Systematic search of bounds for total ?-electron energy

Abstract

We developed a systematic method to improve the known bounds for the total π-electron energy E by designing a method based on the theory of symmetric polynomials and its inequalities. Additionally, the theory of symmetric polynomials applied to the problem of bounds for the total π-electron energy suggests the definition of generalized arithmetic and geometric means, which can then be incorporated into Kober's theorem to obtain very sharp upper and lower bounds, better than those already known, in terms of the determinant of the adjacency matrix of the graph and/or higher-order spectral moments. Having established a connection between the problem of the π-electron energy and the theory of symmetric polynomials and its inequalities, we apply several other theorems from the theory of symmetric polynomials that allow us to obtain new explicit and implicit inequalities and to obtain implicit inequalities that in principle incorporate all spectral moments. In particular, we present an implicit inequality for the total π-electron energy that is so sharp that it is for all practical purposes an equation for that energy. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003