The Hückel approximations applied to ethene

Making approximation (iii) and taking f₁ and f₂ to be normalized (i.e., that S₁₁ and S₂₂ both equal 1) the secular equations in (2) become

Simplification of the Hückel molecular orbital (HMO) matrices

The secular equation for ethene, once the Hückel approximations have been applied, should have the form:

To give this equation a simpler form we divide through each line by b and set x=(a – E)/b to obtain:

or, in matrix form:

The energies are now measured in units of b (which you should remember is a negative number!)

The Hückel secular determinant for ethene