Remark on the moment expansion of total π-electron energy

SummaryThe truncated expansion of the function |x| was frequently used to express the total Hückel π-electron energy (E) in terms of moments. We now present an identity which connectsE with an infinite series of moments. This series is convergent. Lower and upper bounds forE are obtained, based on the same infinite moment expansion.

[1]  Ante Graovac,et al.  On a resonance energy model based on expansion in terms of acyclic moments: Exact results , 1991 .

[2]  C. A. Coulson,et al.  On the calculation of the energy in unsaturated hydrocarbon molecules , 1940, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  I. Gutman.  A class of approximate topological formulas for total π‐electron energy , 1977 .

[4]  Ivan Gutman,et al.  Dependence of spectral moments of benzenoid hydrocarbons on molecular structure , 1991 .

[5]  Ivan Gutman,et al.  Moment expansion of Hückel molecular energies , 1989 .

[6]  I. Gutman,et al.  Mathematical Concepts in Organic Chemistry , 1986 .

[7]  George G. Hall.  The evaluation of moments for polycyclic hydrocarbons , 1986 .

[8]  Nenad Trinajstić,et al.  Graph theory and molecular orbitals. The loop rule , 1973 .

[9]  Jerry Ray Dias.  Properties and derivation of the fourth and sixth coefficients of the characteristic polynomial of molecular graphs—New graphical invariants , 1985 .

[10]  Yuansheng Jiang,et al.  Evaluation of moments and their application in Hückel molecular orbital theory , 1984 .

[11]  Edgar Heilbronner,et al.  Das HMO-Modell und seine Anwendung , 1968 .

[12]  B. Mcclelland.  Properties of the Latent Roots of a Matrix: The Estimation of π‐Electron Energies , 1971 .

[13]  G. G. Hall.  The bond orders of alternant hydrocarbon molecules , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  Klaus Ruedenberg,et al.  Free‐Electron Network Model for Conjugated Systems. V. Energies and Electron Distributions in the FE MO Model and in the LCAO MO Model , 1954 .

[15]  P. Löwdin.  Concepts of convergence in mathematical chemistry , 1990 .

[16]  Ante Graovac,et al.  Topological Approach to the Chemistry of Conjugated Molecules , 1977 .

[17]  Yuansheng Jiang,et al.  Stability and reactivities based on moment analysis , 1989 .

[18]  I. Gutman,et al.  Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons , 1972 .