Hückel Molecular Orbital Theory
The Hückel molecular orbital (HMO) method was proposed by Erich Hückel in 1930. It is a very simple LCAO MO Method for the determination of energies of molecular orbitals of π electrons in conjugated hydrocarbon systems, such as ethene, benzene and butadiene etc.
With the help of HMO we can calculate the energy for molecular orbitals by the following method-
1. HMO theory aaplies to π electrons only.
2. Write free π electron approximation.
3. Take a LCAO π molecular orbital treatment as the XY plane.
4. Calculate the energy of HMO as
Ψπ = C1Ψ1 + C2Ψ2 + C3Ψ3 + ... + CiΨi.
where, Ψi is the ith HMO.
Energy is given by the relation-
Eπ = n1E1 + n2E2 + n3E3 + ... + CiΨi.
where, Ei is the energy of a single electron in Ψi. The factors ni may be 1 or 2 or 0 depending upon whether the HMO Ψi is singly or doubly occupied or unoccupied.
5. Write the secular equation from variation treatment and then the corresponding secular determinant.
6. Solve the secular determinant and calculate the total energy of the system.
