Orbital properties Hiickel approximations

All this suggests a further simplification, which has proved to be eminently successful in many cases. It is known that independent electron treatments, such as the Hiickel (HMO) treatment2 or the extended Hiickel treatment (EHT)172, which do not take the electron-electron interaction explicitly into account, yield—by and large—orbitals derived from sophisticated SCF calculations. In particular, the HMO and ETH molecular orbitals reflect faithfully the symmetry and nodal properties of their counterparts obtained from SCF treatments. 

Summary. Because of the simplicity of the method, carrying out HMO calculations became a favorite pastime of organic chemists, and the results of HMO calculations have been tabulated for hundreds of compounds. (See C. A. Coulson and A. Streitwieser, Jr., Dictionary of ir-Electron Calculations., W. H. Freeman, 1965 A. Streitwieser, Jr., and J. I. Brauman, Supplemental Tables of Molecular Orbital Calculations, Pergamon, 1965 Heilbronner and Straub, Hiickel Molecular Orbitals, Springer-Verlag, 1966.) The HMO method was widely used to rationalize and predict the properties and reactivities of conjugated compounds. In view of the crudity of the HMO approximations, the fact that the method works as well as it does is surprising and not yet fully explained. 

The important conclusion to be drawn from these observations is that the assumption of equivalent bond orbitals 2 as used in an EBO treatment can be validated by the properties of LMOs Aj derived from ab initio calculations. The mathematical formalism for handling LMOs according to equations, 32 and 33 is exactly the same as that of an EBO model, which implies that this Hiickel-type treatment is capable of yielding excellent approximations to the SCF orbital energies Sj and the corresponding CMOs (pj of saturated hydrocarbons. 

The earliest semiempirical methods were well in advance of ab initio methods partly because of the limits on computing power. The first of these is the ir-molecular orbital (MO) theory of conjugated and aromatic molecules proposed by Hiickel " in 1931. Most succeeding semiempirical theories are direct descendants of Hiickel s original approach wherein one or more of the approximations has been improved. It is interesting to note that Hiickel theory in its original form still sees infrequent application to properties such as electric susceptibilities, soliton dynamics, and others. 

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