An Alternative Description Walsh Orbitals

It may be proper at this stage to lead the reader back to the stage where we constructed the localized orbitals of a CH2 group. At that time two valence orbitals were set aside—the 2pv orbital, and the outer (2s, 2pr) hybrid. Both of these orbitals lie in the. r, y plane. Now in our description of cyclopropane, we used bond orbitals to describe the CC bonding these bond orbitals are derived from in-plane (xy y) hybrids on each carbon. The two hybrids which are required on each carbon atom—in ordet to participate in two bond orbitals—are built precisely from the 2py orbital and the (2s, 2pj.) out combination on each CH2 group. 

In the Walsh description, these very same valence orbitals are used on each CH2 group, but one does not go to the trouble of combining them to make new orbitals pointing approximately along the bond directions.11 One uses directly the three local 2pJ/-type orbitals of the three CH2 groups to build one set of three molecular orbitals, and the three local (2s, 2pj.) out -type hybrids to build a second set of molecular orbitals. The procedure is illustrated in Fig. 26. 

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). 

The reader may now wish to compare the three bonding molecular orbitals derived in this manner with the three rcc molecular orbitals shown at the end of the previous section. There is a strong resemblance. This similarity increases if, in the Walsh method, the 2pj/-derived molecular orbitals are allowed to mix with the (2s, 2pz)- 

Another example which illustrates beautifully the mixing of a group orbitals to form delocalized molecular orbitals is benzene. First of all the six crcc bond orbitals interact to give six linear combinations which are delocalized over the entire carbon skeleton. The amplitudes of the various bond orbitals in each rcc molecular 

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