Does scaling or addition provide the correct frequency dependence of beta (omega ; omega, omega) at the correlated level? An investigation for six e sigma molecules

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Abstract
The frequency dependent polarizability α(– ω σ; ω1) and the frequency dependent first hyperpolarizability β(– ω σ; ω1, ω2) have been calculated using both self consistent field (SCF) and multiconfigurational SCF (MCSCF) linear and quadratic response functions for six small molecules: BH, CO, HF, H2O, NH3, and H S. Two approximate ways of using the calculated dispersion at the SCF level to describe the frequency dependence at the correlated level, referred to as scaling and addition, have been tested. Calculated frequency dependent MCSCF results are used to investigate the validity of these approximations. Our results indicate that, if the correlation correction to the static average hyperpolarizability is large, then the approximations do not hold. The same conclusion holds if correlation changes the sign of the average first hyperpolarizability at zero frequency. There is also a tendency towards an underestimation of the frequency dependence if scaling or addition is applied. There does not seem to be a simple way to infer anything about the validity of scaling or addition for β‖ from either the lower lying excitations and their intensities or from the frequency dependence of the dipole polarizability.

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