The second hyperpolarizabilities γ of several atoms and diatomic molecules (He, Ne, H₂, FH, CO and OH^-) have been calculated at RHF/x-aug-cc-pVXZ level (x=0～8, X=T or Q) by coupled-perturbed Hatree-Fock method (CPHF). They exhibit a decided tendency toward smooth convergence as a function of the number of diffuse functions added to the standard cc-pVXZ sets (x-aug dependence). Unfortunately, the attempt to get more accurate converged results failed. When x is more than 4 or 5, γ blows up as a consequence. If the abscissa is x (the number of diffuse functions), then γ, as a function of x, shows an inflexion point. The reason for this seems that the basis sets are not complete enough to describe the wave functions in the area near nuclei. According to our calculations, the γ values at inflexion points are good estimates for the Hatree-Fock limits.

Key words: hyperpolarizability, Hatree-Fock limit, coupled-perturbed Hatree-Fock method, ab-initio calculation