Frontier orbital energies, definition

In Table 6.8, atom type-specific subset correlations of AMI, PM3, PM5, and HF with B3LYP are shown for frontier orbital energies and related descriptors, for parameters based on the charge distribution, and for the PPSA and PNSA descriptors. In contrast to Table 6.4 and Table 6.7, however, now all compounds providing a zero descriptor value by definition (e.g., PPSA-1Z = 0 if, for a given method, the compound has no positively charged heavy atom) were included for generating the statistics. 

The contribution of the frontier orbitals would be maximized in certain special donor-acceptor reactions. The stabilization energy is represented by Eqs. (3.25) and (3.26). Even in a less extreme case, the frontier orbital contribution maybe much more than in the expression of the superdelocalizability. If we adopt the approximation of Eq. (6.3), the intramolecular comparison of reactivity can be made only by the numerator value. In this way, it is understood that the frontier electron density, /r, is qualified to be an intramolecular reactivity index. The finding of the parallelism between fr and the experimental results has thus become the origin of the frontier-electron theory. The definition of fr is hence as follows ... 

We are now in a position to reformulate the Lewis definition of acids and bases in terms of frontier orbitals A base has an electron pair in a HOMO of suitable symmetry to interact with the LUMO of the acid (although lone pair orbitals with the wrong geometry may need to be ignored). The better the energy match between the base s HOMO and the acid s LUMO, the stronger the interaction. 

Definition Two fragments are isolobal if the number, symmetry properties, approximate energy and shape of their frontier orbitals, and the number of electrons occupying them are similar - not identical, but similar. [R. Hoffmann 1982]. 

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