IJPAM: Volume 49, No. 4 (2008)

GRAPH REPRESENTATION OF QUANTUM MECHANICAL
OPERATORS AS MOLECULAR STRUCTURAL FORMULAS

Joseph Alia
Division of Science and Mathematics
University of Minnesota - Morris
600 E 4-th St., Morris, MN 56267, USA


Abstract.A brief overview of the Valency Interaction Formula method, VIF, based on Sinanoglu's covariant quantum mechanics and theory of structural covariance of graphs is made. The use of VIF pictures as one-electron density operators is emphasized. A simple formula for judging the significance of relative interaction strengths in $\sigma$-ring systems is presented and used. This applied toward understanding of the chemical bonding in ethene, cyclopropane, and cyclohexane.

Received: August 14, 2008

AMS Subject Classification: 92E10, 81R15

Key Words and Phrases: molecular structural formula, valency interaction formula, one-electron operators, molecular graph, non-unitary classification, applications in chemistry, quantum mechanics, operator research and algebraic analysis, graph theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4