Ethylene by the LCAO Method

Ethylene is easily treated as a x-electron problem and provides a good starting point for a general approach to un— saturated molecules. We shall assume that the (r-bond framework has conventional properties and concentrate on the rr electrons. Ethylene then becomes a two —orbital problem like H2. The 2 orbitals of carbon are here represented with + and lobes because the X function of a 2p orbital has a node in (and changes sign below) the plane, which is perpendicular to the axis of the orbital and passes through the nucleus. 

The energy levels are as shown, and in the lowest state two electrons have the energy Z a + 3) where a and p have appropriate values for 2p carbon orbitals overlapping in the TT manner. 

Consider how the energy of acetylene might be calculated and possible difficulties in comparison of the value so obtained with E, calculated for ethylene. 

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