Bridging Electron Density Relaxation and XPS Spectroscopy: Orbital-Resolved Trends in Core-Ionized Aum (m = 4, 10, 20) and (TiO2)n (n = 2-4) Clusters.

Core electron binding energies (CEBEs) in nanomaterials encode element-specific chemical information, yet their interpretation is often complicated by quantum size effects and site-to-site heterogeneity in small finite systems. Here, I use all-electron Δ-Self Consistent Field (ΔSCF) density functional theory to quantify site-resolved CEBEs and the accompanying orbital-level relaxation response in two chemically distinct cluster families: metallic Aum (m = 4, 10, 20) and anatase-like (TiO2)n (n = 2-4), including multiple structural isomers. Beyond total-energy differences, I analyze the orbital-resolved Kohn-Sham eigenvalue shift, Δε, induced by a localized core-hole. Finally, I assess a summed eigenvalue-shift descriptor, ΣΔε, as a compact reduction of these data. The results highlight the intrinsically quantum-mechanical origin of core-level shifts in finite systems and suggest that orbital-resolved relaxation patterns may serve as auxiliary, physically interpretable descriptors in future core-level spectroscopy studies.