Huckel molecular orbital method assumptions

In summary, we have made three assumptions 1) the Bom-Oppenheimer approximation, 2) the independent particle assumption governing molecular orbitals, and 3) the assumption of n-molecular orbital theory, but the third is unique to the Huckel molecular orbital method. 

The simplest molecular orbital method to use, and the one involving the most drastic approximations and assumptions, is the Huckel method. One str ength of the Huckel method is that it provides a semiquantitative theoretical treatment of ground-state energies, bond orders, electron densities, and free valences that appeals to the pictorial sense of molecular structure and reactive affinity that most chemists use in their everyday work. Although one rarely sees Huckel calculations in the resear ch literature anymore, they introduce the reader to many of the concepts and much of the nomenclature used in more rigorous molecular orbital calculations. 

The fundamental assumption of HMO theory is that we may calculate molecular orbitals through a process known as LCAO the linear combination of atomic orbitals. That is, we use some combination of the wave functions of the atomic orbitals to produce a set of molecular orbitals. In the Huckel method, we combine a set of atomic p orbitals to produce a set of n molecular orbitals. For a set of n parallel p orbitals, the Huckel molecular orbitals have the form shown in equation 4.1. In this equation is the wave function... 

Within the Extended-Huckel method the bond energy is equal to the difference between the sum of the occupied molecular orbitals in the complex and the sum of the occupied molecular orbitals in the fragments. This follows from Eq.(2.31) when the change in intra-atomic electron-electron repulsion is ignored. This is the last assumption involved in the Extended-Huckel method ... 

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