Due to electron delocalization, the component of hyperpolarizability tensor directed along the backbone of polymeric systems will be increased until a linear evolution is reached. An approach to obtain this asymptotic value is to follow the evolution of the longitudinal hyperpolarizability in larger and larger oligomers and then to extrapolate to the infinite polymer limit. These extrapolation procedures consist in making a least-squares fit of the hyperpolarizability values per unit cell to an analytic function able to present a stabilization behavior when increasing the chain length. A 1/n power series representation has been proposed to be the function. The longitudinal hyperpolarizability values per unit of polymeric chains can be expressed in two main ways: γ(n)/n＝a＋b/n＋c/n² or γ(n)－γ(n－1)＝a＋b/n＋c/n². Thus, the asymptotic values extrapolated were determined by a. Polyethylene, hydrogen model chain, polyacetylene and polysilane have been employed to compare these two formulae. It shows that γ(n)/n yields a consistently improved accuracy and a better theoretical justification than γ(n)－γ(n－1). The reason is that the latter formula comes from a power series representation for γ(n), which has a logarithm term. This term led to wrong effect on the asymptotic behavior.

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