General Theory of Cycle-Dependence of Total pi-Electron Energy

Document Type: Research Paper

Author

Faculty of Science, University of Kragujevac, Kragujevac, Serbia

Abstract

The theoretical treatment of cycle-effects on total pi-electron energy,

mainly elaborated by Nenad Trinajstic and his research group, is

re-stated in a general and more formal manner. It enables to envisage several

other possible ways of measuring the cycle-effects and points at further

directions of research.

Keywords

Main Subjects


1. J. Aihara, A new definition of Dewar–type resonance energies, J. Am. Chem. Soc.
98 (1976) 2750–2758.
2. J. Aihara, Resonance energies of benzenoid hydrocarbons, J. Am. Chem. Soc. 99
(1977) 2048–2053.
3. J. Aihara, Circuit resonance energy: A key quantity that links energetic and
magnetic criteria of aromaticity, J. Am. Chem. Soc. 128 (2006) 2873–2879.
4. S. Bosanac, I. Gutman, Effect of a ring on the stability of polycyclic conjugated
molecules, Z. Naturforsch. 32a (1977) 10–12.
5. D. M. Cvetković, M. Doob, I. Gutman, A. Torgašev, Recent Results in the Theory
of Graph Spectra, North–Holland, Amsterdam, 1988.
6. M. K. Cyranski, Energetic aspects of cyclic π-electron delocalization: Evaluation
of the methods of estimating aromatic stabilization energies, Chem. Rev. 105(2005)
3773–3811.
7. J. R. Dias, Molecular Orbital Calculations Using Chemical Graph Theory,
Springer , Berlin, 1993.
8. A. Graovac, I. Gutman, N. Trinajstić, T. Živković, Graph theory and molecular
orbitals. Application of Sachs theorem, Theor. Chim. Acta 26 (1972) 67–78.
9. A. Graovac, I. Gutman, N. Trinajstić, Topological Approach to the Chemistry of
Conjugated Molecules, Springer, Berlin, 1977.

10. I. Gutman, On cyclic conjugation, Theor. Chim. Acta 66 (1984) 43–49.
11. I. Gutman, Rectifying a misbelief: Frank Harary’s role in the discovery of the
coefficient–theorem in chemical graph theory, J. Math. Chem. 16 (1994) 73–78.
12. I. Gutman, Impact of the Sachs theorem on theoretical chemistry: A participant’s
testimony, MATCH Commun. Math. Comput. Chem. 48 (2003) 17–34.
13. I. Gutman, Cyclic conjugation energy effects in polycyclic π-electron systems,
Monatsh. Chem. 136 (2005) 1055–1069.
14. I. Gutman, Topological resonance energy 40 years later, Int. J. Chem. Model. 6
(2014) 177–189.
15. I. Gutman, A survey on the matching polynomial, in: Y. Shi, M. Dehmer, X.Li, I.
Gutman (Eds.), Graph Polynomials, CRC Press, Boca Raton, 2016, pp.77–99.
16. I. Gutman, Selected Theorems in Chemical Graph Theory, Univ. Kragujevac,
Kragujevac, 2017.
17. I. Gutman, S. Bosanac, Quantitative approach to Hückel rule. The relations
between the cycles of a molecular graph and the thermodynamic stability of a
conjugated molecule, Tetrahedron 33 (1977) 1809–1812.
18. I. Gutman, M. Milun, N. Trinajstić, Topological definition of delocalisation
energy, MATCH Commun. Math. Comput. Chem. 1 (1975) 171–175.
19. I. Gutman, M. Milun, N. Trinajstić, Graph theory and molecular orbitals. 19.
Nonparametric resonance energies of arbitrary conjugated systems, J. Am. Chem.
Soc. 99 (1977) 1692–1704.
20. I. Gutman, O. E. Polansky, Cyclic conjugation and the Hückel molecular orbital
model, Theor. Chim. Acta 60 (1981) 203–226.
21. I. Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry,
Springer, Berlin, 1986.
22. I. Gutman, S. Stanković, J. Ɖurdević, B. Furtula, On the cycle–dependence of
topological resonance energy, J. Chem. Inf. Model. 47 (2007) 776–781.
23. I. Gutman, N. Trinajstić, Graph theory and molecular orbitals, Topics Curr. Chem.
42 (1973) 49–93.
24. X. Li, I. Gutman, G. V. Milovanović, The β-polynomials of complete graphs are
real, Publ. Inst. Math. (Beograd) 67 (2000) 1–6.
25. X. Li, B. Zhao, I. Gutman, More examples for supporting the validity of a
conjecture on β-polynomial, J. Serb. Chem. Soc. 60 (1995) 1095–1101.
26. X. Li, H. Zhao, L. Wang, A complete solution of a conjecture on the β-
polynomials of graphs, J. Math. Chem. 33 (2003) 189–193.
27. V. I. Minkin, M. N. Glukhovtsev, B. Y. Simkin, Aromaticity and Antiaromaticity.
Electronic and Structural Aspects, Wiley, New York, 1994.
28. M. Randić, Aromaticity of polycyclic conjugated hydrocarbons, Chem. Rev. 103
(2003) 3449–3606.

29. H. Sachs, Beziehungen zwischen den in einem Graphen enthaltenen Kreisen und
seinem charakteristischen Polynom, Publ. Math. (Debrecen) 11 (1964) 119–134.
30. L. J. Schaad, B. A. Hess, Dewar resonance energy, Chem. Rev. 101 (2001) 1465–
1476.
31. N. Trinajstić, Computing the characteristic polynomial of a conjugated system
using the Sachs theorem, Croat. Chem. Acta 49 (1977) 539–633.
32. N. Trinajstić, Hückel theory and topology, in: G. A. Segal (Ed.), Semiempirical
Methods of Electronic Structure Calculation. Part A: Techniques, Plenum Press,
New York, 1977, pp. 1–27.
33. N. Trinajstić, New developments in Hückel theory, Int. J. Quantum Chem.
Quantum Chem. Symp. 11 (1977) 469–472.
34. N. Trinajstić, Chemical Graph Theory, CRC Press, Boca Raton, 1983.
35. N. Trinajstić, Autobiographical notes, Iranian J. Math. Chem. 8 (2017) 231–257.