Progress in the Theory of X‑ray Spectroscopy: From Quantum Chemistry to Machine Learning and Ultrafast Dynamics

The development of high-brilliance third- and fourth-generation light sources such as synchrotrons and X-ray free-electron lasers (XFELs), the emergence of laboratory-based X-ray spectrometers, and instrumental and methodological advances in X-ray absorption (XAS) and (non)­resonant emission (XES and RXES/RIXS) spectroscopies have had far-reaching effects across the natural sciences. However, new kinds of experiments, and their ever-higher resolution and data acquisition rates, have brought acutely into focus the challenge of accurately, quickly, and cost-effectively analyzing the data; a far-from-trivial task that demands detailed theoretical calculations that are capable of capturing satisfactorily the underlying physics. The past decade has seen significant advances in the theory of core-hole spectroscopies for this purpose, driven by all of the developments above andcruciallya surge in demand. In this Perspective, we discuss the challenges of calculating core-excited states and spectra, and state-of-the-art developments in electronic structure theory, dynamics, and data-driven/machine-led approaches toward their better description.