NONCROSSING RULE AND DEGENERACY IN HUBBARD MODELS - CYCLOBUTADIENE AND BENZENE

The unexpected crossing of energy levels with the same symmetry, as a function of an on-site correlation U, in the Hubbard model for benzene is shown to reflect the degeneracies of the site Hamiltonian, ℋ0. Diagrammatic valence bond (VB) methods greatly simplify the symmetry analysis and allow a complete treatment of configuration interactions (CI) for both on-site and extended interactions. The single forbidden crossing in the 1A subspace of cyclobutadiene disappears for arbitrarily small nearest-neighbor interactions. The many forbidden crossings in the 1A subspace of benzene also become avoided crossings when nearest-neighbor intersite interactions are included. Since the degeneracies of ℋ0 in benzene are only partially lifted, CI among nondegenerate states is a sufficient, but not a necessary condition for the noncrossing rule. © 1979 American Institute of Physics.