Radical ions pairing theorem

If the transition considered is the HOMO LUMO transition of an alternant hydrocarbon, then first-order theory predicts that inductive perturbation will have no effect at all, because for = fo as a consequence of the pairing theorem. Small red shifts are in fact observed that can be attributed to hyper conjugation with the pseudo-7t MO of the saturated alkyl chain.290 On the other hand, alkyl substitution gives rise to large shifts in the absorption spectra of radical ions of alternant hydrocarbons whose charge distribution is equal to the square of the coefficients of the MO from which an electron was removed (radical cations) or to which an electron was added (radical anions), and these shifts are accurately predicted by HMO theory.291... 

From the pairing theorem, the 7c-electron density at any position in any neutral AH (even AH or odd AH radical) is unity. If atom i is at such a position in both reactants and products, replacing it by a heteroatom will have no first-order effect on the equilibrium. If, however, atom i is active in a reaction involving odd AH ions, the final term in equation (4.92) will not vanish and so the equilibrium will be disturbed by introduction of the heteroatom. 

Although we could not observe this band for PMPrS(-) and PMPS( +) in the present study, well-resolved absorption spectra were obtained in the previous pulse radiolysis experiment for liquid phase (4-9). The radical cation and anion of the same polysilane have the UV band at almost the same wavelength. This result indicates that the Pairing Theorem is valid for the polysilane radical ions and that the interaction with other o -orbital is quite small, (see AppendbO... 

---