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## Hückel theory: applying the Hückel approximation

For the sake of simplicity, the double indexing is omitted, with E, Ψ and ${\mathit{c}}_{\mathit{i}}$ are each an energy ${\mathit{E.}}_{\mathit{n}}$ and the corresponding wave function Ψ_{n}with the coefficients ${\mathit{c}}_{\mathit{ni}}$ meant.

First, in equation 2, the wave function is used as a linear combination of the atomic orbitals.

After multiplying, the integral over the sum is divided into a sum of integrals and the constant coefficients are added in front of the integral. Then the following abbreviations and the normalization of the atomic orbitals are used:

This gives the following equation, in which the Hückel approximations are already indicated by the curly brackets:

Equation 5 is considerably simplified by the Hückel approximations.

In the following, the numerator is abbreviated as Z and the denominator as N.