Limitations of the sum-over-states approach to second-order hyperpolarizabilities: para-nitroaniline and all-trans-1,3,5,7-octatetraene

Abstract

A systematic investigation of the effects of various configuration interaction (CI) approximations, input frequencies, and geometry variations on the sum-over-states calculated second-order hyperpolarizabilities is performed using AM1 semiempirical NDDO theory (NDDO/SOS/CI). Para-nitroaniline and 1,3,5,7-all-trans-octatetraene are chosen as test compounds. It turns out that it is necessary to include at least single and double excitations (CISD) and to have active windows containing the complete scheme of π- and n-type orbitals to get converged CI solutions. These approximations are thus limited to molecules, which are too small to be of interest for application in non-linear optical organic materials. For non-suitable low-level CI-approximations, artificial effects on calculated γ are obtained. Information about the hyperpolarizability resonant regions and the excitation pathways for the compounds can be obtained in a consistent manner by the use of the above-mentioned methodologically stable CI-approximation. The geometry dependence of γ is visualized by hyperpolarizability torsional profiles and hypersurfaces and by comparison of the values for molecule builder-, semiempirical- and DFT-derived structures. From these findings, we emphasize the use of DFT-derived structures as starting points for semiempirical SOS calculations of hyperpolarizabilities.