Bethe-Salpeter Equation Approach for Calculations of X-ray Spectra

Abstract

X-ray spectroscopy is a powerful and widely used tool for the investigation of the electronic structure of a large variety of solid state materials, including crystals materials, liquids, amorphous solids, molecules, and extended states such as clusters or interfaces. The local nature of x-ray mediated electronic excitations, involving transitions to or from localized, atomic-like, core levels, makes them ideal probes of local electronic properties: bonding character, charge transfer, and local geometry. The interpretation of spectra relies on modeling the excitations accurately to provide a concrete connection between specific properties of a system and the resulting x-ray spectrum. As experimental techniques and facilities have improved, including third generation synchrotron sources and the advent of x-ray free electron lasers, measurements have been taken on wider ranges of systems, exploring the effects of temperature and pressure, and at higher resolutions than before, but theoretical techniques have lagged. Our goal is to develop a first-principles theoretical framework capable of achieving quantitative agreement with x-ray absorption near-edge structure (XANES) experiments. This thesis aims to develop the Bethe-Salpeter equation (BSE), a particle-hole Green's function method, for describing the excited electronic state produced in core-level x-ray absorption and related spectroscopies. Building upon density functional theory along with self-energy corrections, our approach provides connection to experiment with minimal adjustable parameters, to both aid in interpretation and highlight unaccounted for physical processes. While a fully parameter-free method for calculating x-ray spectroscopy remains elusive, our method presented here allows for quantitative comparison to experiment without system-dependent fits. This method has been implemented in the OCEAN software package, and results are presented for both insulating and metallic materials, including <italic>3d</italic> transition metal and water systems.