Influence of the Hückel k parameter on the pairing of the eigenvalues of heteroconjugated molecules

The net effect of a heteroatomic center (combined effect of h and k Hückel parameters) on the eigenvalues of certain heteroconjugated molecules is examined. The role of the k parameter is judged by comparing the eigenvalues of the vertex-weighted (self-loop) graphs with those of the vertex-edge-weighted graphs. The pairing of the eigenvalues for the above class of molecules is observed by using the original pairing theorem (Coulson, C. A.; Rushbrooke, G. S. Proc. Cambridge Philos. Soc. 1940, 36, 193-200. Coulson, C. A.; Leary, B. O.; Mallion, R. B. Hückel Theory for Organic Chemists; Academic Press: London, 1978; pp 90-110), the restricted extension form of it (Mallion, R. B.; Schwenk, A. J.; Trinajstić, N. In Recent Advances in Graph Theory; Fiedler, M., Ed.; Academia: Prague, 1975; p 345. Trinajstić, N. Croat. Chem. Acta 1977, 49 (4), 593-633), and a different pairing scheme proposed in this work. The newly proposed scheme for pairing of the eigenvalues for a monocyclic heteroconjugated system containing n atoms and having one or more heteroatoms can be written as x_j + x_n+1-j = 1/2(Σph_p - b) ± a, where p is the number of heteroatoms, a is a numerical quantity, b contains few odd eigenvalues, and 1 ≤ j ≤ n.