AbstractThe Hubbard Hamiltonian, while not one of the most successful models for φ electrons in benzene, has been extensively investigated in the literature. As part of our general study of that model, we have computed all the energy levels for all values of the repulsion parameter—a task that has not been undertaken before. After extracting all the symmetry of the model we found, to our great surprise, many instances of permanent degeneracy of levels with different symmetry and also crossing of levels of the same symmetry. We can also demonstrate that there is no hidden symmetry to account for these effects. Since these results run counter to one of the oldest folk theorems in quantum chemistry, our otherwise uninspiring graphs may be of general intere