Antarafacial, defined

Another anomalous cycloaddition is the insertion of a carbene into an alkene. 6-Electron cheletropic reactions (p. 28) are straightforward allowed pericyclic reactions, which we can now classify with the drawings 3.47 for the suprafacial addition of sulfur dioxide to the diene 2.179 and its reverse. Similarly, we can draw 3.48 for the antarafacial addition of sulfur dioxide to the triene 2.180 and its reverse. The new feature here is that one of the orbitals is a lone pair, which is given the letter co to distinguish it from o- and n-bonds, with suprafacial and antarafacial defined by the drawings 3.45 and 3.46, which apply to all sp3 hybrids and p orbitals, filled or unfilled. 

Fig. 6.9 Suprafacial and antarafacial defined for a p orbital, and the allowed conrotatory interconversion of an aziridine with an azomethine ylid...

Dihydrothiophene-1,1-dioxides (42) and 2,17-dihydrothiepin-1,1-dioxides (43) undergo analogous 1,4 and 1,6 eliminations, respectively (see also 17-38). These are concerted reactions and, as predicted by the orbital-symmetry rules (p. 1067), the former is a suprafacial process and the latter an antarafacial process. The rules also predict that elimination of SO2 from episulfones cannot take place by a concerted mechanism (except antarafacially, which is unlikely for such a small ring), and the evidence shows that this reaction occurs by a non-concerted pathway.The eliminations of SO2 from 42 and 43 are examples of cheletropic reactions, which are defined as reactions in which two a bonds that terminate at a single atom (in this case the sulfur atom) are made or broken in concert. 

So far we have only defined what suprafacial and antarafacial mean on rc-systems (Fig. 2.7), but we need to see how o-bonds are treated by the Woodward-Hoffmann rules. Just as a suprafacial event on a rc-bond has overlap developing to the two upper lobes that contribute to the bond, so with o-bonds (Fig. 3.5a), overlap that develops to the two large lobes of the sp3... 

Day21 has given a careful account of the relationship between the Woodward-Hoffmann rules and Mobius/Hiickel aromaticity, and has defined the terms supra-facial and antarafacial in terms of the nodal structure of the atomic basis functions. His approach makes quite explicit the assumption that the transition state involves a cyclic array of basis functions. Thus the interconversion of prismane (10) and benzene, apparently an allowed (n2s+ 2S+ 2S) process, is in fact forbidden because there are additional unfavourable overlaps across the ring.2... 

In order to describe the ring opening of the aziridine 6.55, we need to define what suprafacial and antarafacial mean when applied to a p orbital. This is shown in Fig. 6.9, and applied there to the conrotatory aziridine opening. When both lines are drawn into the same lobe it is suprafacial, and when there is one line drawn into the top lobe and one into the bottom, it is antarafacial. Since this is neither a n nor a a orbital, it is given the Greek letter uj. The same designations apply whether the orbital is filled (on the left) or unfilled (on the right), and whether it is a p orbital or any of the sp" hybrids. 

A generalization allows easy application of the Rules to any concerted pericyclic reaction involving two-electron bonds for the allowed reaction there must always be an odd number of suprafacial (as opposed to antarafacial) uses of bonds. Here, suprafacial is defined as utilizing both atoms of a C7 bond with retention of configuration or both with inversion with a Trbond, the p orbitals must be used from the same face of the bond. An antarafacial use of a cr bond would give retention at one atom and inversion at the other with a tt bond, the p orbitals must be used from opposite faces of the bond. 

An important pair of terms is suprafadal and antarafacial. These describe the topology of interaction of a given system in a pericyclic transition state, and they are best defined with reference to Figure 15.9. Here, lines which appear as "loops" or "arcs" show where interactions occur on the orbitals. These lines define a geometry for interaction of the orbitals shown with other orbitals. This should become clearer below with examples. 

We have already mentioned the binary nature of the pericyclic reaction rules. If we change the mode of interaction of one of the reactants, we will reverse the allowed / forbidden nature of the reaction. For example, if we change the interaction mode of one of the reaction partners in the cycloaddition from suprafacial to antarafacial, now the [4+2) cycloaddition is forbidden, and the [2 + 2] cycloaddition is actually allowed. The [2+2] cycloaddition is now designated as [ 2 + T 2a]. In Figure 15.10 A we define the [ 2 + 2j] reaction, and in Figure 15.10 B we show a realistic geometry that could achieve the necessary orbital interactions. The two TT systems approach in a perpendicular orientation, and the lines define the suprafacial and antarafacial interactions. 

Figure 15.9 defined suprafacial and antarafacial interactions of a lone pair in a p orbital (called an uj component). Using these definitions, predict if the ring-opening of the cyclopropyl anion shown below will occur in a conrotatory or disrotatory fashion. What will be the stereochemistry of the product ... 

Greek letter w for this purpose. Such to orbitals can interact in a suprafacial or antarafacial sense, as shown in Fig. 3.17. Thus a suprafacial interaction on the occupied -orbital of Xyz is designated 2 (where 2 indicates the presence of two electrons), whereas an antarafacial interaction on the unoccupied p-orbital is denoted by On this basis the electrocyclic conversion of the cyclopropyl cation into the allyl cation (Equation 3.19) is defined as a [ 2g + ] process if it occurs by the disrotatory mode indi-... 

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