Cyclopropane, antibonding orbitals

In the interaction of the local 2pv orbitals, two more bonding molecular orbitals are formed against one less bonding. In all previous cases the opposite occurred. This is due to the negative overlap between adjacent 2py orbitals—whether, by convention, all positive lobes point in the clockwise direction, or whether all positive lobes point in the anticlockwise direction. The two bonding 2pv combinations in fact fall below the two antibonding (hybrid 2s, 2px) combinations. The former each have two electrons while the latter are empty. The six electrons of the three C—C bonds are nicely accounted for. The method creates simultaneously the acc and or c molecular orbitals of cyclopropane (note that the latter three lie relatively close in energy). 

Figure 22.8. Conrotatory ring opening of cyclopropane (7) to what Hoffmann called the (0,0) conformation of propane-1,3-diyl (8). The in-phase combination of Ip-n AOs in the LUMO is destabilized by an antibonding interaction with the re combination of C—H bonding orbitals at C2. A lower energy MO, which is not shown, is stabihzed by h3fperconjugative electron donation that is, the bonding version of this interaction. The out-of-phase combination of 2p-n AOs in the HOMO has a node at C2 hence, it does not mix with the C—H orbitals at this carbon.

A related example is given in equation 1751. Here, both roles of the n-7t excited state are involved. The antibonding electron density opens that a,/J bond which will afford a dicyano-stabilized odd-electron center. Its oxygen p v orbital attacks the ipso carbon of the phenyl group on the cyclopropane ring to give the spiro-diradical species shown. This then opens to photoproduct. 

In the case where the substituent is a donor, its HOMO interacts mainly with the cyclopropane 4 4 orbital (Figure 7.4, p. 196). 4 4 is antibonding between C, and C2 and between C4 and C3, but bonding between C2 and C3. The cyclopropane flattens, but the effect is smaller, 4 4 being more antibonding than 41, is bonding. 

Solution phase reaction of an electrophile with cyclopropane(s) requires favorable interaction of the LUMO of the electrophile with the HOMO degenerate, symmetric or anti-symmetric, orbitals of cyclopropane . The Is orbital of H or one lobe of the p-orbital of a carbocation or electrophile can react with the anti-symmetric (3e ) orbital (Figure 2) with consequent reduction in bonding in adjacent carbon-carbon bonds and relief of C(2)-C(3) antibonding. Completion of this carbon-proton or carbon-electrophile bond results in a corner-protonated cyclopropane (39). Reaction of an electrophile, e.g. proton or carbocation, with the degenerate symmetric 3e orbital (Figure 3) will give an... 

Consideration of the unsaturation of cyclopropane led the author to compare the attack of a proton on cyclopropane with the formation of a 7r complex. Hiickel (3) determined mathematically the most stable structure for a protonated cyclopropane. The representation given is imperfect since it is concerned with only one resonant structure there are three possibilities as one of the p orbitals is antibonding. In fact, it has been calculated that the bonds formed by the overlap of the p orbitals are occupied by four electrons, while only two electrons are associated in the overlap of three sp2 orbitals in the center of the ring. In this representation, the C-H bonds are represented by sp2 hybrid orbitals. 

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