Off-diagonal Interactions, Hund's Rules and Pair-binding in Hubbard Molecules

We have studied the effect of including nearest-neighbor, electron-electron interactions, in particular the off-diagonal (non density-density) terms, on the spectra of truncated tetrahedral and icosahedral ``Hubbard molecules,'' focusing on the relevance of these systems to the physics of doped C$_{60}$. Our perturbation theoretic and exact diagonalization results agree with previous work in that the density-density term suppresses pair-binding. However, we find that for the parameter values of interest for $C_{60}$ the off-diagonal terms {\em enhance} pair-binding, though not enough to offset the suppression due to the density-density term. We also find that the critical interaction strengths for the Hund's rules violating level crossings in C$_{60}^{-2}$, C$_{60}^{-3}$ and C$_{60}^{-4}$ are quite insensitive to the inclusion of these additional interactions.