The Huckel Model

In the Huckel model, the spin density p(, is taken as the square of the coefficient for the ith atom in the orbital to which the unpaired electron is assigned, Cto2. 

Prior to considering semiempirical methods designed on the basis of HF theory, it is instructive to revisit one-electron effective Hamiltonian methods like the Huckel model described in Section 4.4. Such models tend to involve the most drastic approximations, but as a result their rationale is tied closely to experimental concepts and they tend to be inmitive. One such model that continues to see extensive use today is the so-called extended Huckel theory (EHT). Recall that the key step in finding the MOs for an effective Hamiltonian is the formation of the secular determinant for the secular equation... 

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

The question of whether the bond lengths were equal or alternated in an infinite f-PAc chain was first answered satisfactorily using a Huckel model nearly twenty years before the discovery of metallic behaviour in PAc (Longuet-Higgins and Salem, 1959). This work was carried out at a time when the Huckel model was being used to model the evolution of the optical spectra of the polyenes, i.e. polyacetylene oligomers, as the length of the molecules increased. 

As noted above, the Huckel model assumes that the underlying cr-electrons in the polymer backbone provide a framework that supports the 7t-electrons and it is the latter which give rise to the molecular orbitals that determine the... 

The essential parameters which determine the electrochemical process are the electron affinity of the neutral compound, which correlates with the energy of the LUMO, the energies of interaction with the solvent and counterions, the electron-electron repulsion energies and stereochemical factors. A precondition for an electrochemical study is that the chemical reaction which may occur, e.g. with the solvent, is much slower than the electron transfer process, and that the electrochemical reaction is reversible 66). Correlation of half-wave potentials with the energies of Huckel LUMO s has been one of the early successes of the Huckel model 8>2°.67-88>. The power of the electrochemical method in the study of polycyclic anions has been demonstrated recently 69a). Studies on reactions occurring during electrochemical reductions report reductive alkylations of polycyclic systems and their mechanism 70,69b). 

The formal similarity ivith the Hiickel model is obvious The expressions for the n double bond polyene in the Simpson model are entirely equivalent to the expressions for the n n-electron system in the Huckel model. 

In using the Huckel model for calculating the molecuiar orbital energies, e, for electrons in the ir shell of the allyl system, it is necessary to solve the following equation ... 

The total -electron energy is one of the most important parameters of a conjugated molecule that can be obtained from the Huckel MO calculations [65]. It can be used selectively, to relate to the thermodynamic stability of conjugated structures. A parametrization scheme, based on thermodynamic data, by Hess and Schaad [66], has produced agreement with experiment to the same d ee of qumititative accuracy as the much more sophisticated SCF r-MO procedure developed by Dewar (67). In addition. Schaad and Hess [68] have shown that in many instances Bir follows linearly the total (thermodynamically measurable) energy of the conjugated molecule. The physical reasons leading to the answer as to how it Is possible that a model as simple as the Huckel model can ve not only qualitative, but sometimes also fair quantitative... 

The Huckel model [3] was the earliest rr-electron model. Here, the two-electron integrals are completely neglected. Furthermore, the... 

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