Revisiting superdelocalizability. Mathematical stability of reactivity indices

Superdelocalizability, S-r, defined by Fukui et al. as a variant of reactiv ity indices in the Huckel molecular orbital scheme for conjugated hydrocarb on molecules is reinvestigated with particular emphasis on its behavior for infinitely large pi-electronic systems. Surprisingly: almost all the S-r v alues of polyacetylene are found to diverge with the size of molecule, whil e all the S-r values of comb polyene converge to certain values. Similarly, the S-r values of linear polyacene diverge, while those of zigzag polyacen e converge. Whether the super-delocalizability for a series of periodic pol ymers converges or diverges can be predicted, respectively. if the density of states of the infinitely large pi-electron network is shown to have non- zero or zero gap at the Fermi level. The behavior of atom-atom polarizabili ty defined by Coulson et al. is also checked and discussed.