Core-Ionized States and X-ray Photoelectron Spectra of Solids from Periodic Algebraic Diagrammatic Construction Theory

We present the first-ever implementation and benchmark of periodic algebraic diagrammatic construction theory (ADC) for core-ionized states and X-ray photoelectron spectra (XPS) in crystalline materials. Using a triple-ζ Gaussian basis set and accounting for finite-size and scalar relativistic effects, the strict and extended second-order ADC approximations (ADC(2) and ADC(2)-X) predict the core ionization energies of weakly correlated solids within ∼1.5 and 0.5 eV of experimental measurements, respectively. We further demonstrate that the ADC(2)-X method can capture the satellite features in XPS spectra of graphite, cubic and hexagonal boron nitride, and TiO₂, albeit significantly overestimating their energies. The ADC(2)-X calculations reveal that the satellite transitions display strong configuration interaction with excitations involving several frontier orbitals delocalized in phase space. Our work demonstrates that ADC is a promising first-principles approach for simulating the core-excited states and X-ray spectra of materials, highlighting its potential and motivating further development.