A Hubbard model for the second hyperpolarizability in alternating polymers

The static second hyperpolarizability in low polymers of the type …ABAB… is studied using a two-band Hubbard Hamiltonian. For fully reduced bridged metallic polymers, there exists a non-zero value for the metal–ligand energy gap which corresponds to a γ of maximum magnitude. For mixed-valence bridged polymers, |γ| may be increased if the metal–ligand energy gap is increased. This means that |γ| may be enhanced significantly by synthetic alteration of the bridging ligand. Large, negative values for γ are predicted for polymers of the von Kameke type for the system in the mixed-valence state where the number of πd electrons equals twice the number of metal atoms minus one.