Efficient and reliable relativistic all-electron approach for molecular and periodic systems of any dimensionality

• Applicant: Dr. Yannick Franzke
• Subject Area: Theoretical Chemistry: Molecules, Materials, Surfaces
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 518707327

The interaction of systems with different dimensionalities is of great importance in chemistry and materials science. For instance, the interaction of a molecule with a surface is key in heterogeneous catalysis. The same holds for photonics. Here, adsorbed molecules on surfaces are used to tune the optical properties of systems to develop new technologies. Theoretical predictions or calculations to complement experimental findings are pivotal to advance the fundamental understanding of chemistry and materials science, which is essential for a tailored design of chemical reactions and materials. Previous research mainly focused on a non-relativistic description of the electronic structure in density functional theory (DFT). However, such an approach is not applicable across the complete periodic table of elements. A consideration of special relativity and relativistic effects including spin-orbit coupling is essential for quantitatively or even qualitatively correct predictions in computational chemistry and materials science of heavy elements, which play an essential role in basic research and large-scale industrial applications. The theoretical foundation of relativistic quantum chemistry is the Dirac equation, which not only describes the electron but also its antiparticle, the positron. The latter is not relevant for chemistry and consequently a decoupling of the respective energy spectra is highly desirable. Recent progress in this direction was made with the establishment of exact two-component (X2C) theory, which efficiently and accurately decouples the electronic and positronic states. However, X2C is still in a very premature state for periodic systems (chains, polymers, surfaces, solids) and no analytical derivatives were presented. The latter are needed to calculate chemical properties such as the structure. Therefore, the main goal of this project is to develop an efficient, flexible, and robust X2C-DFT approach for ground-state energies and gradients of periodic systems. This covers the following steps. First, local approximations will be introduced, making use of the short-range nature of relativistic effects. This is crucial for reducing computational costs and enables large-scale calculations. Second, the current density will be explicitly included for a rigorous formulation of relativistic DFT. Spin-orbit interaction in X2C and the Dirac equation is a form of magnetic induction and thus induces a current density, which has to be considered. Third, analytical gradients will be derived and implemented. This allows us to optimize the structure of systems of any dimensionality, i.e. molecules, chains, polymers, surfaces, and solids. Fourth, benchmark studies will be carried out to identify best practices. Thus, the projects sets the path for a flexible tool in computational studies of heterogeneous catalysis and photonics.

• DFG Programme: WBP Position