| The design of nonlinear optics materials is one of the important task on the Materials science, and the properties of nonlinear optics materials comes of hyperpolarizabilities component molecules of materials. It can provide useful informations for devising good nonlinear optics materials that accurate calculating the hyperpolarizabilities by quantum chemistry method, so theoretical calculations are important for the study of nonlinear optics materials. The calculation of hyperpolarizabilities requires bigger basis sets, and the choice of basis sets is premise for calculation the hyperpolarizabilities. We carefully study the hyperpolarizabilities of several atoms and small molecules as functions of basis sets, and then extend the result to bigger molecules, finally we study the hyperpolarizabilities of long chain polymer. The second hyperpolarizabilities (γ) of several atoms and diatomic molecules have been calculated at RHF/x-aug-cc-pVXZ (x=0-7 or 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 more than 4 or 5, γblows 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. Then we calculated the second hyperpolarizabilities (γ) of several open shell atoms and molecules C,N,O,F,OH and OH+ at ROHF/x-aug-cc-pVXZ (x=0-5 or 7, X=T or Q) by finite-field method (FF), and it is just as the situation in calculations of close shell atoms and molecules by coupled-perturbed Hatree-Fock method (CPHF). The values at inflexion points are good estimates for the Hatree-Fock limits. According to our calculations,the x-aug-cc-pVTZ basis sets are appropriate not only for SCF but also for high-level correlated calculations of the second hyperpolarizabilities, and the basis sets correspond inflexion points (it is usually 4-aug-cc-pVTZ) are appropriate for the second hyperpolarizabilities of every level correlated. We find that the diverge of γwith the extent of basis set is due to that basis set is not complete enough to describe the wave function in the area near nuclei. In order to overcome this problem, we build a basis set for Ne atom, as an example, which contains three parts and optimized them for E0, α, γrespectively. In this way, we can eliminate the inflexion point and get the accurate hyperpolarizability of Ne atoms. However, it is apparently that the 4-aug-cc-pVTZ basis set is too big for calculating better moleculars. Because the Hartree-Fock limits can be obtained at the 4-aug-cc-pVTZ basis set, this basis set is good estimates for choosing the suitable basis set for the second hyperpolarizabilities (γ). We use the values calculated at CCSD(T)/4-aug-cc-pVTZ level, and calculated at 4-aug-cc-pVTZ basis set by different methods to estimate whether the basis sets are good or bad. The second hyperpolarizabilities (γ) of several molecules H2O, CO, HF,H2 and N2 have been calculated at the expanded basis sets: 6-31G+, D95+, ANO+, aug-cc-pVDZ+, and Hypol, 4-aug-cc-pVTZ basis sets by Finite-Field method (FF) method in the context of electron correlation corrected molecular energies, and the MP2/aug-cc-pVDZ+ level is found to perform well. With the same principle, we choose the 6-31G basis sets to calculate the second hyperpolarizabilities γof the polyethylene species,and study the relationship between the hyperpolarizabilities γand the lentgth of molecular chain.
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