Core Hole Effect to Valence Excitations: Tracking and Visualizing the Same Excitation in XPS Shake-Up Satellites and...

Introducing a core hole significantly alters the electronic structure of a molecule, and various X-ray spectroscopy techniques are available for probing the valence electronic structure in the presence of a core hole. In this study, we visually demonstrate the influence of a core hole on valence excitations by computing the ultraviolet absorption spectra and the shake-up satellites in X-ray photoelectron spectra for pyrrole, furan, and thiophene, as complemented by the natural transition orbital (NTO) analysis over transitions with and without a core hole. Employing equivalent core hole time-dependent density functional theory (ECH-TDDFT) and TDDFT methods, we achieved balanced accuracy in both spectra for reliable comparative analysis. We tracked the same involved valence transition in both spectra, offering a vivid illustration of the core hole effect via the change in corresponding particle NTOs introduced by a 1s core hole on a C_α, C_β, or O atom. Our analysis deepens the understanding of the core hole effect on valence transitions, a phenomenon ubiquitously observed in general X-ray spectroscopic analyses.