Delocalized bonding Huckel method

The Huckel method has been used to obtain n molecular orbitals, and their associated enei gies, for butadiene and benzene. The n electron energy is found to be lower than it would be for localized n bonding, and this difference is known as the delocalization energy. 

There are two approximate starting points in quantum chemistry the molecular orbital (MO) and valence bond (VB) methods. The MO theory derived from the Huckel treatment ignores the interactions between the electrons, whereas the VB theory forms the basis for the electron-paired chemical bond, and for the resonance concept [14]. In MO theory the electrons are delocalized (without any correlation), as contrasted to VB theory, where they are supposed to be localized. 

The predictions of the various approaches diverge more widely when nonben-zenoid conjugated systems are considered. The simple Huckel method using total 77-energy less the energy of the equivalent number of isolated double bonds fails. It predicts delocalization energies of the same order of magnitude for such unstable systems as pentalene and fulvalene as it does for the much more stable aromatics. Both the HMO and SCF-MO methods, which are referenced to polyenes, do much better. They show drastically reduced stabilization for such systems, and, in fact, indicate destabilization in some cases. 

In recent years the fundamental ideas of Huckel molecular orbital theory, the Huckel rule, and other aspects of aromaticity have been extended to polyhedral three-dimensional inorganic structures regarded as aromatic like the two-dimensional aromatic hydrocarbons. Such an extension of Huckel molecular orbital theory requires recognition of its topological foundations so that they can be applied to three-dimensional structures as well as two-dimensional structures. In this connection graph theoretical methods can be used to demonstrate the close analogy between the delocalized bonding in two-dimensional planar aromatic systems such as benzene and that in three-dimensional deltahedral boranes, and carboranes. Related ideas can be shown to be applicable for metal carbonyl clusters, bare post-transition metal clusters, and polyoxometallates. ... 

Abstract A simple Hiickel Hamiltonian is used and modified to describe localized states, where the electron pairs are confined to bonds between two atoms, or to lone pairs. The electronic delocalization can be considered either as a mixmre of these localized states, or through a standard Huckel calculation. The two Huckel-Lewis methods described here attempt to find the coefficients of the mixture, based on energy or overlap consistence with the standard Huckel results. After the description of the two methods, test examples are used to show advantages and drawbacks of the different approaches. In any case, the results are compared to the NBO-NRT approach which is used on the electronic density obtained from standard DFT hybrids calculations such as B3LYP/6-31+G(d). This chapter ends with an introduction to the HuLiS program in which the two methods are implemented. 

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