Linear and nonlinear polarizabilities of t r a n s-polysilane from a b i n i t i o oligomer calculations

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Abstract
Linear and nonlinear static electronic polarizabilities of the σ‐conjugated polymer trans‐polysilane (t‐PSi) are obtained at the Hartree–Fock level by extrapolation of ab initio calculations on the oligomers H3Si–(SiH2)N–SiH3 (N odd). For the longitudinal components, in particular, a 6–31 G basis is shown to yield accurate values if the chains are long enough. No computational advantage is found in using effective core potentials. Chain lengths through N=13 are sufficient to give limiting infinite chain polarizabilities with relatively small uncertainty. The calculated longitudinal linear polarizability per SiH unit is about the same as the corresponding property in the prototype π‐conjugated polymers polyacetylene (PA) and polydiacetylene (PDA), but the longitudinal second hyperpolarizability is significantly less in the σ‐conjugated polymer. In t‐PSi the conjugation length is about half that in either PA or PDA. Frequency‐dependent vibrational distortion contributions are estimated in the doubly harmonic approximation and turn out to be important in trisilane and pentasilane even at optical frequencies. An analysis is developed which sheds light on the expected behavior for increasing chain lengths. Reasonable agreement with experiment is obtained for both the electronic and vibrational longitudinal second hyperpolarizabilities.