Semiempirical calculations of hyperpolarizabilities for extended π systems: Polyenes, polyynes, and polyphenyls

The dipole moments (μ), polarizabilities (α), hyperpolarizabilities (β), and second‐order hyperpolarizabilities (γ) of polyenes, polyynes, and polyphenyls have been calculated by a finitefield method with the PM‐3 parameterization of the semiempirical MNDO Hamiltonian at the optimum geometries. These results were compared to experimental values obtained from EFISH and THG measurements. The calculations reproduce the magnitudes of β and γ, as well as the effect of the substituents and the effect of bond alternation on β and γ. The coefficients of the power law, which describes the dependence of β and γ on the number of π centers, were calculated. For β, exponents of 1.5–2.2 and 0.03–0.04 were obtained for polyenes and polyynes, respectively, and for γ, exponents of 3.9–4.9, 2.9–3.3, and 2.5–2.7 were obtained for polyenes, polyynes, and polyphenyls, respectively. These results confirm the efficiency of enhancing γ by insertion of C = C double bonds into a chain.