CLUSTER-EXPANSION OF THE HUBBARD-MODEL ENERGY OF ACYCLIC CONJUGATED HYDROCARBONS

Regularities in the ground state energy of acyclic conjugated hydrocarbons have frequently been noted at the level of Huckel molecular orbital calculations. In this paper it is shown that the Hubbard model, which includes electron correlation, shows the same types of regularties even in the highly correlated limit. These regularities are rationalized by showing that the Hubbard energy can be fit to a (rapidly convergent) cluster expansion which embodies the physically appealing notion that a molecule consists principally of localized bonds which interact progressively more weakly with more distant parts of the molecule. Relations to previous expressions for the energy, derived within the Huckel approximation, are also given.