Simulating Third-Order Nonlinear Optical Properties Using Damped Cubic Response Theory within Time-Dependent Density Functional Theory

A general implementation for damped cubic response properties is presented using time-dependent density functional theory (TDDFT) and Slater-type orbital basis sets. To directly calculate two-photon absorption (TPA) cross sections, we also present an implementation of a reduced damped cubic response approach. Validation of the implementations includes a detailed comparison between response theory and the sum-over-states approach for calculating the nonlinear optical properties of LiH, as well as a comparison between the simulated and experimental TPA and third-harmonic generation (THG) spectra for the dimethylamino-nitrostilbene (DANS) molecule. The study of LiH demonstrates the incorrect pole structure obtained in response theory due to the adiabatic approximation typically employed for the exchange-correlation kernel. For DANS, we find reasonable agreement between simulated and experimental TPA and THG spectra. Overall, this work shows that care must be taken when calculating higher-order response functions in the vicinity of one-photon poles due to the approximate kernels typically used in the simulations.