Accurate density functional calculations on frequency-dependent hyperpolarizabilities of small molecules

In this paper we present time-dependent density functional calculations on frequency-dependent first (beta) and second (gamma) hyperpolarizabilities f or the set of small molecules, N-2, CO2, CS2, C2H4, NH3, CO, HF, H2O, and C H4, and compare them to Hartree-Fock and correlated ab initio calculations, as well as to experimental results. Both the static hyperpolarizabilities and the frequency dispersion are studied. Three approximations to the excha nge-correlation (xc) potential are used: the widely used Local Density Appr oximation (LDA), the Becke-Lee-Yang-Parr (BLYP) Generalized Gradient Approx imation (GGA), as well as the asymptotically correct Van Leeuwen-Baerends ( LB94) potential. For the functional derivatives of the re potential the Adi abatic Local Density Approximation (ALDA) is used. We have attempted to est imate the intrinsic quality of these methods by using large basis sets, aug mented with several diffuse functions, yielding good agreement with recent numerical static LDA results. Contrary to claims which have appeared in the literature on the basis of smaller studies involving basis sets of lesser quality, we find that the static LDA results for beta and gamma are severel y overestimated, and do not improve upon the (underestimated) Hartree-Fock results. No improvement is provided by the BLYP potential which suffers fro m the same incorrect asymptotic behavior as the LDA potential. The results are however clearly improved upon by the LB94 potential, which leads to und erestimated results, slightly improving the Hartree-Fock results. The LDA a nd BLYP potentials overestimate the frequency dependence as well, which is once again improved by the LB94 potential. Future improvements are expected to come from improved models for asymptotically correct exchange-correlati on potentials. Apart from the LB94 potential used in this work, several oth er asymptotically correct potentials have recently been suggested in the li terature and can also be expected to improve considerably upon the relative ly poor LDA and GGA results, for both the static properties and their frequ ency dependence. (C) 1998 American Institute of Physics. [S0021-9606(98)305 47-4].