Study of static and dynamic first hyperpolarizabilities using time-dependent density functional quadratic response theory with local contribution and natural bond orbital analysis

We apply time-dependent density-functional quadratic response theory to investigate the static and dynamic second-order polarizabilities (first hyperpolarizability) beta. A new implementation using Slater-type basis functions, numerical integration, and density fitting techniques is reported. The second order coupled perturbed Kohn-Sham equations are solved and the second-order perturbed charge density is obtained. It is useful to highlight atomic and bond contributions to understand the relation between molecular structure and properties. Four moderately sized molecules (para-nitroaniline and derivatives thereof) are investigated to assess the accuracy of the time-dependent density-functional theory computations and to investigate the distribution of the second-order charge density as well as the "beta density." Our results highlight the contributions from atoms and bonds on different functional groups to the total value of beta with Mulliken-type and natural bond orbital (NBO) analyses, and demonstrate in some cases how contributions from a particular bond may be identified easily by visual inspection of the beta density. In addition, the position of side group substitution on carbon-carbon bonds significantly affects the hyperpolarizability. A contribution analysis as performed here might be helpful for the design of new materials with desired properties.