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Estimating the angle of total pi-electron energy

Gutman, I
Türker, Burhan Lemi
The angle theta of total pi-electron energy of an alternant hydrocarbon is defined via: E-pi = 2rootne cos theta, where 2n or 2n + 1 is the number vertices and e the number of edges of the molecular graph, and E-pi is the respective HMO total pi-electron energy. The angle theta is sensitive to the structural differences between isomeric alternant hydrocarbons. Recently [J. Mol. Struct. (Theochem) 584 (2002) 183] an identity cos theta = [(e + n)/(2rootne)](1 + alpha - rootalpha2 + 2alpha) has been deduced, with alpha being a topology-dependent parameter, whose value is much less than unity. We now establish lower and upper bounds for alpha in terms of n and e. By this, the structure-dependence of angle theta and the range of its variation are better understood.