On the Core Hole Effect to Valence Excitations: Tracking and Visualizing the Same Excitation in XPS Shake-Up and UV-Absorption Spectra

Introducing a core hole significantly alters the electronic structure of a molecule, making various X-ray spectroscopy techniques valuable for investigating the valence electronic structure in the presence of a core hole. In this study, we visually demonstrate the influence of core hole on valence excitations by computing ultraviolet-visible (UV) absorption and the shake-up satellites in X-ray photoelectron spectra (XPS) of pyrrole, furan, and thiophene, This is complemented by the natural transition orbital (NTO) analysis of transitions, both with and without a core hole. Employing equivalent core hole time-dependent density functional theory (ECH-TDDFT) and TDDFT methods, we achieved balanced accuracy for both the two spectra, Our results not only align well with experiments but also facilitate a reliable comparative analysis. We tracked the same involved valence transition in both spectra, offering a vivid illustration of the core hole effect through the alteration in corresponding particle NTOs introduced by a 1s core hole on a C$_\alpha$ or C$_\beta$ atom or the O atom. Our analysis deepens the understanding of the core hole effect on valence transitions which exist in general X-ray spectroscopies.