Systematic generation of electron models for second-principles density functional theory methods

We present a systematic, quasiautomated methodology for generating electronic models in the framework of second-principles density functional theory (SPDFT). This approach enables the construction of accurate and computationally efficient models by deriving all necessary parameters from first-principles calculations on a carefully designed training set. A key feature of our method is the enforcement of space-group symmetries, which reduces both the number of independent parameters and the required computational effort. The formalism includes improved treatments of one-electron Hamiltonians, electron-lattice coupling, through both linear and quadratic terms, and electron-electron interactions, enabling accurate modeling of structural and electronic responses. We apply the methodology to ${\mathrm{SrTiO}}_{3}$, LiF, and metallic Li materials that present a wide variety of properties as corresponds to a transition-metal perovskite, a wide-band-gap ionic insulator, and a free-electron metal, respectively. In all cases, the resulting models reproduce DFT reference data with high fidelity across various atomic configurations and charge states. Our results validate the robustness of the approach and highlight its potential for simulating complex phenomena such as polarons and excitons. This work lays the foundation for extending SPDFT to real-time simulations of optoelectronic properties and further integration with machine-learning methods.