Antarafacial component

The Woodward-Hoffman rules (1) state that "A ground state pericyclic change is symmetry allowed when the total number of (4q + 2) suprafacial and (4r) antarafacial components is odd". 

The reaction via a planar transition state is n2s + n2s. Here only one of the two new C—C bonds can be formed. This will raise its activation energy impossible to be reached. So there are two (4q + 2) electron suprafacial components and no antarafacial component. Since the total number of counting components is two, an even number, the reaction is thermally disallowed. 

The linear cheletropic reactions in which the polyene is a suprafacial component (i.e., involving disrotatory motion of the termini) will be allowed if it has a total of (4n + 2) electrons. But linear cheletropic reactions in which the polyene is an antarafacial component (i.e., involving conrotatory movement of the termini) are allowed if it has a system of 4n electrons. 

Cycloadditions of ketenes and alkenes have been shown to have synthetic utility for the preparation of cyclobutanones.101 The stereoselectivity of ketene-alkene cycloaddition can be analyzed in terms of the Woodward-Hoffmann rules.102 To be an allowed process, the [2n + 2n] cycloaddition must be suprafacial in one component and antarafacial in the other. An alternative description of the transition state is a [2ns + (2ns + 2ns)] addition.103 Figure 6.6 illustrates these transition states. The ketene, utilizing its low-lying LUMO, is the antarafacial component and interacts with the HOMO of the alkene. The stereoselectivity of ketene cycloadditions can be rationalized in terms of steric effects in this transition state. Minimization of interaction between the substituents R and R leads to a cyclobutanone in which these substituents are cis. This is the... 

This argument demonstrates in an entirely general way that the number of phase inversions in the interaction diagram for a simply connected pericyclic transformation is zero if the number of antarafacial components is even and one if the number of antarafacial components is odd. In order to complete the link between the Woodward-Hoffmann and Dewar-Zimmerman points of view, it remains only to find the total number of electrons in the completed ring. A 4q system contains an even number of pairs and a 4q + 2 system an odd number of pairs therefore any system obtained by joining components will have a total number of electrons satisfying the formula 4q (even number of pairs total) if there are an even number of 4q + 2 components and a total number satisfying 4 + 2 (odd number of pairs total) if there are an odd number of 4q + 2 components. 

A problem with this explanation is that it is a bit more difficult to explain those pericyclic reactions that we shall come to in Chapter 4, which smoothly take place in spite of their having a total of 4n electrons. We shall find that these all show stereochemistry involving an antarafacial component. It is possible to include this feature in the aromatic transition state model—if the... 

In a [1,7] hydrogen shift, the allowed pathway is an antarafacial shift, in which the hydrogen atom leaves the upper surface at C-l, and arrives on the lower surface at C-7. This can be drawn 5.3 as a [a2s+n6a] process or 5.4 as a [a2a+K6s] process. This time it is structurally an antarafacial shift, but the developing overlap that happens to be illustrated can be described with one suprafacial and one antarafacial component either way round. It is helpful to draw as many suprafacial components as possible, i.e. preferring 5.1 to 5.2, since the structurally suprafacial reaction is then also described with suprafacial overlap developing. Similarly it is helpful to draw 5.3 rather than 5.4, since that makes the antarafacial component the triene system, from one side of which to the other the antarafacial shift of the hydrogen is taking place. 

Now what about the suffixes s and a The suffix s stands for suprafacial and a for antarafacial. A suprafacial component forms new bonds on the same face at both ends while an antarafacial component forms new bonds on opposite faces at both ends. See how this works for the Diels-Alder reaction. Here is the routine. 

In the routine above, we chose to use our <7 bond so that we got inversion at one end and retention at the other. That was why we identified it as an antarafacial component. If we had chosen another style we should have got different descriptions of the components, but the reaction would still have been allowed—for example, changing just one connecting line. 

Reactions involving a total of (An) electrons (an even number of curly arrows) are allowed if there is one antarafacial component and all the others are suprafa-cial. In this case, if the dashed, bold or coloured lines include only one antarafacial component, the number of (4q + 2)s and (4r)a components will add up to an odd number, and the drawing will show the geometry of a symmetry-allowed reaction. 

This is known as the linear approach, in which the carbene, with its two substituents already lined up where they will be in the product, comes straight down into the middle of the double bond. The two sulfur dioxide reactions above, 6.127 and 6.128, are also linear approaches, but these are both allowed, the former because the total number of electrons (6) is a (An I 2) number, and the latter because the triene is flexible enough to take up the role of antarafacial component. The alternative for a carbene is a nonlinear approach 6.130, in which the carbene approaches the double bond on its side, and then has the two substituents tilt upwards as the reaction proceeds, in order to arrive in their proper orientation in the product 6.131. The carbene is effectively able to take up the role of the antarafacial component as with ketenes, it is possible to connect up the orthogonal orbitals, as in 6.132 (dashed line), to make the nonlinear approach classifiably pericyclic and allowed. This avoids any problem there might be with reactions like 6.127 and 6.128 being pericyclic and the clearly related reaction 6.130—>6.131 seeming not to be. Similar considerations apply to the insertion of carbenes into cr bonds. 

A thermally activated pericyclic reaction will proceed via a Mobius topology containing one antarafacial component if the cyclically conjugated TT-electrons equal [4n] (n = 0, 1,2,...). 

Thermally, it will proceed via a Mobius topology involving one antarafacial component. Both methyl groups will rotate in the same direction conrotation) leaving one endocyclic and one exocyclic. However, under photochemical conditions, a [4n] ir-reaction is predicted to proceed via a Hiickel topology with suprafacial (disrotation) bond formation. 

Inversion of stereochemistry counts like antarafacial and two antarafacial components count like suprafacial. 

Why is it that ketenes are able to react antarafacially, and alkenes are not After all, the ir orbital of the ketene that reacts antarafacially is also present in an alkene. In ketenes, one of the C atoms has only the sterically undemanding O atom attached to it. Common alkenes have sterically demanding substituents on both ends of the antarafacial component. The substituents at one end of the antarafacial alkene jut directly into the path of the other alkene in the TS, sterically inhibiting the reaction. 

The Woodward-Hoffmann rules for all pericyclic reactions (Table 4.6) are as follows. A pericyclic reaction involving an odd number of electron pairs must have an even number of antarafacial components under thermal conditions and an odd number of antarafacial components under photochemical conditions. A pericyclic reaction involving an even number of electron pairs must have an odd number of antarafacial components under thermal conditions and an even number of antarafacial components under photochemical conditions. In practice, of course, even number of antarafacial components means no antarafacial components, and odd number of antarafacial components means one antarafacial component. ... 

Thus the opening of cyclobutene to butadiene is, in a sense, the cycloaddition of the <7-bond to the rc-bond (Fig. 4-17). The HOMO and the LUMO are then smoothly connected, with a suprafacial component on the rc-bond and an antarafacial component on the c-bond. It is therefore a [n2s + [Pg.103]

In a very small number of reactions, the twisted geometry of one of the components makes it possible for antarafacial attack to take place on one of the components. In these rare cases, since the opposite lobe of the antarafacial component is being used, the An+ 2 rule is broken, and An electrons becomes the favoured total. Heptafulvalene (2) has a twisted structure (Figure 7.9) and reacts antarafacially with tetracyanoethene to give the adduct 3 (reaction 7.4). 

We have established earlier in the chapter that there will be favourable Frontier Orbital HOMO-LUMO interactions when two molecules approach for a cycloaddition reaction if there are 4n + 2 electrons involved in a fully suprafacial reaction, or 4n electrons if there is an antarafacial component. For delocalization of electrons in the transition state, the fully suprafacial cycloaddition reaction will result in a continuous cyclic overlap of atomic orbitals in the transition state without a phase change, for which 4n + 2 electrons will give aromatic stabilization. For a cycloaddition with one antarafacial component, the cyclic overlap of orbitals will give a Mobius system for which 4n electrons will provide stabilization. Thus the two approaches, Frontier Orbitals and the Aromatic Transition State will always be in agreement favourable... 

Figure 7.14 Reaction paths for 1 pericyclic reactions involving aromatic and non-aromatic numbers of electrons. Number of aromatic electrons is 4n + 2 for Huckel systems with no antara-facial components, or An electrons for Mobius systems with one antarafacial component...

Two ethene molecules do not react thermally to give cyclobutane (reaction 7.2). This 4n system has the wrong number of electrons for suprafacial attack to take place, and geometric reasons make it impossible for overlap to take place from a p-orbital lobe away from the direction of approach to give an antarafacial component (Figure 7.15). 

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