California Association of Chemistry Teachers I
tion Mechanisms in Oraanic Chemistrv
Perhaps the most significant development in organic chemistry over the past several years has been the elucidation of factors that control the mode and feasibility of concerted reactions. That a large number of organic reactions take place in one elementary step has been long recognized but has been difficult to establish experimentally and difficult to explain on any rational basis. Why, for instance, does the familiar SN2reaction of alkyl derivatives proceed in a concerted and stereospecific manner to give inversion of configuration a t carbon? Why is the stereochemistry of diene and dienophile preserved so completely in Diels-Alder cycloadditions? Questions such as these and many others have found answers in recent theories of orbital symmetry control of concerted reactions proposed by Woodward and Hoffmann ( I ) , Fukui ($), Salem (3) and others (4). The state of the art has developed to the point where it is appropriate and desirable to introduce the topic into the undergraduate curriculum in organic chemistry. Having made one questionable attempt thus far to discuss concerted reactions with sophomore students representing potential majors in the physical and life sciences, two points became abundantly clear to the writer-if not to the students. First, there is no point in discussing the theory of orbital symmetry until the reactions to which the theory applies have been treated in sufficientdetail to provide some appreciation for their special nature, pssticularly their selectivity and stereospecificity. Second, the theory itself, as it is currently propounded, can best be described in the students' own words as "heavy." With this background of doubtful success in communicating the relationship of orbital symmetry to concerted reactions, an attempt is made in the present article to treat the subject in as straightforward and general a manner as possible-hopefully without introducing misconceptions due to oversimplification. Manifestations of Concerted Reactions
Many reactions of organic chemistry are a composite of several sequential steps, each step by definition being concerted. The overall sequence from reactants to products involves either radical or ionic processes with formation of intermediates that may or may not be isolahle but can frequently be detected directly or indirectly by chemical or physical methods (6). There are, however, many reactions that occur in only one Presented in part at the Eleventh Summer CACT Conference, Asilomar, California, August 1969.
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s k p ; among these are certain displ:rceme.~~t react,ions (e.g., SN2,Sh.2')1eliminatio~lreitctious (EL), renrmngements (Claisen, Cope) and cycloadditions (Diels-Alder), to name just a few. Reactions of the concerted type have been described as the IT-ilight zone" of organic chemistry or, as having "no mechanism" (6) simply because most of our usual probes of reaction mechanism are of little value when applied to one-step reactions. Thus, they are internally self-sufficientrequiring nothing energy to but the requisite thermal or get them "over-the-hill." It is not possible to arrest coucerted reactions by chemical means or to accelerate them with the aid of catalysts. Solvent effects are not usually pronounced and structural variations in the reactants produce relatively minor changes in reaction rates except when steric factors are involved-and these may be exceedingly important (e.g., SN2). Reaction rates are often characterized by large negative entropies of activation, suggestive of highly organized transition states. Concerted reactions are also remarkably stereospecific and selective as to vhether they will occur thermally and/or photochemically. Even when a reaction exhibits the above-mentioned behavior, this constitutes no proof that it is concerted. Concertedness can be established vith certainty only from a detailed description of the transition state-and it is precisely this description that is so hard to obtain. There is also some uncertainty as to the correct vay to define concertedness in a reaction. In the present context, concertedness implies that there is no discontinuity in the electron reorganization that takes place during reaction although the degrees of bond-making and bond-breaking may not necessarily be equally advanced in the transition state. The broad scope of reactions that are considered to be concerted are illustrated in the following sections. The examples chosen are representative rather than exhaustive and illustrate the most salient features of reaction. The theory of orbital symmetry control of concerted reactions is briefly discussed, and the generalized Woodward-Hoffmann selection rule ( I ) for concerted reactions is stated and illustrated with pertinent examples. Displacement and Elimination Reactions
To facilitate discussion of the orbital symmetry requirements of concerted reactions, it will help at the outset to recognize the reacting orbitals, the product orbitals, and the number of electrons involved. In SN2 reactions, for example (eqn. (I)), the entering
nucleophile ?! utilizes a nonbonding orbital, designated as my, which is filled with two paired electrons. This orbital, written as w $ to show that it is doubly occupied, becomes part of the new C-Y bonding molecular orbital (a&) in the product. The other participating reactant orbital is the filled C-X bonding molecular orbital (o&) and the other product orbital is o;. The overall reaction may then he formulated as in eqn. (2) which shows more clearly the occupied reactant and product orbitals that are involved. According to the theory on which orbital symmetry control is based, antibonding orbitals are also important but we will not specifically consider their role until later.
&:.,+ re, + 4, There are many unimolecular elimination reactions of synthetic value that are thermally induced and proceed in a stereospecific manner. Examples include the pyrolysis of carboxylic esters, xanthates (Chugaev reaction), amine oxides (Cope elimination), and alkyl halides. While thesereactionsmay not all be concerted, many of them are and proceed by way of cis elimination (10). Six-membered cyclic transition states I1 and 111are strongly implicated for both ester and xanthate pyrolysis, respectively. The participating reactant and product orbitals are included in eqns. (5) and (6).
e. + a,, + &, The most remarkable feature of SN2reactions is summarized in Ingold's words: "Substitution oy mechanisms S N involves ~ inversion of configuration independently of all constitutional details" (7). Thus, with reference to the displacement reactions of 1-phenylethyl derivatives summarized in eqn. (3), inversion of configuration occurs regardless of the nature of the entering nucleophile Y or the leaving group X.
Cyclization Reactions
Concerted elimination reactions of the E2 type often occur concurrently with SN2reactions, and the stereoelectronic requirement for the E2 reaction is a coplanar transition state which frequently but not invariably leads to trans elimination (8). For example, dehalogenation of a vicinal dibromide with iodide (eqn. (4)) is evidently a concerted elimination (9) in which the nuclei associated with the reacting orbitals, w t aLBr dBr, have a coplanar, or near coplanar configuration in the transition state I. The product orbitals are a:, a& mi,.
A cyclization reaction of considerable synthetic utility is the Diels-Alder reaction (II), which is the addition of an alkene (dienophile) across the 1,Cpositions of a conjugated diene to form a six-membered ring (eqn. (7)). This type of reaction is frequently 2) or (2 2 2) cycloaddition to labeled as a (4 indicate that there are four reacting electrons from one component (diene) and two from the other (dienophile).
+
+ +
+
+
+
+
The fact that the configurations of both the diene and (lienophile we prescrved;~n cycloaddition (cqn. (7)) implies that the trnnsitiou state resembles I V in ivhicl~the diene assumes the s-cis conformation in a plane roughly Volume 48, Number 12, December
1971
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parallel to that containing the nuclear framework of the dienophile. In terms of the participating orbitals, the reaction is usually described as (a4 a2)going to (a2 as a2). We will conform to this notation up to a point since it is used in the generalized Woodward-Hoffman rule, but we wish to emphasize that the notation a4can be very misleading. It must not be interpreted to mean that one a molecular orbital is occupied by four electrons. No molecular orbital may be occupied by more than two electrons (paired!). The notation a' does mean, however, that a system of s-molecular orbitals is occupied by four electrons. Precisely which of the molecular orbitals in the a system of the diene are involved is the subject on which the theory of orbital symmetry control is based. In contrast to (2 2 2) cycloadditions, which are strictly thermal reactions, concerted (2 2) or 1,2cycloadditions to give cyclobutane derivatives (eqn. (8)) are generally induced photolytically. The participating orbitals are easily seen to be (a2 aZ)going to (a2 u2).
+
+ +
+ +
+
+
+
cis-trans-2,4-hexadiene (VI) uncontaminated by either the cis-cis or trans-trans isomers (eqn. (10)) (12). The orbital system may be written as (a2 a2 as) for the reactant going to ( s 4 [d wO])in the products. As explained previously, the diene orbital system is designated as s 4 ; the other product (SOz)is designated as [wZ wn]. Cleavage of two sigma bonds to sulfur leaves two atomic orbitals on the heteroatom, one of which is doubly occupied (a2). The wn orbital becomes part of the SO2multiple bonding.
+
+
6
(&
+ & + nL)
+
+
+
(A2 + &J
VI
Intramolecular cycloadditions in which the terminal sp2 hybrid carbon atoms of a conjugated polyene combine by forming a new a bond are known as electrocyclic reactions (4a). The simplest example is the formation of cyclobutene from butadieue (eqn. (11)).
.+ + n2
+
The orbital systems are s4for the diene giving (a2 a2)in the product. In fact,reactions of this general type may occur in either direction, depending on the system, and may be induced thermally and/or photolytically. They are completely stereospecificbut the mode of ringopening or ring-closing depends on whether the reaction is a thermal process or a photochemical process. For example, pyrolysis of cis-3,4-dimethylcyclobutene(VII) gives only cis-trans-2,4-hexadiene (VIII) (IS), by a reaction in which the sigma bond breaks such that the methyl groups appear to move in the same direction. This is described as a conrotatory motion. In contrast, photolysis of cyclopentadiene I X results in sigmebond formation by a twist of the two a termini in opposing directions, which is described as a disrotatory motion. The product is the highly-strained bicyclo [2.1.0]-2pentene (X) (14). n
Designation of the carbene orbital system as [w2
(nEccc)
v
"I
2) type wherein the two Cycloadditions of the (2 participating filled sigma orbitals are associated with the same atom have been named cheletropic reactions (1) and also as 1,l-cycloadditions. A familiar example is the addition of singlet methylene to cis-2-butene (eqn. (9)). The reaction is stereospecific and occurs thermally. The participating orbitals may be formulated as a2for the alkene and [w2 wn] for the carbene, giving (a2 a2)in the products.
+ +
+
a
+
wo] may appear unfamiliar, but we have chosen to label
it in this way to keep the orbital accounting straight.
It should be noted that the number of component atomic orbitals as well as the number of reacting electrons must remain unchanged on going from reactants to products. On the product side of eqn. (9), the sigma bonds comprise four atomic orbitals, hence there must be four atomic orbitals on the reactant side. Two of these are obviously the 2p atomic orbitals of the a bond and the other two must be the nonbonding orbitals of the carbene one of which is doubly occupied (w2)-the other is unoccupied (wO). Unimolecular elimination reactions of yclic reactants are essentially the reverse of cycloaddition reactions and have been called for this reason cycloreversions (1). They have also been referred to as extrusion, fragmentation, retro Diels-Alder, and cheletropic reactions depending on the nature of the reactant. An interesting example is the pyrolysis of the cyclic sulfone (V) to give 784
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X (+ + 6 ) The related reactions of conjugated trienes reacting as a6systems proceed thermally in a disrotatory fashion and photochemically in a conrotatory fashion (eqn. (12)). This is precisely opposite to the mode of reaction in the diene a4system.
Rearrangement Reactions
Rearrangement of 1,s-hexadiene derivatives (eqn. (13)) is specificallyknown the Cope rearrangement, or more generally as a sigmatropic rearrangement (1). The net result of the reaction is certainly a rearrangement when the system is appropriately substituted, but from the orbital standpoint it is a 2 2 2 reaction similar to the elimination, cycloaddition, and electrocyclic reactions of eqns. (5)-(7), (lo), and (12).
+ +
A closely related reaction is the familiar Claisen rearrangement of vinyl allyl ethers or aryl allyl ethers (eqn. (14)). The presence of a heteroatom does not change the number or type of orbital participants.
Both the Claisen and Cope rearrangements are thermal reactions that occur with complete stereospecificity (6, 15) and it has been established that the preferred transition state assumes a chair-like conformation (eqn. (15)) (16).
Theorelicol Considerations
For a reaction to proceed in one concerted step the participating orbitals of the reactants must transform by way of the transition state into the product o~bitalswith preservation of orbital symmetry. This is most simply illustrated by the formation of an electron-pair bond from the interaction of t x o atomic orbitals (e.g., 1s and 2p) associated with different atoms. These two orbitals may combine in two ways to produce two molecular orbitals which differ in energy and symmetry, as shown in Figure 1. The stable or bonding molecular
Figure 1.
Molecular orbit019 formed from the interoct#onot otomic I s and
2p orbitals.
orbital (a) can only be formed directly from a pair of interacting atomic orbitals having the same symmetry or nodal properties as a, namely the combination (1s 2p). Likewise, the antibonding molecular orbital (a*) can only be formed from the combination (Is - 2p). In orbital symmetry terms, the a orbital is said to "correlate" with (Is 2p) simply because the nodal properties are unchanged on transforming the one into the other. For the same reason, o* correlates with (1s - 2p). Orbital theory further predicts that reaction of the atoms in their ground states will produce a stable molecule since the lowest energy populated reactant orbital combination (Is 2p) correlates directly with the ground state a orbital of the product. I n general terms, for a thermal reaction to be energetically feasible, the ground state reactant orbitals must have the same symmetry or nodal properties as the ground state product orbitals. While this may not be the only condition for determining the feasibility of a thermal reaction it is certainly a necessary condition. As will become clearer in subsequent discussion, orbital symmetry controls the configuration of the reactants in the transition state. It is convenient, therefore, to be able to describe the configuration of a transition state in condensed form. For this reason, the terms suprafacial addition and antarafacial addition have been introduced and will be briefly defined here. Suprafacial addition implies that bond making or breaking occurs on the same face of the reacting orbital system. This is illustrated below for T,, a,, and a, orbitals where the arrows indicate the suprafacial mode and the subscript s denotes suprafacial addition. It will be noted that suprafacial addition to a a orbital can occur in two ways to give either retention or invevsion of configuration at both atomic centers.
+
+
+
One of the best known rearrangement reactions is the migration of hydrogen, aryl or alkyl groups to a neighboring electron-deficient atom, usually carbon, nitrogen, or oxygen. When the terminus is a positive carbon atom, the reaction is classified as a 1,2-carbonium ion rearrangement or Wagner-Meerwein rearrangement (eqn. (16)) involving the participation of (a2 wo) orbitals.
+
It is well documented that the migrating group R retains its configuration during 1,2-rearrangements of this kind. However, the related 1,3-rearrangements (eqn. (17)) are relatively rare but have been observed to proceed with inversion of configuration (17).
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I 1
=
Is
1 1
1
cs(retention)
J
-
cs(inversion)
1J
8 Wg
(arrows denote direction of orbital overlap with other reacting orbitals) Antarafacial addition implies that bond making or breaking occurs on opposing faces of the reacting orbital system as shown below for a., re and o., where the subscript a denotes antarafacial addition. For a r orbital, antarafacial addition would give inversion of configuration a t one atomic center and retention a t the other.'
1
inv.
ret.
ret.
I
I
f""1 " U V I S L. V l Y l l Y l U l Y g r Y l l l ,Or rnermm r)rc,oW4L,,nrm o r e r n y e n e ro gwe mode. Note thot the ground stde ( G S ) recyclobutone inthe [rea raz] acting orbitals correlote with a doubly excited state IES) of cyclobutone. Reaction in this mode is energetically unfeasible b y thermal means due to prohibitively high activation energy.
+
(2
+
+ 2 ) Cyclooddition
The simplest cycloaddition reaction is the dimerization of alkenes to give cyclobutanes which is the a2 aZcycloaddition of eqn. (8). Concerted reactions of this type are usually photoinduced. In analyzing the orbital interactions in this and related reactions the steps involved may be listed as follows
+
1 ) The occupied and unoccupied reactant and pmduct orbitals must be recognized. I n the (nZ r a ) rase, the four reactant orbitals are the two bonding orbitals, n, and rs,and t,he two antibanding orbitals, r,* and rSa. The subscripts 1 and 2 are used t,o differentiate the reacting r bonds even though they are of equivalent energy. The product orbitals are a,,02,,'rc and m*,where again the subscripts are used to differentiateotherwise equivalent orbitals (Fig. 2).
+
8 ) A specific configuration for the reacting molecules is adopted. In the present example, we will first consider a four-center planar transition state for a [ r Z 2 r2] process.
+
+
terivtics of t h e ( r , r 2 ) orhit,d are the same as t h e (a, n2) orbital. In ot,her words, (r, r2) is said to correlate with (c, m). However, it is obvious from Figure 2"hat ( r , - r.) does not correlate with (a,- m) but with a higher energy orbital (v,* ma). The bondinglevel (m - m )correiatev with the antibonding reactant combination (m* a%*). 4 ) The lowest energrj reading orbitals i n a thermal process are populated with the participating electrons (two paired electrons per wbiial). If these orbitals eorrelale directly with the lozuest energy product o~bitals,a concerted thermal reaclion is energetically feasible. Clearly, such is not the casein a thermal ( s S Z n,*) cyclmddition. Figure 2 shows that the ground state of two perturbed ethylene r 2 ) and ( r , - r 2 ) orbitals are hot,h molecules in which the ( r , doubly occupied, correlates with a doublzj excited state of cyelabutane. The adivation energy for s m h a process would be prohibitively high-higher than the band dissociation energies of the combining moleci~leu. A concerted cycloaddition is not then expected to occur in the chosen configuration becanse other dissociative reactions would intervene. If, however, one of the electrons of one of the isolated ethylene molecules is promoted to a s * level by irradiation, then the comhination orbital (ma ?.*) becomes singly occupied (Fig. 3). There is now a. correlation hetween the orbitals of the first excited state of the reactants and the first exoited state of the product. This implies that s concerted ( r V 2 as2)reaction is energetically feasible when photoinduced, ar observed experimentally. The
+
+ +
+
+
+
+
+
3) The reacting inolerules are cornidwed to approach i n the adopted configuratia such that orbital interaction occurs. The participating orbitals of the inte~actingreactants a m thus "perturbed." The elect~onsare thereby dclocalined within a set of orbitals that msst t~ansfonninto the product orbitals with preservalion of wbital symmetry. The lowest energy interacting or perturbed set of reactant molecular orbitals for the (rea r,' )ease are ( r , r s ) and (n, nz) (Fig. 2). The lowest energy interacting set of product molecular orbitals %re(rr m) and (c, - cx). The symmetry charac-
+
+
+
I n order to see that the terms antamfacial and suprafacial may he used effectivelyto designate configuration of reactants in the transition state, the reader may wish to verify the following: (a) the S Nreaction ~ of eqn. (2) conforms to the r.*)mode; (b) t,he transition state I V in the Iliels-Alder reaction of eqn. (7) curresponds to the (r,' n 2 ) mode; (c)the conrotatory process of eqn. (12) corresponds to r b F? (r,' C . ~ )or (r.' c , ~ ) ,and the disrotatory process to ' . r e (ra4 cs2)or (r." rat): The relative energies of the interacting orbitals shown in t,he correlation diagrams of Figures 2-8 are based on the premise that energy increases with increasing number of nodes.
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isolated elhykes(ES) intamcmg.sthylenes0 cyclobulam o r b i i (I3l (G$ Figure 3. Photoinduced ~ y ~ l o ~ d d i t of i o nethylene to give cyclobvtone in
+
the [rVsr n 2mode. ] Note thot the occupied orbitals of the flrst excited =tote of the combining reactants correlote with the occupied orbitals of the is therefore predicted to Rrrt excited state of ~ y c l o b ~ tCyclooddition ~ ~ ~ . be energetically feasible when photoinduced.
+
price of attaining the antibonding level (a*' my)'from the bonding level ( T , - rrd1 is met by the energetically favorable correlation of ( m * an*)' with (o, - or)'.
+
Intmmoleculor Cycloodditions
Before analyzing the orbital systems involved in the cyclization of 1,3-dienes to cyclobutenes and the reverse reaction (eqn. ( l l ) ) , brief mention of the a molecular orbitals of the diene might he useful. The system is more complex than the simple a-type or a-type orbital considered thus far in that the a system is assumed to be made up of a linear combination of four atomic Zp orbitals, one from each of the four sp2-hyhridized carbon atoms (18). This gives rise to four molecular orbitals of unequal energy, two of which are bonding (al and a%)and two are antibonding (a,* and a&*). These orbitals, as derived from simple Huckel molecular orbital theory, are shown diagrammatically in Figure 4. The energy of these orbitals increases with
of the diene are a,, a%,aa*, and ad*; those of cyc10butene are a, a*, a , and a*. There are two configurations for the transition state to consider-one involving disrotatory reaction, the other a conrotatory reaction. With reference to Figure 5, which represents the orbital participants in a conrotatory process, it can be easily seen that a1 correlates with the combination a ) and a 2 with (a a*). Since we are orbital (a* mainly concerned with populating the ground state orbitals for a thermal reaction, we can restate this by saying a12and ~~"orrelatewith a2and as, respectively, which means that a thermal conrotatory reaction is energetically feasible since the ground state reactant orbitals correlate with ground state product orbitals. A thermal conrotatory reaction in the reverse direction may he stated in the following may: A filled bonding a orbital interacting with a vacant antibonding a* orbital correlates uith a12in the product. Likexvise, a filled bonding a orbital interacting with a vacant antibonding a* orbital correlates with as2. The overall aa2) reaction is the thermally allowed aa4 (as2 process. In the disrotatory mode, the orbital diagram of Figure 6 shows the symmetry relationships betxeen a1 and (a a), a p and (a* a*), aa* and (a - a), and
+
+
+
+
+
+
Figvre 4. Diogrommatic representation of the s molecular orbitals of r-cis1.3-butadiene according to ~ i m p l eH k k e l theory. The heavy circles in the structure. represent nodes.
increasing number of nodes which is zero, one, two and three for the al, a,, a,*, and ad* orbitals, respectively. In the ground state of the diene, the four a electrons will populate the a, and levels only. The basic reaction of interest is the electrocyclic reaction of l,3-butadiene to give cyclobutene or the reverse process. It is immaterial to the argument which we choose as the reactant. The participating orbitals
Mdene n molecub wbitds (GS)
interacting orbitols
cyclobutene ortilab (ES)
Figure 6. Orbital diagrom for the transformation of 1.3-butadiene to cyclobvtene b y o thermal disrototory process. Note that the ground state readant orbitals correlate with a doubly excited state of the product-making the reoction energetically unfeasible in this mode.
I
Ixrtadiine n mdewlar orbitals (GS)
interacting orMds
cyclobutene wbitals (GS)
Figure 5. Orbital diagram for the transformation of 1.3-butodiene to cyclobutene b y o thermal canrotatory process. The forming 9igma bond in the interacting orbitolr i s drawn to show its specific intermtion with the forming T bond.
a&*and (a* - a*). Ground state butadiene in which both and a2are filled would therefore try to produce a doubly excited cyclobutene molecule by disrotatory ring closure. Since the activation energy for such a process would be unattainable by thermal means, reaction in this mode will not occur. If,however, butadiene is irradiated such that one of the electrons of the a 2 orbital is promoted to the a,* orbital, then the orbitals of the first excited state of hutadiene correlate directly xith the first excited state of cyclobutene. This is evident from 7 where alzcorrelates with (a a)$ and hence with a2, m' with [a* a*I1 and hence with a*',a3*' with (a - a)' and Photoinduced cyclization of hutadiene hence with to cyclobutene is therefore an allox~edconcerted process in the disrotatory mode, namely as4$ as2 a,".
+
+
+
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9 Figure 7. Orbital diagram for the tranrform~tionof i,3-butodiene to cyciobutene by 0 photoinduced disrototary process. Note that the flrrl excited rtote of the reactants carrelater with the first excited =tote of the products. A photoinduced reocfion in the disrototory mode is therefore wnmetry-allowed.
Figure 8.
Thermal cyciooddition of methylene and ethylene.
Q@
QQ
@Fa
dk
H H Cheldropic Reactions
To illustrate the operation of orbital symmetry in controlling cheletropic reactions, the simplest example to consider is the addition of methylene to ethylene (eqn. (18)).
Combining the nonbonding methylene orbitals with the a and a* orbitals of ethylene produces thc correlation diagram shown in Pigure 8. The combination orbital of lowest energy, [s wx], correlates with the symmetric product orbital, [ol az]. The antisymmetric product orbital, [ol - az] has the symmetry of the reactant combination, [a* wx]. The doubly occupied orbital [a wl+W2l2 may be regarded as the interaction of a filled bonding s orbital of ethylene with the unoccupied nonbonding methylene orbital (wl o z ) Similarly, [a* o 1 2 p represents the interaction of the filled nonbonding (w, - wz) orbital with the unoccupied antibonding a* orbital of ethylene. I n short, (@I - w2) is occupied and (wL wz) is vacant in the methylene reactant. Furthermore, the (w~- oz) orbital reacts in an antarafacial mode so that the overall reaction mode conforms to an allowed thermal reaction designated as aZ2 (w, - 02),2. TOclarify that (w, up)reacts antarafacially, note that the plane of the CH, molecule is also a nodal plane with respect to (wl - oz), and in this respect the (wl - w2) orbital resembles a 2p orbital. Reaction of (w, - wr) on opposite sides of the nodal plane containing the nucleus represents antarafacial reaction.
+
+
+
+
+
+
+
The transition state for this reaction is chosen to conform with the experiment,al fact that singlet carbenes add to alkenes nith preservation of configuration about the alkene carbons. For example, cis-1,2-disubstituted alkenes give cis-1,2-disnbstituted cyclopropanes, and this is consistent with the alkene reacting in the sS2 mode. Also, the methylene molecule is shown in eqn. (18) as bonding with the ethylene molecule by way of a transition state that resembles the configuration of the nuclei in cyclopropane. There is then a minimum change in the positions of the nuclei as electron-reorganization occurs on going from reactants t,o products. This approach to (2 2) cheletropic reactions may appear different from that presented by Woodward and Hoffmann ( I ) , hut it is entirely equivalent as will be seen from the following discussion. Having adopted a configuration for the interacting reactants, the problem now is to see if the reacting orbitals have the right symmetry to lead to the ground state product orbitals. First we have to consider the symmetries of the two nonbonding orbitals on the methylene carbon. For convenience, they may be designated as wl and wz. There are two possible combinations of these orbitals, one of which is symmetric (0, w2) and the other antisymmetric (w, - 0%)with respect to the plane passing through the three nuclei.
+
-
nodal , -
+
+
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w,
- w,(antarafacial)
2 p (antarafacial)
The type of reaction just discussed has been called a nonlinear disrolatory cheletropic reaction. It is disrotatory because the a component reacts in the ax2mode. I t is nonlinear because the methylene molecule reacts in the (w, - wz),%ode; and for the filled (w, - w~) orbital to correlate with the filled spz-hybrid orbital of singlet methylene with preservation of orbital symmetry, the nuclei have to change positions as shown below
+
node
!
cyclobutane by a (as2 as2)process is predicted by t,he rule to be photocheinically "allowed" since the total number of orbital participants (1 1) is even. Like2) reaction of cyclobutene wise, the electrocyclic (2 to give 1,3-butadiene by a conrotatory (usZ re2) or (a,2 as2) process is thewnally allowed since (1 0) or (0 1) is odd; a disrotatory (ua2 an2)or (ua2 process is photochemically allowed since (0 0) or (1 1) is even.. Further, the rule predicts that (2 2) cycloaddition of methylene to ethylene (eqn. (18)) is an allored thermal reaction in the (sa2 we2) mode; this reaction mode was described previously in some detail to establish that the antisymmetric nonbonding orbit,al on the methylene unit reacts antarafacially (Yig. 8). 1Iany more examples showing the application of this rule could be cited but space limitations preclude their mentiou here. The main difficulty in applying the rule comes when two or more allowed reaction modes are predicted for one reaction. Sometimes these turn out to be equivalent, as in (2 2) electrocyclic reactions just discussed-but they may not always be equivalent. While cert,ain modes of reaction may be rejected as sterically impossible, a clear choice as to the preferred mode may not always be made, especially when subtle steric factors are involved. Hovever, when used with intuitive reasoning, the generalized selection rule becomes a powerful predictive tool of considerable value, particularly to the synthetic organic chemist.
+
+
+
+
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This means that,, as singlet methylene approaches ethylene, it has to undergo rehybridization wit,li a change in the positions of the hydrogen nuclei to form orbitals of the correct symmetry to give cyclopropane product. Generalized Selection Rules
The orbital symmetry arguments developed in the previous section may be applied to many other reactions-but it is impractical t,o consider more t,han a few examples in an art,icle of t,his kind. The reader, however, may be interested to pursue this independently, and several reactions for which orbital diagrams may be easily constructed are listed in the Appendix. Recently, a generalized selection rule bas been proposed by Woodxard and Hoffmann ( 1 ) in order to con~pactly summarize the principles of conservat,ion of orbital symmetry in concerted or element,ary react.ions. The selection rule may be simply stated as: A veactio?~.nzay pvoceed thernlally i v a conceited ma?lnev alien the total numbev of w,", wX2,as2", aa2"', us2", and oG2"'pavticipants i s odd, where 7 r and m ave odd aad euen integew, vespeclively. Fov a photochemical concevterl pvocess, the total n,unzbev of pavticipants must be euen. The total number of orbital participants referred to in t,his rule may be det,ermined from the table vhich states that a system of orbitals in ~ ~ h i the c h number of electrons is a multiple of four (0, 4, S) counts one if it reacts antavajacially and zero if it reacts supvafacially. The remaining type of orbital systems ~ ~ i 2,t h6, 10 etc., electrons counts one in the supvajacial mode and zeyo in the antarafacial mode. To apply the rule to a given reaction, the orbital participants and the numbers of electrons associated xith each participant must be identified. Zach participant is then counted as zero or unity according to the reaction mode, antarafacial or suprafacial, as summarized in t,he table. If the sum of the participants (counted as zero or unity) is odd, the reaction is predicted to be thermally allowed (i.e., energetically feasible). All the reactions sho~vnearlier to be energetically feasible by detailed orbital symmetry arguments may also be shown to conform to the generalized selection rule. Thus (2 2) cycloaddition of ethylene to give
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Appendix: Reactions for which Diagrams are Easily Constructed 1) Thermal ryrloxddition of ethylene to cyclobutane may he shown to be energaticslly feaible by way of a t.mnsit,ion state cormsponding to n (r2 s2)process. This eunfigorat.ion is shown in s t n ~ c t n r eXI. The forward s component. is shown to react ~ntarafaeially(r2)with its imdear framework perpendicular to the plane of the paper. The rear r component reacts suprafacially ( T , ~and ) projects toward the viewer such bhat the rear r lobes are eclipsed.
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The wbital diagram eomesponding t,u (.his co~digorat,iooshows r.*)' correlates with (a- d2, and that the combination (r. (T,* s,)l correlates with (m ~ 1 ) ~ . 2) A wvelsible 8 ~ displacement 2 reaction (eqn. (10)) proceed) ' . c process ing wit,h inversion of configorstion iu a (was
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Orbital Participants (a2", sZm,P , P Counted as Unity or Zero
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w2, wo)
The retention mechanismis a(wsB+o . ' ) process. T h e orbital d i e grams corresponding to each of these mechanisms predict that the ret,eotioamechanism should have the higher activabion energy (:$I. 3 ) Cyclosddition uf hubadiene aud ethylene to give cyclohexene by the (r,' z,Z) mode (Iliels-Alder) shows that t,he combination of ground reacting orbitals (s, r)%, (7,- *)%and ( m r*)¶ correlates with (o, m T)', ( m * cz' r)%,and (c, - m r*)* and hence with the filled product orbit,ala (a, a)%, m2, and ( n - Q ) ~respectively. ,
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Volume 48, Number 12, December 1971
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Literature Cited
4) Thermal deeomposit,ian of the cyelicsolfone V in eqn. (10) is a c,Z or (r,' ma2)process. All ot.bilnl dingram corresponding to this eonfignraliun shows that thesymmetric nonbonding combination orbital (w w2) is doubly occupied in the SO* prodnat and the antisymmetrio (al - wi) o h i l a l is vacant. The SO, moleerile depsrts in n linear mxtrtre~.-hence the (el.minalogy linear ehelelropic reaction (1). 5) 1,3-Sigmat,ropic reawangemeots (eqn. (17)) ran be shown to involve a ( o 2 *.I) pt.ocess with inversion a t the migmting group R for there to be good orbital o v e h p and gnlund state orbital correlation. The combination ~.eaelanlol.bilals (s r ) % and (s - r)acorrelste, respectively, wilh *land oZinthcpraduet. 6) Ring-opening of cyclop~~opyl calions l o ally1 cations3 may be predicted as thermal disrulat,ory processes (o,' w?) and as photochemical canrotatory processes (n,' wP). 7) 1,2-Carbanion rearrangements may be predicted tu orem. with inversion of configoration a t the migrating gmltp for a truly concerted process (
