative agreement with electrophilic substitution partial rate factors (II ). It is not surprising that a fundamentally different approach ~~~
~
~
.~~. ~~~
-.
(18, 19) cointerparts of the Woodward-Hoffmann rules, which will he briefly outlined in the next section, a simple .
.
resonance theory simply involves choosing the appropriate transition state valence model and the counting of resonance structures. It is, therefore, suitable for presentation in elementary courses. Aromaticity Rules for Pericyclic Transition States It will be assumed that the reader is conversant with the
- -
able foibackground material. Examples of allowed pericyclic reactions are the conrotatory cyclobutene butadiene and the disrotatory cyclopropyl cation ally1 cation electrolytic reversions, the Diels-Alder cycloaddition reaction, and the sigmatropic 1,6-hydrogen shift. T o avoid an abstract discussion, reactions of these types will he used to exemplify the theoretical procedures
u-< e
(conrotatory ring-opening) (disrotatory ring-opening)
+
e.+I1-0
(suprafacial, both components)
. .
molecular orbital correlation diagrams, they formulated rules which permit a distmction between those react~onsthat are
..
perturbation theory approach (15). However, imparting a comprehension of perturbational molecular orbital theory is probably appropriately postponed from elementary organic chemistry to later advanced courses. The purpose of this article is to show that structure-resonance theorv can be used to understand the effects of struc-
..
theory i;afforded. A limitation of the Woodward-Hoffmann rules is a general inapplicability to rationalizing or predicting the large effects of suhstituents or structural modifications on rates of thermal pericyclic reactions. Forhidden concerted processes could be expected to proceed with more difficulty than allowed reactions (14), or to occur by multi-step mechanisms (12,13), hut no other simple precept can he offered to the student. Of course, a number of approximate quantum mechanical theories of reactivity have been developed, and many have been applied to various aspects of pericyclic reactions. The most highly tested methods are those based on a molecular orhital
By definition, the transition state for each pericyclic reaction involves a conjugated circuit of orhitals. Two types of conjugated circuits may exist. If all basis orbitals overlap in phase, the conjugated circuit is of the Huckel-type, whereas a single phase dislocation in the overlap of the basis orbitals gives rise to an anti-Hiickel conjugated circuit (18, 19, 24, .25).1.2Hiickel systems with 4n + 2 electrons and anti-Hiickel systems with 4n electrons are aromatic, i.e., resonance stahilized by cyclic delocalization. Conversely, 4n Huckel systems and 4n + 2 anti-Huckel systems are resonance destabilized and anti-aromatic. The principle to he utilized is that thermal ' More genera ). . hucke canj..gatad circt!'ls cunU n an even nmber ano anti-rLc*e,con,*gatcd c rculls canlam an odd numuer of oro#tal pnase o slocatmons 1 l R , 19, 24 25) The simper uefm Inon .s sufl~c~ent for the analysis of most pericyclic reactions. Anti-Huckel systems have been termed Mobius systems in previous work ( 18, 19, 24). Dewar (257points out that no pericyclic transition state has yet been reported which has Mobius-type topology. Volume 58
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371
pericyclic reactions take place preferentially via the aromatic Hiickel or anti-Hiickel transition states (16). Disrotatory electrocyclic bond-breaking or bond-making always gives transition states with Huckel-type conjugated circuits, and the conrotatory processes lead to anti-Huckel type transition states. These processes are illustrated for cyclopropyl ion below.
The transition state for the cation rearrangement contains two pericyclic electrons, and the allowed mode of reaction is, bntadiene reartherefore, disrotatory. The cyclobutene rangement is a four-electron case, preferring an anti-Hiickel aromatic transition state which is formed with conrotatory sigma bond fission
-
For the student, attention should be foeused on the number of transition state ~ericvclic . . electrons, since this number always determines the type of preferred aromatic transition state, which in turn controls the geometry of the electrocyclic reaction mode. The number of basis orbitals may differ, but this is not the determining factor. As an example, five and six basis orbitals are respectively involved in the two electrocyclic cyclopentenyl anion and reactions, pentadienyl anion hexatriene cyclohexadiene. However, both reactions make use of six pericyclic electrons which requires a Huckel-type aromatic transition state, so the mode of electrocyclic ringclosure is predicted to be disrotatory.
-
-
+
The transition state for the Diels-Alder [2 41 cycloaddition reaction involves six pericyclic electrons, four from the diene moiety and two from tne dienophile. The Huckel-type aromatic transition state depicted below
372
Journal of Chemical Education
with nu phnnt d~iiawalionin the mcrlap ., hii i $.rl,it;~l* ~i requirnl. 'I he, ;tcrec,chemicnl ri; principle 1261tor L)~clc-.Alder re;wtit 11: i~ a c ~ m s t q w n 4c ~l h e Inmdin; w n ~ t r ~ l i 1~1n1 l~ p ~ ~ ~ 1 ~ 1 ~ 11). t h ~ rrqulrvnlent. s Anothvr nnpurtdllt aspevt d t h t r)~cI+l u,ht rvtwcoditterenr Alder r t : j ~ t i c e ~iaselectivt.reg~.~chemisrry orientations (e.g. ortho or meta) of suhstituents may result. This problem will he considered later from the point of view of structure-resonance theorv. The majority of sigmatropic rearrangements involve six nericvclic electrons and the transition state must he of the ~ i i c k t ~ to p ebe aromatic. A suprafacial 1,5-shift of hydrogen atom would then be allowed as shown below for cyclopentadiene.
The Cope rearrangement and the Claisen reaction are often cited (20-23) as examples of pericyclic six electron [3,3] sigmatropic shifts.
The use of the Cope rearrangement as a general example is probably no longer justified since the mechanism of the reaction seems to vary depending upon substitnent pattern (27, 28). Valence Models for Pericyclic Transition States The procedures of structure-resonance theory allow one to calculate the resonance energies of a wide variety of n-hydrocarhons (8,9,11,29), ions (11,30),and radicals (31,321. The results are quickly obtainable by simply counting structures (33, 34), and precise correlations with a variety of experimental properties have been established. To apply structure-resonance theory to pericyclic reactions, the primary assumption will be that the transition state can be modeled by the corresponding completely conjugated hydrocarbon n system. Then the calculated resonance energy of the model n system, or its structure count, will be a determinant of transition state stabilizing factors. An algorithm, the logarithm of the number of structures (In SC), is a very good approximation for determining resonance energies (11, 29-32). Actual relative rates of reaction would be controlled by relative differences in stabilities of ground states and transition states, proportional to the log of the structure count ratio (transition statelground state). Model n systems for transition states of disrotatory electrocylic reactions, all suprafacial cycloadditions, and suprafacial sigmatropic shifts are always Huckel-type n systems with all basis orbitals overlapping in phase. They will be represented by the same types of molecular graphs that are used to depict the analogous isoconjngate ground state n systems, but the models will be enclosed in braces (I)) to emphasize the distinction between the model systems and the actual transition states. As an example, the model n system
for the disrotatory ring opening of cyclopropyl cation is cyclopropenium cation n system.
An allowed pericyclic reaction utilizing six pericyclic electrons and six basis orbitals is obviously modeled hy the benzene n-system. The structure count (SC) for benzene is two, and benzene is stabilized by resonance. The stabilizing or destabilizing effects of substituents on henzene would then be expected to parallel transition state substituent effects in pericyclic reactions. However, it is likely that only a fraction of a particular ground state substituent effect would be manifested in a transition state. A crude model of this type can be justified only by comparisons with experimental data, and some appropriate examples will be given later. In the cases where the pericyclic transition state involves a basis orbital phase change, the corresponding anti-Huckel hydrocarbon n 'system serves as the model. For example, anti-Hiickel cyclobutadiene n system models the transition state for conrotatory ring-opening of cyclobutene.
Anti-Huckel cyclohutadiene is of course stabilized by resonance, SC = 2, in the same way that benzene is stabilized. Anti-Hiickel orbital networks actually exist in ground state complexes of the iron-tricarbonyl moiety with hydrocarbon ~r systems (32,35, 36), and one does find resonance stahilization associated with 4n delucalized electrons in these systems (36, 37). The convention of representing the orbital position a t which the phase change occurs by a heavy dot in the molecular graph has been adopted in the earlier work, and will also be used here.
Modeling the pericyclic transition state with the corresponding n hydrocarbon is not a new idea. Huckel molecular orbital calculations have previously been used in conjunction with these same models to interpret successfully many structural and steric effects in . uericvclic . reactions (38-40). The advantage of a structure-resonance theory approach is that essentiallv no comuutation is reauired and the results generally agree with those obtained in the previous work. An attemot will be made now to demonstrate this assertion with three examples.
-
Cyclobutene Ring Openings
The cyclobutene butadiene rearrangement has been the subject of many quantitative structure-reactivity investigations, summarized in review articles (40-42). The large amount of quantitative data is useful for testing theoretical formulisms (40), and for illustrating the applications of theory. As explained earlier, the cyclobutene electrocyclic ring opening is a conrotatory process that gives a four-orbital, four-electron pericyclic transition state modeled by antiHuckel cyclohutadiene n system. The SC changes from reactant SC = 1to transition state SC = 2. The SC ratio is 2 (transition statelreactant) and can he determined by simply drawing all of the resonable structures. Reasonable structures are those in which electrons are paired as far as possible, and in which n electron pair honds are allowed only between atoms that are adjacent in the molecular framework. Structures of this type have been called "principal resonance structures" (43). The term "KekulB Structures" delimits the principal resonance structures for neutral n hydrocarbons and could be used in this instance. The resonance structures for reactant 3-pbenylcyclobutene, and model transition state anti-Hackel phenylcyclobutadiene are depicted on the next page
Model n
Reactant
> a
Transition State
Product
Reactant State
Transition Stale SC
AH+ SC
~atio
kcal
(ExP~.)
ph) Ph
aData taken from reference
144 Volume 58
Number 5
Mav 1981
373
sc=1
SC=4
The SC for the reactant is taken to be the same as unsuhstituted cyclohutene, on the grounds that the phenyl substituent a orhitals are not effectively conjugated with the pericyclic orbitals in the reactant structure. However, the delocalized transition state is assumed to involve a conjugated phenyl substituent, giving an SC ratio = 4 for the ring-opening. Conseouentlv. should he more reactive .. 3-~henvlcvclohutene . . . than rvclobutenr. ('onvenely, ronjugating suhstitumts on the doul~lebond at thr I - or 2-puiirion should have littleeffect cm react1c.n rate since they dt, nt~taffect rhr SC r;~ti--D
SC ratio = 4.0
sc=1
SC = 4
Figure 1. Summary of
states.
SC's ot the aubstiMed cycl~ropylions and banslion
hut complete data for testing the deduced orders of substituent effects just cannot he ohtained from the literature. Rates are highly variable depending upon reaction conditions, and the types and orientations of leaving groups and substituents. This case is mainly included to illustrate how one can make detailed predictions using structure-resonance theory.
< - {at}
i".
-
,fA
(&1
SC ratio = 1314 = 3.25
c ,- (b*} (&+I
Dlels-Alder Reactions
Three aspects of the Diels-Alder cycloaddition reaction that are extremelv interesting are (1) The effects of substrate
structure oniates, (2) s&stitukdt effects on rates, and (3) reeioselectivitv. Results from the exwerimental investieations ofk three to& are suitable for presentation to students. For examwle, the fact that accewtor substituents in dienowhile and dono; ~"bstituentsin diene facilitate the reaction is usually pointed out in elementary textbooks. Structure-resonance theory can be used in discussing all three topics and generally gives results that correlate well with experiment. The 6-orbital, 6-electron pericyclic transition state is, of course, modeled by an aromatic sextet of electrons. The most extensive quantitative studies of the effect of structure on reactivity in the Diels-Alder reaction have been concerned with cvcloadditions of maleic anhvdride to aromatic hydrocarbons ( 4 8 6 0 ) . The reaction occurs readily with any aromatic hydrocarbon containing three or more linearly annelated rings.
SC ratio = 512 = 2.5
+
SC ratio = 1014 = 2.5
?+ 'C+ - [b+]
SC ratio = 512 = 2.5
SC ratio = 612 = 3.0
A
SC ratio = 1014 = 2.5
A~
+
cA ['Qf+]
SC ratio = 1014 = 2.5
A
Figure 3. SC ratios tor Diels-Alder reactions
Typical rate data (501, obtained at 91.5'C in trichlorobenzene and covering a range of reactivity larger than lo6, are shown in Figure 2. The SC for each three-dimensional delocalized transition state is the sum of the SC for reactant hydrocarbon plus tbe SC of the ?r system fragments that remain after Diels-Alder reaction. The SC's are obtained most easily using published graph-theory algorithms (33, 34). The SC ratio
Wreactant) SC(T.S.) SC ratio log k
SC(reactant) SC(T.S.) SC ratio log k
= 40 = 65 = 1.625 = 0.24
= 13 = 7 = 1.857 = 2.13
Wreaetant) SC(T.S.) SC ratio log k
SC(reactant) = 4 SC(T.S.) =8 SC ratio = 2.00 log k = 3.36
= 19 = 34 = 1.789 = 1.45
SWeactant) = 1 4 SC(T.S.) = 30 SC ratio = 2.14 log k = 4.41
Figure 2.Rate data and SC ratios for Diels-Alder reactions of aromatic hydrocarbons.
again gives a good qualitative correlation of the rate data (corr. coeff. for in (SC ratio) versus I n k = 0.990). In most Diels-Alder reactions the dienowhile component normally contains at least one electron-withdrawing suhstituent (51, 52). Figure 3 shows how resonance effects of additional suhstitutibn in the diene component using electron-donating and conjugating groups, can he modeled and rationalized. The SC for reactants is taken as the number of structures for diene and dienophile, considered as a single super molecule. The transition statelreactant SC ratios are in excellent aereement with observed reeioselectivities of Diels-Alder reactions ( (52-55). Ortho- anipara-substituted products are alwavs the wredominant products in reactions of 1- and 2suhstitutedbienes with monosubstituted dienophiles. Also, as far as can be ascertained from reaction temperature, time, and yield data, the SC ratios give a sensible correlation of relative rate data, wredictin~that both ortho- para-type products and meta pk~dnctswill be formed at faster rates than in the case of unsubstituted diene and dienophile. The result could be comuared with Huckel molecular orbital calculations based on the same models (40) which predict, for example, rate retardation with either of the suhstituent patterns, polar substituent in dienophile or polar dienophile suhstituent and conineatine vinvl suhstituent in diene.
2.50 (see Fig. 3) in disagreement with the experimental observations. However, it can he pointed out that previous theoretical work (56, 57) has established that these reactant suhstituent patterns are exactly those that should favor nonconcerted stepwise reaction pathways. In these cases, diradical intermediates as shown below Volume 58
Number 5
May 1981
375
many of thestructure-resonance theory concepts. Finally, the financial support of the Robert A. Welch Foundation of Houston, Texas, is gratefully acknowledged.
Literature
nccount ior the olwrved r e g i o c h e m i s t r y , and the w n c l u s i ( t n t h a t t h t w r e a c t l o l l s may involve dirodi,als or diradicaloid transition states seems riasonable. An apparent failure of structure-resonance theory occurs in considering the reaction of a monosubstituted diene with unsuhstituted ethylene.
Cifed
Psuling. L., "The Nature of the Chemical Bond," Third Ed.. Cornell Univenily Press. Ilhnes. N.Y., 1960,Chpts. 6 and 8. Wheland,G. W.,"Re%onanceinorranieChemistry?John Wileyand&,nn.lnc.. New York, N.Y.. 1955. Hieasi. K., Balm, H.. and R~mbaum.A.."Quantum o,#a,icChemirtr\.."Inle~ienc. Pahlirherr. New York. N.Y.. 1965.Chpl.2. P1att.J. K. in"Handbueh desPhysik? Vd. XXXVIII2, S. Flugge lEditur),SpringerVerlap. Berlin. 1961. pp. 202-203. Randii. M., Chem P h y s Letts. 38.68 11976);J. Amrr. Chem. Sac,. 99.444 11977): Td.rahc,drnn 33,1905 (1977). &war, M. J. S..Aduon. Chem.Phyhyr..& 121 119661. Blealuw. R.. Chem. Eng. News, 43126). An 119651; Accls. Chem. Re'.. 6.393 (19131. Herndon, W. C., J Amer Chem. Soc ,95.2404 119731. Herndon, W. C.,and Ellzey, M. L., Jr., J . Ampi Chrm. Soc.,96,6631 119741. Whe1and.G. W.. J Amsr. Chsm. Soe..61.900 11942). Herndon, W.C.. J. O n . Chem.40.3SR3 119751~ Wmdward, R. L a n d Hoffmenn. R.. Aneeu. Chem. In,. Ed. Engl., 8,781 (1969). Wooduard,R. &and Hoffmann, R.."The Conservation oforbital Symmetry,"Aea. demicPress, NPWYolk, N.Y., 1971. Baldwin. .I. E i n "Pericyclic Renefions." Vol 2. Marehsnd, A. P.. and Lehi. R. E. , Yerk, N.Y.. 1977,Chpt. 5. liidttars). Academic P l e ~ rNow For n ,went rovievEce Hour. K. N, i n "Poricyclic Reaetiuns," vol. 2, March8"d.A. P..and Lehr, R. B. 1Edil"rsl.Academie Pres-. NevYork. N.Y., 1977.ChpL4. Dewsr. M. J . S.. T~lrohc,dronSuppl.. 8.75 11966): Anye"; Chem.Inl. Ed. Engl., 10.
Wensrn Piers. New Ynrk, NY.. 1975. 1181 Zimmerman. H. B..Alc. C h r m Rus.4.272 119711. (19) Zimmcrman. H. B., "Pericydie Reaetiunr:'Vol. 1. Marchand. A. P.. and 1ahr.R. E.
Frontier molecular orhital theory predicts a rate increase for any single suhstituent in either diene or dienophile (581,hut these structure-resonance theory results infer that the single conjugating suhstituent would have no effect, and the single donor suhstituent at the 1-position would have a retarding effect on rate. The only experimental results located to compare with theory concern the reactions of hutadiene, 1methvlhutadiene. and 2-methvlbutadiene with ethvlene. ~ e a c t i o nconditions and yields i r e ZOO', 90 atm., 17 h;, 18% (59):250". 70 atm., 4 hr, 20% (60); and 240'. 70 atm., 4 hr, 20% (60),respectively. The best that can be said is that these experimental data are not in clear disagreement with the structure-resonance theory calculations. Other important features of Diels-Alder reaction stereochemistry are the "cis" princ~pleand the "endo" rule (61). Structure-resonance theory as presented here cannot account for the steroechemical patterns embodied in these rules. Presumably secondary effects of various types (62) do provide explanations, hut the details of these explanations usually would not be presented to students in elementary courses.
Conclusions The sigmatropic shift has not been discussed in this article, although the theoretical approach would be quite similar to that in the given examples. Extrapolation of the present work to other varieties of pericyclic reactions will also not be difficult. In general, the results are expected to give at least as good aereement with exoeriment as do the results of Hiickel molecular orhital calc;lations. This couclusion follows from the fact that it has heen shown that auantitative structure-resonance theory calculations are tantamount to SCF-LCAO-MO calculations in ~reviouswork. In those cases where struct u r e - r t w n a n c e ;hvury is applicable. it could be the method of r h g i w , h o t h ig,r c o r r e l i r ~ i < mof s e a l , e r i m e n r a l data and for teaching purposes. Acknowledgment The interesting results of Carpenter and his co-workers (38-40) where thev used Hiickel molecular orhital theorv to correlate rate effects in pericyclic reactions provided impetus for the oresent work. An article hv Ettlineer and Lewis (63) . . on resonance theory applied to the transition state of the Diels-Alder reaction helped the present author to formalize
376
Journal of Chemical Education
Academic Press, New Ymk. N.Y.. 1976. 1231 Fleming. I.. '"Frontier Orbitals and OrganieChemical Reactions," John WileyandSona, New Yurk.N.Y.. 1976.
11975). (30) Herndon, W. C.. J. A m w Chem. Soc., 98,887 (197%). (311 Stein. S. E..snd Golden. D.M., J . Ore. Ch~m..42.83911977). (321 Horndu,n. W. C.,/smelJ. Chrm ,20.27611980). (:I31 Horndon. W. C., Tefmhedron.29.3 11973). 51. 10119741. 1341 Herndon. W. C., J.CHEM. EDUC., 1151 Mineos, D. M. P.. J. C.S. Dalton, 20, 26, 31 11971). I : I ~ I~ e . n d ~ nW. . c., J. ~ m e crh p m SOC. 1n2. 1588 (1980). 1371 Aihsre.J..Buil. Chom. Soc. Jop..51.1541119781. 1381 Carpenter. R., Tetr~hedmn,34.1S7711978l. 13s) Wilcor, Jr., C. F.Carpenter. B. K.. and Dolbier, Jr.. W, R., Tdrohedmn, 35. 707 ,,am, ,.".",.
(40) Wileox, Jr., C.F..andCsrpenter,B. K., J. Amer. C h s m S o c , 101,3897 119791. 141) Criegee, R., Seehach. D.,Winur,R.E., Burretzsn.B..andBrune.H.-A,. Chem. B p i , 98.2839 11965). (421 Willeott, M. R., Cargill, R. L., Seam, A. B., Prag Phya. 01g. Chem., 9.25 (19721. 1431 Longust-Higgmr. H. C., J Chpm Wys., 1% 265 11950). 1441 Cava, M. P.,Shirley,R. L.,andErickson.B. W., J. Ore. Chem., 27,755 (19621. I451 Carpenter, B. K., Little, R. D.. and B e m n , J. A,, J. Amrr Chrm. Soc. 98. 5728
