Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis

The static and dynamic second hyperpolarizability γ has been investigated by time-dependent density functional cubic response theory. The third-order coupled perturbed Kohn-Sham equations were solved to obtain the third-order perturbed charge density. Calculations on a number of small molecules (N2, CO2, C2 H4, CO, HF, H2 O, and C H4), paradisubstituted oligoacetylene chains, benzene, and eight paradisubstituted benzenes were performed to verify the implementation and to assess the accuracy of the nonhybrid and hybrid time-dependent density functional theory computations. Nitroaniline and a derivative were taken as examples to investigate the distribution of the " γ density" and to demonstrate the feasibility of analyzing cubic response functions in terms of contributions from natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). The results highlight the contributions from atoms and bonds on different functional groups to the total value of γ based on the NBO/NLMO analysis, which might be helpful for new nonlinear optical materials design.