On the Türker Angles in the Theory of Total \pi-Electron Energy

Authors: Ivan GUTMAN

Abstract: The Türker angles $\theta, \alpha$ and $\beta$ are quantities invented by Lemi Türker, and are used in the theory of total $\pi$-electron energy $(E)$ of unsaturated conjugated hydrocarbons. We report here expressions for $\theta, \alpha$ and $\beta$ in terms of $E$ and the parameters $n$ (= half the number of carbon atoms) and $e$ (= the number of carbon-carbon bonds). The forms of these expressions are remarkably similar. Numerical calculation performed on a representative set of benzenoid hydrocarbons reveals that the dependence of the angles $\alpha$ and $\beta$ on molecular structure is very similar, and that their ratio is almost constant $(\alpha/\beta \approx 1.564 \pm 0.015)$.

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