Sigma-pi separation

The Hückel method or Hückel molecular orbital method (HMO), proposed by Erich Hückel in 1930, is a very simple linear combination of atomic orbitals molecular orbitals (LCAO MO) method for the determination of energies of molecular orbitals of pi electrons in conjugated hydrocarbon systems, such as ethene, benzene and butadiene. It is the theoretical basis for the Hückel's rule. It was later extended to conjugated molecules such as pyridine, pyrrole and furan that contain atoms other than carbon, known in this context as heteroatoms. The extended Hückel method developed by Roald Hoffmann is computational and three-dimensional and was used to test the Woodward–Hoffmann rules.

It is a very powerful educational tool, and details appear in many chemistry textbooks.

The method has several characteristics:

The results for a few simple molecules are tabulated below:

The theory predicts two energy levels for ethylene with its two pi electrons filling the low-energy HOMO and the high energy LUMO remaining empty. In butadiene the 4 pi electrons occupy 2 low energy MO's, out of a total of 4, and for benzene 6 energy levels are predicted, two of them degenerate.

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