Efficient basis sets for core-excited states motivated by Slater's rules.

X-Ray photoemission spectroscopy is a commonly applied characterization technique that probes the local chemistry of atoms in molecules and materials via the photoexcitation of electrons from atomic core orbitals. These measurements can be interpreted by comparison with previous literature or through the calculation of core-electron binding energies (CEBEs) for model systems. However, physically and numerically accurate description of the core-excited electronic structures demands specializations beyond routine ground state setups. Inspired by Slater's rules, we focus on developing computationally efficient and physically motivated contractions to reproduce the core-excited atomic orbitals which led to improved numerical accuracy of calculated CEBEs. When applied to carbon 1s excitations in a wide range of molecules, these core-excited basis sets produce total energy differences (ΔSCF) using a hybrid exact-exchange density functional (B3LYP) that can reproduce core-excitation energies within experimental accuracy (∼0.1 eV). Due to missing relativistic effects, heavier elements (N, O) exhibit slightly larger systematic absolute errors, but still maintain a satisfactory 0.2 eV mean average error for relative CEBEs. We also connect the known variability in the core level binding energy with local atomic charge to demonstrate how the transferability of a given model should be measured against a diverse test set. We conclude by exploring one outlier, CO, and the outlook for extending this approach to other elements.