Extension of second-principles density functional theory into the time domain

We present an extension of second-principles density functional theory (SPDFT) to perform time-dependent simulations. Our approach calculates the real-time, real-space evolution of the density matrix using the Liouville-von Neumann equation of motion, enabling the determination of optical and transport properties in very large systems, containing tens of thousands of atoms, on modest computational platforms. Unlike other methods, SPDFT is applicable to a wide range of materials, including both metals and insulators. We demonstrate its capabilities by computing the spectra of ${\mathrm{SrTiO}}_{3}$, diamond, and metallic lithium. While SPDFT results for ${\mathrm{SrTiO}}_{3}$ closely match those obtained from DFT with linear perturbation theory, significant improvements are observed for diamond and metallic lithium. In diamond, the inclusion of electron-electron interactions during the density-matrix evolution yields spectra that more accurately reproduce Bethe-Salpeter equation results than perturbative DFT. In lithium, time-dependent SPDFT captures both interband transitions and the Drude peak, enabling detailed ab initio studies of transport properties beyond usual approximations.