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

(4)

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

(6)

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

The Hückel secular determinant for ethene