Introduction to the Hückel method

Since the Hamiltonian is written simply as a sum of one-electron terms:

[Equation #1]

it follows that the total energy is the sum of one-electron energies. The sum is over all electrons. Since each molecular orbital is doubly occupied (for a normal closed shell hydrocarbon, which is the class we shall restrict ourselves to for now), this is twice the sum of energy terms for each molecular orbital:

[Equation #2]

The [epsilon] terms are called orbital energies. The sum is over the m occupied molecular orbitals. This corresponds to the simple picture of filling orbitals in order of ascending energy.

[Orbital energy picture]

Each molecular orbital [psi]i is now described as a linear combination of atomic orbitals, [phi]µ:

[Equation #4]

Our aim is to find the values of the coefficients Cµi that give the best molecular orbitals. The sum is over n atomic orbitals. Since we are describing the [pi] electron system of an aromatic or conjugated hydrocarbon, n is simply the number of carbon atoms in the conjugated system. We will simply call this "the number of atoms" in future.

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