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

ProSpectS was a project aimed at the development of relativistic computational methods for the prediction of optical properties of solids. I pursued the project at the Max Planck Institute for the Structure and Dynamics of Matter (MPSD) in Hamburg, Germany, for the outgoing phase lasting two years and at the University of Tromsø (UiT) for the returing phase during the final year. The theory group at MPSD lead by Prof. Angel Rubio is a world leader in several fields including computational solid state physics and light-matter interactions. I brought to the group my expertise in relativistic methods and the development of computer program ReSpect. Within ReSpect I worked on novel methods for calculating spectroscopic properties, particularly X-ray absorption spectra where relativistic effects are prominent. We also introduced a new relativistic Hamiltonian called amfX2C to the calculation of X-ray spectra. This method significantly decreases the computational cost of relativistic calculations while preserving accuracy, especially in the description of spin-orbit coupling, thus improving upon previous approaches. These development were included in the public release of the ReSpect program. Parallel to the development of ReSpect, we pursued an alternative path to the project's goals by implementing a relativistic Hamiltonian into the computer program Octopus developed at MPSD. The Octopus program had existing functionality for calculations of linear and non-linear optical properties of molecules and solids but lacked a treatment of relativistic effects. I implemented relativistic description of electronic structure at the level of ZORA Hamiltonian into Octopus and linked it with the optical property calculations. This method was included in the most recent public release of the Octopus program and a scientific article is currently in preparation. Besides the main project, we started two additional collaborative projects. The first was focused on combining relativistic description of electronic structure with the quantum description of light as photons. The resulting method is relativistic quantum electrodynamical density functional theory and enables the description of molecules and materials in optical cavities, i.e. nanostructures confining light, in cases when relativistic effects are important. This is a modern field of research that promises a new way of doing chemistry by manipulating molecular properties using the photon modes of optical cavities. These phenomena were demonstrated experimentally and the group in Hamburg is a leading place for their theoretical studies. The second is focused on theoretical description of ultrafast spectroscopies, i.e. modern experimental techniques enabled by recent advances in laser technology that allow to follow quantum dynamics in time. The importance of this research field was highlighted by the award of the 2023 Nobel Prize in Physics to the pioneers of attosecond science. We published a joint article on ultrafast X-ray absorption spectra while a follow-up work is currently being finalized. To conclude, ProSpectS led to methodological advances in relativistic calculations published in several academic articles with more under review and in preparation, the development and public release of new capabilities of two scientific program packages, ReSpect and Octopus, and initiated a collaboration between UiT and MPSD that will last beyond the duration of the project.

The outcomes of the project are novel computational methodologies implemented and released in two quantum chemical program packages. Within the relativistic spectroscopy DFT program ReSpect developed at UiT we implemented a novel method for calculations of X-ray absorption spectra based on the amfX2C Hamiltonian allowing computationally efficient access to molecular properties with accurate treatment of spin-orbit coupling, as well as a real-time method for simulation of attosecond pump-probe spectroscopies, currently important and rapidly advancing spectroscopic techniques. Within a real-time real-space DFT program Octopus developed at MPSD we implemented a relativistic method based on the ZORA Hamiltonian for electronic structure and optical properties of molecules and solids. Moreover, we developed a linear response relativistic quantum electrodynamical density functional theory that combines relativistic description of electronic structure with quantized description of light confined in photonic structures such as optical cavities. This novel field of cavity control or polaritonic chemistry has recently attracted a lot of interest from the scientific community due to its perspective for controlling molecular and material properties and influencing the outcome of chemical reactions. By combining it with relativistic quantum chemistry we opened a new direction of research that has become a foundation of further projects.

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.