Improving the McClelland inequality for total π-electron energy

The McClelland inequality, E⩽2mn, estimates the total π-electron energy (E) of a conjugated hydrocarbon by means of the number of carbon atoms (n) and the number of carbon–carbon bonds (m). We now show that in the general case 2m/n+(n−1)(2m−4m2/n2) is a better (n,m)-type upper bound for E. An even better estimate, 4m/n+(n−2)(2m−8m2/n2), holds for alternant hydrocarbons.