The second hyperpolarizabilities (γ) of several open shell atoms, ion and molecule C, N, O, F, OH and OH⁺ have been calculated at ROHF/x-aug-cc-pVXZ level (x=0～5 or 7, X=T or Q) by finite-field method (FF).The γ exhibits 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) at first.Then when x is more than 4 or 5, γ blows up as a consequence.It is just as the situation in calculations of close shell atoms and molecules by coupled-perturbed Hatree-Fock method (CPHF).If the abscissa is x (the number of diffuse functions), then γ, as a function of x, shows an inflection point.And the γ values at inflexion points are good estimates for the Hatree-Fock limits.The average relative error of γ values at inflexion points is 1.79% for x-aug-cc-pVTZ and 1.91% for x-aug-cc-pVQZ respectively, so the x-aug-cc-pVTZ basis sets are suitable for calculations of hyperpolarizabilities.The second hyperpolarizability γ of Ne has also been calculated at CCSD(T)/5-aug-cc-pVTZ level by FF method, and the result is close to the experimental value.It has been found that the x-aug-cc-pVTZ basis sets are appropriate not only for SCF but also for high-level correlated calculations of the second hyperpolarizabilities.

Key words: hyperpolarizability, Hatree-Fock limit, finite-field method, ab-initio calculation