Interaction Between Two Orbitals An Important Chemical Model

Qualitative quantum-chemical discussion often relies on a simplified model wherein all interactions are neglected except for the primary one. For example, in considering how a Lewis base and a Lewis acid interact, one might consider only the highest occupied 

MO (HOMO) of the base (electron donor) and the lowest unfilled MO (LUMO) of the acid (electron acceptor). Consideration of the ways two levels interact wiU provide some useful rules of thumb and also consohdate some of our earher findings.  

We label the unperturbed orbitals and energies ifa, ifb, and Ea, Ej,. We wiU work within the Hiickel type of framework so that state energy differences may be written as orbital energy differences. The orbitals are allowed to interact with each other by virtue of close approach. We will assume that the perturbation felt by the orbitals is proportional to the overlap between them. (If the systems involved are ions, strong electrostatic interactions will exist as well. Therefore, we assume aU systems to be neutral.) 

Since the overlap of ira on in, is the same as that of in, on ira, the energy change to first order is the same for both levels and hence we ignore it (imless the levels are degenerate—an eventuality we discuss shortly). 

If Ea = Eb, we must set up a 2 x 2 first-order perturbation determinant using ira and ifh as basis, and find the two roots. Just as was true in the polarizability calculation of Section 12-7, we will find that one root lies above Ea, and the other lies an equal distance below. Thus, for degenerate levels, the repulsion between levels becomes a 

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Section 12-9 Interaction Between Two Orbitals An Important Chemical Model... 

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