Bond energy localized electron model

We have seen that the localized electron model is of great value in interpreting the structure and bonding of molecules. However, there are some problems with this model. For example, it incorrectly assumes that electrons are localized, and so the concept of resonance must be added. Also, the model does not deal effectively with molecules containing unpaired electrons. And finally, the model gives no direct information about bond energies. 

From a thermodynamic viewpoint, we may imagine that, in an actinide metal, the model of the solid in which completely itinerant and bonding 5 f electrons exist and that in which the same electrons are localized, constitute the descriptions of two thermodynamic phases. The 5f-itinerant and the 5 f-localized phases may therefore have different crystal properties a different metallic volume, a different crystal structure. The system will choose that phase which, at a particular T and p (since we are dealing with metals, the system will have only one component) has the lower Gibbs free-energy. A phase transition will occur then the fugacity in the two possible phases is equal e.g. the pressure. To treat the transition, therefore, the free energies and the pressures of the two phases have to be compared. We recall that ... 

Surface states can arise simply because the atomic bonding at a semiconductor surface is necessarily different from that in the bulk. For example, in a Si lattice, the bonds at the Si surface are not ftilly coordinatively saturated. To relieve this unsaturation, either a surface reconstruction can occur and/or bonds to the metallic material can be formed. This distinct type of surface bonding results in a localized electronic structure for the surface which is different from that in the bulk. The energies of these localized surface orbitals are not restricted to reside in the bands of the bulk material, and can often be located at energies that are inside the band gap of the semiconductor. Orbitals that reside in this forbidden gap region are particularly important, because they will require modifications of our ideal model of charge equilibration at semiconductor/metal interfaces. ... 

If the Coulomb interaction between electrons of different pairs is ignored, each localized bond and lone pair contribute independently to the total energy, which implies a perfect additivity of bond energies. In the independent-particle model, the localized bond function can be visualized as a two-center molecular orbital occupied by two electrons. Nevertheless, it is possible to reproduce deviations from additivity rules within this scheme, for instance, by taking into account overlap (for a review, see e.g. 2>). 

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