Frontier orbital approximation limitations

This problem illustrates some of the limitations of rule 2 and the frontier orbital approximation. We begin by describing the carbonyl group in terms of an interaction between an sp2-hybridized C atom and an sp oxygen. We will place the molecule in the xy plane and orient the CO bond along the x-axis ... 

To use frontier orbital theory efficiently, we have to understand its approximations, which define its limitations. This is not really complicated and requires more common sense than mathematical skills. So, don t worry about words like operator or about maths that we do not need to use.1 Just to prove how little maths is in fact required, let us re-examine the previous section point by point. 

These second-order perturbation expressions connect unoccupied with occupied orbitals. Orbitals Ej denote adsorbate orbitals, Ci surface metal orbitals. Relations such as Eq.(2.236) are commonly used in quantum chemistry, limiting the summation terms to the highest occupied and lowest unoccupied orbitals. The theory based on that approximation is called HOMO-LUMO or Frontier Orbital theory. The first term is the electron donation term (electrons are flowing from the adsorbate surface to the surface), the second is the electron backdonation term (electrons are flowing back from the surface to the adsorbate). We will show that Eq.(2.236) leads to ideal weak adsorption theory, but needs adaptation if one wishes to apply it to the quasi-surface molecule situation, which applies in most chemisorption processes. 

However, some anomalies are not easily anticipated. We have discussed the 3-carboxylate-3-methylcyclobutene case. It would be useful to be able to predict these exceptions. The problem amounts to determining the limitations of the Rondan-Houk theory which requires an analysis of the approximations made. Clearly one important approximation is the assimilation of the cyclobutene FOs to the o34 and o 34 orbitals, because the frontier coefficients at C4 and C2 are far from negligible.15 Dropping this approximation but representing R by a carbon 2p orbital, we can then model the molecule by a pentadiene (numbered as in Figure 6.1) ... 

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