We investigate the solution of a recently proposed [J. Chem. Phys. 117, 9977 (2002)] improved valence bond model in a basis of Kekule functions. The model, which has the form of an extended Heisenberg Hamiltonian with next-nearest-neighbor and ring permutation terms, operates in the space of all covalent valence bond structures which grows very rapidly with molecular size. It is found that truncation of the basis to include only the very much smaller number of nearest-neighbor spin pairings, the Kekule functions, yields better than 98% of the exact energy in most cases. Extensions to excited states are discussed. As an illustration of the applicability of the model to large molecules, we solve it for the ground and first excited H-u singlet state of C-60 buckminsterfullerene, and obtain results in good agreement with other theoretical treatments. The model shows promise of being an easily applied semiquantitative valence bond model for large molecules. (C) 2003 American Institute of Physics.