Benchmark Study of Core-Ionization Energies with the Generalized Active Space-Driven Similarity Renormalization Group

X-ray photoelectron spectroscopy (XPS) is a powerful experimental technique for probing the electronic structure of molecules and materials; however, interpreting XPS data requires accurate computational methods to model core-ionized states. This work proposes and benchmarks a new approach based on the generalized active space-driven similarity renormalization group (GAS-DSRG) for calculating core-ionization energies and treating correlation effects at the perturbative and nonperturbative levels. We tested the GAS-DSRG across three data sets. First, the vertical core-ionization energies of small molecules containing first-row elements are evaluated. GAS-DSRG achieves mean absolute errors below 0.3 eV, which is comparable to high-level coupled cluster methods. Next, the accuracy of GAS-DSRG is evaluated for larger organic molecules using the CORE65 data set, with the DSRG-MRPT3 level yielding a mean absolute error of only 0.34 eV for 65 core-ionization transitions. Insights are provided into the treatment of static and dynamic correlation, the importance of high-order perturbation theory, and notable differences from density functional theory in the predicted energy ordering of core-ionized states for specific molecules. Finally, vibrationally resolved XPS spectra of diatomic molecules (CO, N₂, and O₂) are simulated, showing excellent agreement with experimental data.