An improved valence bond model, in the form of an extended Heisenberg model including next-nearest-neighbor transpositions and six-cyclic permutations, is developed to describe the low-lying "covalent" portion of the Hubbard model eigenspectrum (at half filling). The use of a cluster expansion including all diameter 1 and 2 subgraphs plus the diameter 3 six-membered ring allows the coefficients in the extended Heisenberg model to be determined from the results of accurate calculations of the Hubbard spectrum of benzene. The model is found to predict the lower energy states of two test molecules, styrene and naphthalene, rather accurately, and is thus expected to be generally applicable to benzenoid aromatic hydrocarbons.