Orbitals bonding, allylic system

Problem 8.28 (a) Apply the MO theory to the allyl system (cf. Problem 8.26). Indicate the relative energies of the molecular orbitals and state if they are bonding, nonbonding, or antibonding, (b) Insert the electrons for the carbocation C,H, the free radical C,H, and the carbanion CjH, and compare the relative energies of these three species. 

The ring opening of cyclopropyl cations (pp. 345, 1076) is an electrocyclic reaction and is governed by the orbital symmetry rules.389 For this case we invoke the rule that the o bond opens in such a way that the resulting/ orbitals have the symmetry of the highest occupied orbital of the product, in this case, an allylic cation. We may recall that an allylic system has three molecular orbitals (p. 32). For the cation, with only two electrons, the highest occupied orbital is the one of the lowest energy (A). Thus, the cyclopropyl cation must... 

In order to construct a bonding model for a planar conjugated ring, we follow the procedure outlined for the allyl system in the previous section and make the choice of sp2 hybridization on each carbon. The a framework is then constructed from these sp2 hybrids and the hydrogen lj orbitals, leaving a p orbital on each carbon. We next concentrate on the interactions among these p orbitals."... 

As an example of the Hiickel method we will examine the allyl system. There are three basis orbitals, numbered as shown in 1. Atoms 1 and 2 tire bonded to each... 

In allylic systems, favorable overlap of the p orbitals of the n system should require a coplanar arrangement of the three sp2 carbons and their five substituent atoms evidence that such a structure is indeed preferred comes, for example, from proton magnetic resonance observations that demonstrate barriers to bond rotation in the isomeric dimethylallyl ions 21, 22, and 23. These ions form stereo-specifically from the three dimethylcyclopropyl chlorides (Section 12.2), and barriers to rotation about the partial double bonds are sufficiently high to prevent interconversion at low temperature. At — 10°C, 21, the least stable isomer,... 

Another way to describe delocalized bonding uses die MO approach. The same principles of overlap of AOs can be applied to systems where more than two p AOs overlap to form n systems. First, die number of MOs produced by die overlap will be die same as die number of atomic p orbitals which interact. Thus for the allyl system where three contiguous p orbitals interact, there will be three MOs produced from die interaction of three 2p AOs. For the butadienyl system where there are four contiguous p orbitals interacting, four MOs will result, and so on. 

In MO theory a o and a n bond are both just two overlapping orbitals and a monosub-stituted bond is similar to an allyl system. Did you realize that 42 must have the same structure as the HOMO of an end (p. 29) ... 

For analysis of the photochemical reaction, the interaction of the hydrogen Is orbital with -tt3 of the allyl system is used. The interaction is bonding at both the migration origin and terminus, so the [ 1,3] sigmatropic rearrangement is photochemically allowed. 

Conjugated compounds undergo a variety of reactions, many of which involve intermediates that retain some of the resonance stabilization of the conjugated system. Common intermediates include allylic systems, particularly allylic cations and radicals. Allylic cations and radicals are stabilized by delocalization. First, we consider some reactions involving allylic cations and radicals, then (Section 15-8) we derive the molecular orbital picture of their bonding. 

Remember that no resonance form has an independent existence A compound has characteristics of all its resonance forms at the same time, but it does not resonate among them. The p orbitals of all three carbon atoms must be parallel to have simultaneous pi bonding overlap between Cl and C2 and between C2 and C3. The geometric structure of the allyl system is shown in Figure 15-10. The allyl cation, the allyl radical, and the allyl anion all have this same geometric structure, differing only in the number of pi electrons. 

Just as the four p orbitals of buta-1,3-diene overlap to form four molecular orbitals, the three atomic p orbitals of the allyl system overlap to form three molecular orbitals, shown in Figure 15-11. These three MOs share several important features with the MOs of the butadiene system. The first MO is entirely bonding, the second has one node, and the third has two nodes and (because it is the highest-energy MO) is entirely antibonding. 

Bromine is more electronegative than carbon and so the C-Br bond is polarized towards the bromine. If this bond were to break completely, the bromine would keep both electrons from the C-Br bond to become bromide ion, Br, leaving behind an organic cation. The end carbon would now only have three groups attached and so it becomes trigonal (sp2 hybridized). This leaves a vacant p orbital that we can combine with the n bond to give a new molecular orbital for the allyl system. 

These labels are useful where there is a choice of type of bonding as with allylic ligands. The metal can either form a c bond to a single carbon (hence T 1), or form a ft complex with the p orbitals of all three carbons of the allyl system and this would be ry If the n complex is M. 

The two p orbitals of ethylene are described as being conjugated with each other in making the % bond. To make longer conjugated systems we add one p orbital at a time to the % bond to make successively the allyl system, butadiene, the pentadienyl system and so on. We continue to separate completely the a framework (using the 2s, 2px and 2py orbitals on carbon with the Is orbitals on hydrogen) from the % system made up from the 2pz orbitals. 

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. 

We can gain further insight by building the picture of the n orbitals of the allyl system in another way. Instead of mixing together three p orbitals on carbon, we can combine two of them in a re bond first, and then work out the consequences of having a third p orbital held within bonding distance of the C=C n bond. We have... 

Even this very approximate procedure uncovers the inherent stability of a delocalized system that is not obvious in this single example. The solution of the 2 x 2 determinant for a system of two p orbitals, such as the p system in ethylene, yields two MOs with energy values of a + p (bonding) and a - p (antibonding). This means that the energy for two electrons in the allyl system (2o + 2 2p) is more stable than two electrons in the ethylene n system. Thus, the... 

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