INFLUENCE OF THE HUCKEL K-PARAMETER ON THE PAIRING OF THE EIGENVALUESOF HETEROCONJUGATED MOLECULES

The net effect of a heteroatomic center (combined effect of h and k Hu ckel parameters) on the eigenvalues of certain heteroconjugated molecu les is examined. The role of the k parameter is judged by comparing th e eigenvalues of the vertex-weighted (self-loop) graphs with those of the vertex-edge-weighted graphs. The pairing of the eigenvalues for th e above class of molecules is observed by using the original pairing t heorem (Coulson, C. A.; Rushbrooke, G. S. Proc. Cambridge Philos. Soc. 1940, 36, 193-200. Coulson, C. A.; Leary, B. O.; Mallion, R. B. Hucke l Theory for Organic Chemists; Academic Press: London, 1978; pp 90-110 ), the restricted extension form of it (Mallion, R. B.; Schwenk, A. J. ; Trinajstic, N. In Recent Advances in Graph Theory; Fiedler, M., Ed.; Academia: Prague, 1975; p 345. Trinajstic, N. Croat. Chem. Acta 1977, 49 (4), 593-633), and a different pairing scheme proposed in this wor k. The newly proposed scheme for pairing of the eigenvalues for a mono cyclic heteroconjugated system containing n atoms and having one or mo re heteroatoms can be written as x(j) + x(n + 1 - j) = (1)/(2)(Sigma(p )h(p) - b) +/- a, where p is the number of heteroatoms, a is a numeric al quantity, b contains few odd eigenvalues, and 1 less than or equal to j less than or equal to n.