Ab initio calculations of the static longitudinal second hyperpolarizability were reported for the trans-polysilane H₂N(SiH₂SiH₂)_nNO₂ up to n＝30. The magnitude of the electric fields used in the calculations was 0.0, ±0.0008, ±0.0012, ±0.0016 and ±0.0020 a.u. These fields were found suitable for the range of values to characterize the second hyperpolarizabilities of trans-polysilane. For the definition of the electrical property value per unit cell it was suggested to use average value γ(n)/n, instead of the difference value γ(n)－γ(n－1). These asymptotic values were obtained by extrapolating the expression of γ(n)/n＝a＋b/n＋c/n² to infinite length, of which the parameters have been obtained by fitting the molecular results. The most stable region in data set range (n1, n2) was selected to those least squares fit to asquire a subunit value for the infinite polymer property. The molecular geometry optimization increased Dγ(¥) value by about 20%, and the calculated Dγ(∞) value with 6-31G(d) was approximate 15% lower than that obtained with 6-31G basis set. Electron correlation increased the magnitude of Dγ(∞) strongly, and the MP2 values were nealy 100% higher in magnitude than the self-consistent-field values calculated by 6-31G and 6-31G(d) basis sets. Our best value for Dγ(∞) of H₂N(SiH₂SiH₂)_nNO₂ reached 0.8364×10⁶ a.u. with MP2/6-31G(d)//RHF/6-31G level.

Key words: polysilane chain, hyperpolarizability, fitting function, asymptotic limit, ab initio