Nonresonant frequency dispersion of the electronic second hyperpolarizability of all-trans polysilane chains: An ab initio TDHF oligomeric approach

The frequency-dependent electronic second hyperpolarizability of increasingly large polysilane chains is computed for the most common nonlinear optical (NLO) processes at the time-dependent Hartree-Fock level with the 6-31G atomic basis set. Due to σ-conjugation, the longitudinal component (γ_L ^e) turns out to be dominant. Its nonresonant dispersion relations are described by the coefficients of the power expansion formula, γ_L ^e[(-ω_σ; ω_a, ω₂, ω₃) = γ_L ^e(0; 0, 0, 0)[1 + Aω_L ² + Bω_L ⁴ + Cω_L ⁶ + ⋯], where ω_L ² = ω_σ ² + ω₁ ² + ω₂ ² + ω₃ ² and γ_L ^e(0; 0, 0, 0) is the static limit value. In the infinite chain length limit, the CHF/6-31G static longitudinal electronic second hyperpolarizability per Si₂H₄ unit cell is estimated to attain 463 ± 10 × 10³ a.u. whereas the A coefficient reaches 27.8 ± 0.9 a.u. The accuracy that could be reached from using this power expansion expression for estimating the second hyperpolarizability for other optical frequencies is discussed.