Linear and Non-linear Response Properties and Spectroscopy of Solids from Relativistic TDDFT

During the second year I worked in the host group in Hamburg while also collaborating with the group in Tromsø where I returned after spending the my years abroad. Our work comprised several tasks related to relativistic description of linear and non-linear properties of solids. First, we concluded the development of a computational method for calculating X-ray spectra with relativistic X2C Hamiltonians and successfully published the results. These results highlight the amfX2C Hamiltonian as an approach that allows both accurate and computationally efficient relativistic calculations of ground and excited state properties. Our current work is focused on extending this development into the realm of periodic solids where the combination of accuracy and efficiency is crucial. Moreover, I implemented the the relativistic ZORA Hamiltonian into the computer program Octopus that is being developed by the host group. The Octopus program has versatile functionality for calculations of linear and non-linear optical properties of molecules and solids while being unique in performing the calculations on a real-space grid. We showed that this capability can be combined with relativistic description of electronic structure. We are currently testing the methodology on molecular and solid-state properties and are writing a manuscript summarizing this development. In addition, we worked on two parallel projects that combine the expertise of the Tromsø and Hamburg groups thus strengthening the collaboration started by my visit. One is a relativistic description of attosecond spectroscopies published earlier this year. This is a timely project given the fact that the pioneers of attosecond science were awarded the Nobel Prize in Physics in 2023 highlighting the importance of this research field within modern science. Finally, we started a project focused on combining relativistic description of electronic structure with the quantum description of light into a relativistic quantum electrodynamical density functional theory for molecules and materials in optical cavities which is a new and exciting direction in theoretical chemistry.

ProSpectS is a project aimed at the development and applications of a novel computational methodology for the prediction of linear and second-order non-linear optical properties of solid-state materials. These spectroscopic properties are measured to characterize materials for applications in electronics, optics, or photonics. Moreover, the development of novel radiation sources such as X-ray free electron lasers drives the adoption of new types of spectroscopies based on ultrafast and multi-photon processes. These advances create demand for new theoretical tools able to predict and interpret the results of such experiments. ProSpectS aims to respond to this demand by delivering a computer program that will include relativistic effects in full four-component Dirac regime. This will enable its applicability for materials containing all elements across the periodic table including heavy elements. The combination of relativistic effects with all-electron description in localized basis sets will, in turn, ensure correct description of X-ray spectra. Finally, the damped response time dependent density functional theory approach to material properties will offer favourable balance between accuracy and computational cost and allow treatment of near-resonant, high-frequency, or high-density of states spectral regions.