Evaluation of the molecular static and dynamic first hyperpolarizabilities

By considering two prototypical π-conjugated compounds, several technical aspects associated with the evaluation of the first hyperpolarizabilities have been addressed in this article, that is, (i) the automatization of the Romberg's scheme to improve the numerical accuracy in the finite field method, (ii) the evaluation of the frequency dispersion at correlated levels using approximate schemes, and (iii) the deviations from Kleinman's symmetry conditions. It results from this study that accurate numerical derivatives can be obtained by resorting to the Romberg's method and by analyzing the Romberg's table in terms of two quantities, the field error and the iteration error. Indeed, the resulting first hyperpolarizability values are in close agreement with those obtained using an analytical differentiation procedure. The reliability of the multiplicative and additive approximate schemes to describe the frequency dispersion at correlated levels from using HF (Hartree-Fock) frequency dispersion has been confirmed to be limited to large wavelengths or far-from-resonance wavelength regions. Kleinman's symmetry conditions have been assessed, showing that for off-diagonal components of these two π-conjugated compounds, the deviations could be substantial. Nevertheless, good accuracy can be achieved for experimentally related quantities like β_HRS because the diagonal tensor components are dominant. © 2014 Wiley Periodicals, Inc. Predicting nonlinear optical properties of molecules remains a challenging task for quantum chemistry. This article addresses several technical aspects associated with the evaluation of the first hyperpolarizabilities, such as the automatization of the Romberg's scheme in the finite field method and the frequency dispersion. Practical clues on the use of computational techniques are provided, as well as reference values obtained for model systems.