Core-Level X-ray Absorption Spectroscopy within Time-Dependent Density Functional Theory

Abstract

X-ray absorption spectroscopy is an important technique for studying the unoccupied electronic structure of materials. In particular, core-level excitations make it possible to investigate the local electronic structure and bonding characteristics in an element-specific manner. However, describing these excitations theoretically is challenging because the excitation of a core electron creates a strong interaction between the excited electron and the remaining core hole. Therefore, reliable theoretical methods are required to properly describe these effects. In this thesis, core-level X-ray absorption spectra are investigated using time-dependent DFT. The calculations were performed using the exciting code, which is an all-electron full-potential electronic-structure package based on the linearized augmented plane wave plus local orbital (LAPW+lo) method[51]. First, ground-state density functional theory calculations were carried out and convergence tests were performed to determine suitable computational parameters. After obtaining a converged ground-state electronic structure, core-level spectra were calculated within the linear-response TDDFT framework using several exchange–correlation kernels, including the the adiabatic local density approximation (ALDA), random phase approximation (RPA), and long-range corrected kernels in both static and dynamic forms. The method was applied to study the Li K-edge and F K-edge spectra of lithium fluoride (LiF) and the Al L₂,₃-edge spectrum of aluminum nitride (AlN). For LiF, the Li K-edge spectrum shows a strong peak near the absorption edge, which originates from the interaction of the Li 1s core hole and the excited electron. The calculations show that the spectral shape and intensity depend on the choice of exchange–correlation kernel. In contrast, the calculated F K-edge spectra are very similar for all kernels considered, indicating a weaker sensitivity to the kernel choice. For AlN, the calculated Al L₂,₃-edge spectrum reproduces the main features of the near-edge structure observed experimentally. Overall, the results demonstrate that TDDFT can provide a useful and computationally efficient approach for studying core-level excitations. The work also highlights the importance of the exchange–correlation kernel in describing excitonic effects in X-ray absorption spectra. Future work could extend these calculations to additional materials and explore improved exchange–correlation kernels for a more accurate description of core spectroscopy.