Summary The Simple HMO Method for Hydrocarbons

The assumption is made that the tt-electron energy can be minimized independently of a electrons. This is an approximation. 

The assumption is made that each n electron sees the same field (the repulsion due to the other n electrons is presumably included in effect, in a time averaged way) so that the n electrons are treated as independent particles. This approximation leads to a total wavefunction that is a simple product of one-electron MOs and a total tt energy that is a sum of one-electron energies. Except for use of the Pauli principle to build up configurations, no explicit treatment is made of electron spin. 

The basis set is chosen to be a 2pjj AO from each carbon atom in the unsaturated system. Choosing a basis set of AOs means our MOs will be linear combinations of AOs, and so this is an LCAO-MO method. 

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