Scaling law for second-order hyperpolarizability in poly(triacetylene) molecular wires

Poly(triacetylenes) are rodlike molecules with electrons delocalized over a one-dimensional path. We show that they exhibit a power-law dependence of the second-order hyperpolarizability gamma on the monomer unit n for short molecules and a smooth saturation toward a linear increase in longer molecules. The power law of gamma?n(a) with a approximately 2.5 from dengenerate four-wave mixing and third-harmonic generation measurements is in good agreement with quantum-chemical calculations. The critical conjugation length for saturation in the three cases is shown to be approximately 60 carbon-carbon bonds, which indicates the upper boundary for the electron delocalization in such a one-dimensional molecular wire.