Cations with three atom allyl system

There are other stereochemical features which have nothing to do with the symmetry of the orbitals, and are much less powerfully controlled. In many cycloadditions, there are two possible all-suprafacial approaches one having what is called the extended transition structure 2.102, in which the conjugated systems keep well apart, and the other called the compressed 2.103, where they lie one above the other. Both are equally allowed by the rules that we shall see in Chapter 3, but one will usually be faster than the other. This type of stereochemistry applies only when the conjugated systems have at least three atoms in each component it is therefore only rarely a consideration. It shows up in the cycloadditions of allyl cations to dienes, where the two adducts 2.56 and 2.57 on p. 13 are the result of the compressed transition structure 2.104 and the extended 2.105, respectively, with the former evidently lower in energy. 

The cation, radical and anion have the same a framework 1.4, with fourteen bonding molecular orbitals filled with 28 electrons made by mixing the Is orbitals of the five hydrogen atoms either with the 2s, 2px and 2py orbitals of the three carbon atoms or with the sp2 hybrids. The allyl systems are bent not linear, but we shall treat the % system as linear to simplify the discussion. 

The n system is made up from the three pz orbitals on the carbon atoms. The linear combination of these orbitals takes the form of Equation 1.9, with three terms, creating a pattern of three molecular orbitals, tpi, ip2 and 3. In the allyl cation there are two electrons left to go into the n system after filling the a framework (and in the radical, three, and in the anion, four). 

The symmetries of the MOs of conjugated tt systems with odd numbers of atoms also alternate. The allyl system has three MOs i/fQ (symmetric), tj/i (antisymmetric), and 1//2 (symmetric). In the allyl cation, is the HOMO and i/ri is the LUMO, whereas in the allyl anion, i/fj is the HOMO and ifc is the LUMO. The pentadienyl system has five MOs. In the pentadienyl cation, i/fi (antisymmetric) is the HOMO and ip2 (symmetric) is the LUMO, while in the pentadienyl anion, ip2 is the HOMO and 1/ 3 (antisymmetric) is the LUMO. 

Figure 3.12 shows how the -electrons of the double bond of an allylic cation can move towards the carbon atom bearing the positive charge. This generates an isomeric allylic cation, with the positive charge on the opposite end of the 3-atom system. In free allylic cations, this exchange is so rapid that the two isomers are indistinguishable. In fact, in molecular orbital theory, we consider the system to consist of a single set of orbitals which stretches across all three atoms. Since there is single bond character in each of the bonds, rotation is possible and the three cations, viz. geranyl (3.22), neryl (3.21) and linalyl (3.23), become equivalent. This is often represented as a smear of electrons as shown in structure (3.24) at the foot of Figure 3.12. Therefore in reactions such as those of...

The dication of 5-indacene (19), however, provided a 10 7i-electron periphery free optimization gave Z>2h symmetry and bond orders and charges as shown. A quite different electronic structure has been obtained in this case from that in the dianion. Whereas the latter has a peripheral delocalized 7i-electron system, the cation appears to have a 6 n-electron system in the central ring with allyllic 2 7i-electron systems in the outer rings. Charge is largely concentrated on the end atoms of the allyl systems however, there is little interaction between the three delocalized systems <84T4455>. 

Where is the electron density in the allyl anion it system The answer is slightly more complicated than that for the allyl cation because now we have two full molecular orbitals and the electron density comes from a sum of both orbitals. This means there is electron density on all three carbon atoms. However, the HOMO for the anion is now the nonbonding molecular orbital. It is this orbital that contains the electrons highest in energy and so most reactive. In this orbital there is no electron density on the middle carbon it is all on the end carbons. Hence it will be the end carbons that will react with electrophiles. This is conveniently represented by curly arrows. 

This image focuses our attention on the continuous system of p orbitals, which functions as a conduit, allowing the two it electrons to be associated with all three carbon atoms. Valence bond theory is inadequate for analysis of this system because it treats the electrons as if they were confined between only two atoms. A more appropriate analysis of the allyl cation requires the use of molecular orbital (MO) theory (Section 1.8), in which electrons are associated with the molecule as a whole, rather than individual atoms. Specifically, in MO theory, the entire molecule is treated as one entity, and all of the electrons in the entire molecule occupy regions of space called molecular orbitals. Two electrons are placed in each orbital, starting with the lowest energy orbital, until all electrons occupy orbitals. 

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