Density Functional Theory for Molecular and Periodic Systems in TURBOMOLE: Theory, Implementation, and Applications

This work provides a detailed overview of density functional theory (DFT) methods for treating molecular and periodic systems within the TURBOMOLE software package. The implementation employs Gaussian-type orbitals and is based on efficient real-space techniques and density-fitting approaches for Coulomb interactions. Recent developments are reviewed, including the treatment of relativistic effects with effective core potentials, the incorporation of spin-orbit coupling via two-component formalisms, and the extension to real-time time-dependent DFT (RT-TDDFT). Embedding schemes based on frozen-density and projection-based approaches are also discussed, enabling the combination of DFT with high-level correlated wave function methods and many-body perturbation theory for selected subsystems. Representative applications demonstrate the capabilities across bulk materials, surfaces, low-dimensional nanostructures, and adsorption processes. Additionally, a web-based graphical interface has been developed to support input generation, structure manipulation, and output analysis. By consolidating theoretical foundations, implementation strategies, and application examples, this work provides a reference for the use of periodic DFT methods in quantum chemical and materials science studies.