Peter Brown Arizona State Universitv Tempe, 85281
I I
Models to lllus+rate Orbital Symmetry Effects in Organic Reactions
In the past five years, our understanding of the detailed mechanisms of a vast number of concerted organic reactions has been literally revolutionized by the particular considerations of orbital symmetry effects widely known as the "WoodwardHoffman Rules," after their most enthusiastic proponents (1-8). Such reactions are characterized by the continuous transformation of reactant molecular orbitals (MOs) into product MOs, and in which conservation of orbital symmetry produces a relatively low energy transition state (provided that steric effects do not intrude seriously). The principles underlying orbital symmetry conservation in organic reactions have been reviewed extensively (I-&'), and a flood of new research touched off as their rationales and predictions (5) are put to the often ingenious experimental test. At this time, the conservation of orbital symmetry is already part of the everyday language of physical organic chemistry (9I S ) , and will doubtless prove to be of considerable value in the interpretation of inorganic reaction mechanisms also (8,14,15). From a pedagogic point of view, conservation of orbital symmetry is easily assimilated by students with a rudimentary knowledge of simple MO theory and of symmetry. We have found in teaching over the past three years a t both graduate and undergraduate levels, that use of a simple set of orbital models, as described below, has enormous advantages as a visual aid in the construction and assignment of symmetry elements to
Figure 1. Orbital model of u end u* MOI for a thermol [ r 2 cycloaddition reaction.
Figure 2. Orbital model of electrocycliration.
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of butadiene for o thermal conrotatory
the appropriate semi-localized Hiickel-type MOs, and in following their stereochemical fate in concerted reactions. Orbital Models
For example, the requisite model of the frontier molecular orbitals (6-8) of two ethylene molecules approaching a transition state for a thermal concerted [r2 a21 cycloaddition reaction is depicted in Figure 1, and the unfavorable interaction of the highest occupied MO (HOMO) a in one molecule with the lowest unoccupied 1\10 (LUMO) a* in the other is immediately obvious. In a corresponding model for a thermal concerted [r4 a21 cycloaddition reaction (Diels-Alder), the favorable interaction of the termini of $3 (HOMO) in the diene (shown in Fig. 2) with r* (LUMO) in the dienophie can be seen very clearly. Elaboration of the model to represent the Diels-Alder addition between $2 (HOMO) and $Z (LUMO) of two butadiene molecules permits ready visualization of the secondary orbital overlap effects that are now believed (6) to account for the experimentally observed preference for r2] cyendo-addition (the Alder Rule) in the [a4 cloaddition process. To illustrate orbital models of electrocyclic processes, the cisoid conformation of $2 (HOMO in ground electronic state) of a trans,trans-1,4disubstituted-1,3butadiene is reproduced in Figure 2, and conrotatory rather than dirotatory thermal cyclization leading to the trans-3,4disubstituted cyclobutene is easily demonstrated. I n contrast, a model of the all cis conformation of J.a (HOMO in ground electronic state) of a trans,trans-1,6-disubstituted-1,3,5-hexatrienecan be constructed, and disrotatory rather than conrotatory thermal cyclisation to a cis-5,6-disubstituted-1,3-cyclohexadiene is immediately apparent. To illustrate orbital models of sigmatropic reactions, in Figure 3 is depicted $Z (HOMO) of an unexcited ally1 radical interacting with a hydrogen radical. It is quite clear from the viewpoint of conservation of orbital
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Figure 3. Orbit01 model of rigmatropic reaction.
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ally1 for a thermal mtorofocial [1,3]
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symmetry that a thermal [l,3]-hydrogen shift is forbidden suprafacially, but allowed antarafacially (this also applies to a [1,3]-carbon atom shift with retention of configuration). In contrast, the orbital model of a hypothetical transition state appropriate to a suprafacial thermal [1,3]-alkyl shift accompanied by inversion a t the migrating carbon atom, where a horizontally aligned p orbital replaces the hydrogen s orbital in Figure 3, is quite clearly symmetry allowed.
p-orbital Cardboard type
sp"-orbital Styrofoam type
I n Figure 4, the relevant orbital model of the ground electronic state of a cis-2,3-disubstituted cyclopropyl carbonium ion is given, e.g., as derived from solvolysis of a trans-I-tosylate. The experimentally observed (16) disrotatory thermal ring opening to $1 (HOMO in ground electronic state) of the tran8,trans-disubstituted allyl carbonium ion is then readily appreciated. Appropriate molecular orbital models of many other systems and for other reactions (e.g., from electronic excited states) have been and can be assembled readily from the component p and spn atomic orbitals herein described. In all cases, this particular type of molecular orbital model permits a very clear classroom exposition of the vitally important stereochemical relationships, for both orbitals and substituents, between reactants and products in concerted reactions.
(Fig. I), allyl (Fig. 3), cyclopropyl (Fig. 4), butadiene (Fig. 2), pentadienyl, hexatriene, benzene, etc. Each individual p orbital can be rotated about the axis of the wire framework, thus permitting quick conversion of the model without disassembly into other molecular orbitals of the same system, but of different energies and/or symmetries. Two sp2 type a bonds made from a single piece of wire bent a t 120°C can be clipped on instantly to terminal carbon p or sp" orbitals (e.g., see Figs. 2, 4), so that orbital (and hence substituent) rotations during the course of a reaction may be followed and perceived with great clarity. A convenient length for the wire C-C a bond in ethylene (Fig. 1) is 13.4 cm (actually -1.34 A), and other bond lengths are scaled accordingly, to a first approximation. We have found that a set of about 12 p orbitals and 8 spn orbitals to be a useful size in practice. Additional orbital models not shown but often used include u and u* representations of diatomic molecules such as HZ. These are fabricated from two 4.5 om diameter styrofoam balls cemented together, of the same and opposite colors respectively.
Description of the Models
Literature Cited
Figure 4.
Orbital model o+ ground state cyclopropyl corbonivm ion.
The relevant atomic orbitals under consideration are carbon p (e.g., Figs. 1-4) and hybrid spn (e.g., Fig. 4), where n = 2-3. Both two-dimensional (Fig. 4) and three-dimensional (Figs. 1 3 ) model atomic orbitals have been constructed, the former from colored cardboard (e.g., red and yellow) and the latter from spraypainted styrofoam shapes. Two colors are utilized to represent and - signs of the wave function. Constructional details are given in Figure 5. The cardboard orbitals were cemented to their unplasticized polypropylene centers with epoxy resin, and the styrofoam type affixed to their aluminum supports using white glue. The atomic orbitals are assembled into crude representations of semilocalized molecular orbitals by simply sliding into position on 20-gauge steel wire (dry cleaner coat hangers are ideal), cut and bent to the lengths and angles appropriate to the u-bond framework of the particular system a t hand, e.g., ethylene
(1968).
(2) V o ~ r a a ~ J. n . J.. A N D Ssnvls, K. L., J. CHEM. EDUC., 45. 214 (1968). (3) VOLLMER, J. J., A N D SBRVIB, K. L..J. CHEM. EDOC., 47, 491 (1970). (4) Wooow*no, R. B.. in "Aromatieitv," Special Publioatmn No. 21 of the Chemioal Societv. London. Endand. 1967.. o. 217. . (5) B e ~ s o wJ,.. Accounfs Chem. ~8s.;1, 152 (1968). (6) Wooow*no. R. B., AND HOFFMINN, R., "The Conrrvation of Orbital Symmetry." Academic Press Inc.. New York, 1970. This is areprint of a major review article first published in Angew. Chem. I d . Ed. E d . , 8, 781 (1969). (7) Ps~nsolr,R. G., Chem. Ew. News, 48, No. 41, 66-72 (September 28,
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Journal of Chemical Fducofion
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(8) Fuxur, K., Aceolrnfs Chem. Res.. 4, 57 (1971). (9) M*RCX.J.. "Advanced Organio Chemistry," MoGraw-Hill Ina., NBIV York. 1968, pp. 6334. (10) L ~ e s n ~ mA,. . "Introduction to Theoretical Organio Chemistry," MoMillsn. New p k . 1968, pp: 7OB-10. (11) Koaowen. E. M.. An Introduot~onto Phyeioal Organic Chemistry," John Wiley & Sons, Ino., Nerv York, 1968, Chaps. 1.8 and 1.9. (12) DEWAX, M. J. S.. "The Moleoulsr Orbital Theory of Organic Chemistry," McGraw-Hill Ino.. New York, 1969, Chap. 8. (13) INGOLD. C. K., "Stm~tureand Mechanism io Organic Chemistry," 2nd Ed.. Cornell University Press. Ithsos. 1969, pp. 870-8. (14) ( 8 ) MAN.% F. D., AND SOH*OHTSOIINEID*R. J. H.. J . AmW. Chem. So&, 89,2484 (1967); (b) M m a o . F. D., A N D ~ C ~ A C ~ T S O ~ N E ZJ.D? E ~I . .. J . Amer. Chem. Soc.. 91, 1030 (1969). (15) WHLTESIDES, T. H., J . A m m . Chem.~Soc..91, 2395 (196s). (16) Soa~mren.P. YON R.. VAN DLNE, G. W., SCHGLLKOPB,U., A N D PABSF. J., J . Amer. Cham. Soc., 88, 2868 (1966). and refs. cited therein.
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