The Description of Molecules by Sigma and Pi Orbitals

An orbital pointing toward an adjacent orbital is called a r orbital (sigma orbital), and the bond involving the cr orbitals of two atoms is called a o- bond (sigma bond the Greek letter a is analogous to s). Thus in methane the four tetrahedral orbitals of the carbon atom are a orbitals, and the four C—H bonds are cr bonds. 

The two descriptions of ethylene and acetylene, the bent-bond description and the o-.Tr-bond description, represent in fact essentially the same structure. Quantum mechanical calculations carried out for a bent-bond wave function and a o-.Tr-bond wave function give the same results. It is essentially a matter of personal choice that determines the use of one description or the other. 

For example, each description requires that the ethylene molecule be planar. In the bent-bond description the plane perpendicular to the plane of the molecule is the plane of the two bent bonds, and in the cr,7T-bond description it is the plane of the two tt orbitals. In each case rotation of the two ends of the molecule out of the plane decreases the overlap of the atomic orbitals and weakens the bonding. 

As described in the preceding section, the bent-bond picture provides an explanation of the observed decrease in carbon-carbon distance from 154 pm in ethane to 133 pm in ethylene and 120 pm in acetylene. The cr.TT-bond picture does not, because it is not evident that there is a relation between bond lengths for sp a- bonds, sp- cr bonds, and tt bonds. With a little experience, however, it becomes possible to discuss the properties of substances in terms of their structure in a satisfactory way on the basis of either of the two descriptions. 

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