Resonant orbital energy

Fig.2a. Trajectory for the real and imaginary parts of the resonant orbital energy E denoted by dots ( ) as a function of the real scale factor p. The starting value is p = 0.65 at top left, and the increment Ap is 0.025. The rotation angle is fixed at a = 0.38.

The developers of ZINDO found that the parameters required to reproduce orbital energy orderings and UV spectra are different from those required to reproduce accurate structures by geometry optimization. They introduced anew pair of parameters, called the overlap weighting factors, to account for this. These parameters are provided in HyperChem in the Semi-empirical Options dialog box. Their effect is to modify the resonance integrals for the off-diagonal elements of the Fock matrix. 

With this simplification in mind, the stabilization energy AE can be given by equation 15, homo and lumo being orbital energies, C A, C A and Cjy, Cp being the relevant orbital coefficients at the carbon centers to which the new bonds are being formed fi AD and f A,D, are the resonance integrals for the overlap at the sites of interaction. 

It is a simple matter to calculate the orbital energies for the hypothetical complex C6H5X—Cr, since all the required matrix elements, Hu (coulomb terms) and //<7 (resonance integrals) of the secular determinant... 

In the case of the triphenylmethyl radical shown in Figure 4.86, it is possible to write many different resonance structures but in a small free radical such as the methyl radical there is only one possible structure. The reactivity of the radical decreases as the unpaired spin density at each site decreases, and the radical also becomes more stable because of the resonance energy. This resonance stabilization is zero for the phenyl radical, since the unpaired electron resides in an orbital which is orthogonal to the it system. By contrast, the methylphenyl radical has a resonance stabilization energy of some 10 kcalmol-1, and the larger methylnaphthyl radical is stabilized by about 15 kcalmol-1. These resonance stabilizations can have important consequences for the energy balance of photochemical reactions (see e.g. sections 4.4.2 and 4.4.4). 

Another possibility concerns the resonance integrals /Sab which appear in the Klopman-Salera equation. In a Hiickel picture, these are independent of the orbital energy, but in a double-zeta or better description we would expect the more tightly-bound electrons to have more contracted orbitals, and the higher virtual orbitals to be more diffuse.131 It may be that the HOMO and LUMO have the optimum spatial distribution for strong interaction, and that interactions involving more contracted and more diffuse orbitals are weaker.122... 

Although the Dewar-Klopman expression is more complicated than the resonance expressions so far discussed, they point out that attempts to use simpler expressions resulted in less success. Thus, the omission of the terms /< and Ij gave results for unsaturated molecules such as ethylene in which the orbital energies appeared in the wrong orders, while the omission of the term in R resulted in incorrect heats of formation. 

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