The McClelland approximation and the distribution of π-electron molecular orbital energy levels

The total π-electron energy E of a conjugated hydrocarbon with n carbon atoms and m carbon-carbon bonds can be approximately calculated by means of the McClelland formula mn g E 2 ≈ , where g is an empirical fitting constant, g ≈ 0.9. It was claimed that the good quality of the McClelland approximation is a con- sequence of the fact that the π-electron molecular orbital energy levels are distribu- ted in a nearly uniform manner. It will now be shown that the McClelland ap- proximation does not depend on the nature of the distribution of energy levels, i.e., that it is compatible with a large variety of such distributions.