2ND HYPERPOLARIZABILITY OF ONE-DIMENSIONAL SEMICONDUCTORS

The static second hyperpolarizability gamma(N) is calculated for one-dimensional semiconductors consisting of N-coupled two-level systems. Coulomb interactions are treated exactly in the complete basis set of zero, one, and two electron-hole (e-h) pairs. Analytical solutions for the per-site response gamma(N)/N are obtained in the polymer limit for both the strong- and weak-localization (free-particle) regimes. The double e-h pair states play a crucial role in determining the sign and magnitude of gamma(N) near the strong-localization limit and prevent unphysical divergences in the per-site response as N increases. Applications to generic polysilanes are discussed.