1. Divide the matrix by b, and find the new matrix?
2. If the diagonal elements are represented with x, what is x in terms of a, b, and E.
3. Update the matrix using x on diagonal elements?
4. Find the determinant of the matrix and solutions for x?
5. Now represent E in terms of a and b by replacing the values of x.
6. Now find |₁ using the positive value of x and |₂ using negative value of x.
7. Assuming |₁ corresponds to HOMO and ₂ corresponds to LUMO, what is the E_LUMOE_HOMO?
8. Normalize each molecular orbital wave function if you can, what is the normalization coefficient?

7. Molecular orbital theory has been very successfully applied to large conjugated systems, especially those containing chains of carbon atoms with alternating single and double bonds. An approximation introduced by Hckel in 1931 considers only the delocalized p electrons moving in a framework of A-bonds. This is, in fact, a more sophisticated version of a free-electron model. The simplest hydrocarbon to consider that exhibits a bonding is ethylene (ethene), which is made up of four hydrogen atoms and two carbon atoms. The bonding is shown below: 1 H Since Hckel theory is a special consideration of molecular orbital theory, the molecular orbitals yi) can be described as a linear combination of the 2pz atomic orbitals o at carbon with their corresponding {ci} coefficients: vi)=c101)+c2 02). This equation is reduced into the following