DOES SCALING OR ADDITION PROVIDE THE CORRECT FREQUENCY-DEPENDENCE OF BETA(PARALLEL-TO)(-OMEGA(SIGMA) OMEGA(1), OMEGA(2)) AT THE CORRELATED LEVEL - AN INVESTIGATION FOR 6 MOLECULES

The frequency dependent polarizability alpha(-omega(sigma);omega(1)) a nd the frequency dependent first hyperpolarizability beta(-omega(sigma );omega(1),omega(2)) have been calculated using both self consistent h eld (SCF) and multiconfigurational SCF (MCSCF) linear and quadratic re sponse functions for six small molecules: BH, CO, HF, H2O, NH3, and H2 S. Two approximate ways of using the calculated dispersion at the SCF level to describe the frequency dependence at the correlated level, re ferred to as scaling and addition, have been tested. Calculated freque ncy dependent MCSCF results are used to investigate the validity of th ese approximations. Our results indicate that, if the correlation corr ection to the static average hyperpolarizability is large, then the ap proximations do not hold. The same conclusion holds if correlation cha nges the sign of the average first hyperpolarizability at zero frequen cy. There is also a tendency towards an underestimation of the frequen cy dependence if scaling or addition is applied. There does not seem t o be a simple way to infer anything about the validity of scaling or a ddition for beta(1) from either the lower lying excitations and their intensities or from the frequency dependence of the dipole polarizabil ity.