Molecular Orbital Models of Benzene, Biphenyl and the Oligophenylenes

A two state (2-MO) model for the low-lying long axis-polarised excitations of poly(p-phenylene) oligomers and polymers is developed. First we derive such a model from the underlying PariserParr-Pople (P-P-P) model of π-conjugated systems. The two states retained per unit cell are the Wannier functions associated with the valence and conduction bands. By a comparison of the predictions of this model to a four state model (which includes the non-bonding states) and a full P-P-P model calculation on benzene and biphenyl, it is shown quantitatively how the 2-MO model fails to predict the correct excitation energies. The 2-MO model is then solved for oligophenylenes of up to 15 repeat units using the density matrix renormalisation group (DMRG) method. It is shown that the predicted lowest lying, dipole allowed excitation is ca. 1 eV higher than the experimental result. The failure of the 2-MO model is a consequence of the fact that the original HOMO and LUMO single particle basis does not provide an adequate representation for the many body processes of the electronic system.