Extending and modifying the Hall rule

The Hall rule claims that the HMO total π-electron energy (E) of isomeric benzenoid hydrocarbons is a linear function of the number of Kekulé structures (K). We now show that already in the case of benzenoid isomers with a small number of hexagons (4 ⩽ h ⩽ 9), E is better reproduced by a linear function of Kλ, where the exponent λ is significantly smaller than unity. This exponent is found to be a decreasing function of h and its limit value (for h → ∞) seems to be equal to, or near to, 1/3. A simple model of such a K-dependence of E is constructed.