Carbocations HOMO-LUMO interactions

The internal production of radicals, carbanions or carbocations in polymers also leads to intrinsic polarons or solitons. The charged states lie between the HOMO-LUMO states on account of interactions with the environment, i.e. in the band gap (see, for example, [379]). 

One way to consider the orbital interactions is to think of the process as migration of a carbocation across a butadiene tt system. This is a reasonable choice because, in contrast to Example 6.25, the reacting species is already charged. If we consider the reaction as interaction between the LUMO of the carbocation (atomic p orbital) and the HOMO of the butadiene tt system ( P2X we can represent the interaction visually as follows ... 

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... 

Carbocations are electron-deficient species that are the most important intermediates in several kinds of reactions. A common model for carbocation stmcture is a planar species exhibiting sp hybridization, as shown in Figure 2.4 for methyl cation. The p-orbital that is not utilized in the hybrids is empty and is often shown bearing the positive charge since it represents the orbital available to accept electrons. There is a vacant p orbital perpendicular to the plane of the molecule this is the LUMO (lowest unoccupied molecular orbital). In all reactions of carbocations there is an interaction between this LUMO and the HOMO (highest occupied molecular orbital) of another molecule. A structure with an empty p orbital should be more stable than a structure in which an orbital with s character is empty. In general, a carbocation is a purely ionic species. 

---