Extending the McClelland formula for total π -electron energy

Abstract

© 2017, Springer International Publishing AG. The McClelland formula, based on the upper bound 2mn, is capable of reproducing over 99.5% of the total π-electron energy (Eπ) of a conjugated hydrocarbon, whose molecules possess n carbon atoms and m carbon–carbon bonds. Its weak point is that it predicts equal Eπ-values for all isomers. We now show how this failure can be overcome, offering a general strategy for extending McClelland’s formula. By means of one of these extensions, Eπ is related with the energy of the highest occupied molecular orbital, and the error of the new formula is diminished by more than 50 % relative to the standard McClelland approximation.