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

Rama K. Mishra*, Swarna M. Patra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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 xj + xn+1-j = 1/2(Σphp - b) ± a, where p is the number of heteroatoms, a is a numerical quantity, b contains few odd eigenvalues, and 1 ≤ j ≤ n.

Original languageEnglish (US)
Pages (from-to)495-500
Number of pages6
JournalJournal of Chemical Information and Computer Sciences
Volume37
Issue number3
DOIs
StatePublished - Jan 1 1997

ASJC Scopus subject areas

  • Chemistry(all)
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

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