Estimating the angle of total π-electron energy

Abstract

The angle θ of total π-electron energy of an alternant hydrocarbon is defined via: E π =2 ne cos θ, where 2 n or 2 n+1 is the number vertices and e the number of edges of the molecular graph, and E π is the respective HMO total π-electron energy. The angle θ is sensitive to the structural differences between isomeric alternant hydrocarbons. Recently [J. Mol. Struct. (Theochem) 584 (2002) 183] an identity cos θ=[(e+n)/(2 ne )](1+α− α 2+2α ) has been deduced, with α being a topology-dependent parameter, whose value is much less than unity. We now establish lower and upper bounds for α in terms of n and e. By this, the structure-dependence of angle θ and the range of its variation are better understood.