The Hückel secular determinant for ethene is:

Therefore E=a + b (for x = –1), or E=a – b (for x = 1).

To find the coefficients, i.e. to find the MO, for the lower energy E₁=a + b (x = –1), we substitute into the secular equations (eq. 6):

This gives c₁₁=c₁₂

y₁ = c₁₁ ( f₁ + f₂ )

The normalization condition is:

Therefore the lower energy p MO of ethene is:

Summary: the Hückel MOs of ethene