Extended Huckel method

The extended Hückel method is a semiempirical quantum chemistry method, developed by Roald Hoffmann since 1963.^[1] It is based on the Hückel method but, while the original Hückel method only considers pi orbitals, the extended method also includes the sigma orbitals.

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The extended Hückel method can be used for determining the molecular orbitals, but it is not very successful in determining the structural geometry of an organic molecule. It can however determine the relative energy of different geometrical configurations. It involves calculations of the electronic interactions in a rather simple way where the electron-electron repulsions are not explicitly included and the total energy is just a sum of terms for each electron in the molecule. The off-diagonal Hamiltonian matrix elements are given by an approximation due to Wolfsberg and Helmholz that relates them to the diagonal elements and the overlap matrix element.^[2]

H_ij = K S_ij (H_ii + H_jj)/2

It is common in many theoretical studies to use the extended Hückel molecular orbitals as a preliminary step to determining the molecular orbitals by a more sophisticated method such as the CNDO/2 method and ab initio quantum chemistry methods. This leads to the determination of more accurate structures and electronic properties.

The method was first used by Roald Hoffmann who developed, with Robert Burns Woodward, rules for elucidating reaction mechanisms (the Woodward-Hoffmann rules). He used pictures of the molecular orbitals from extended Hückel theory to work out the orbital interactions in these cycloaddition reactions.

A closely similar method was used earlier by Hoffmann and William Lipscomb for studies of boron hydrides.^{[3] [4]} The off-diagonal Hamiltonian matrix elements were given as proportional to the overlap integral.

H_ij = K S_ij.

This simplification of the Wolfsberg and Helmholz approximation is reasonable for boron hydrides as the diagonal elements are reasonably similar due to the small difference in electronegativity between boron and hydrogen.

The method works poorly for molecules that contain atoms of very different electronegativity. To overcome this weakness, several groups have suggested iterative schemes that depend on the atomic charge. One such method, that is still widely used in inorganic and organometallic chemistry is the Fenske-Hall method. ^{[5] [6]}

A recent program for the extended Hückel method is YAeHMOP which stands for "yet another extended Hückel molecular orbital package".^[7]

References

See also

• Erich Hückel
• Roald Hoffmann