Exact results on homopolar singlet excitation energies of the hubbard model for linear polyenes

Abstract

AbstractThe Lieb–Wu equations for homopolar singlet excited states of the Hubbard model of linear polyenes are formulated in a form tractable by numerical calculation. They are solved to obtain exact excitation energies of the lowest two excited states, corresponding to the 1B and 1E states of the benzene molecule, for systems with up to 50 and 30 electrons, respectively. These results may be particularly useful for checking accuracy of approximate methods for the homopolar states for which the conventional CI method is very difficult to apply. Calculation is also carried out for the 1B+ ionic excited state involving a spin excitation, which corresponds to the 1B state of the benzene molecule. The length dependence of the excitation energies is examined and shown to have no N−1 dependence for large N, where N is the number of electrons. This supplements the result on the 1E ionic state obtained in our previous paper.