McClelland-type lower bound for total π-electron energy

Abstract

For a conjugated hydrocarbon possessing n carbon atoms and m carbon–carbon bonds McClelland showed that the expression (2mn)^1/2 is an upper bound for the total π-electron energy (E). We now demonstrate that in the case of benzenoid hydrocarbons, g(2mn)^1/2, g=(16/27)^1/2= 0.77 is a lower bound for E. This explains the remarkable success of the McClelland approximation E≈a(2mn)^1/2, where a is an empirical parameter, found to be 0.908.