Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectroscopy by the Δ Self-Consistent-Field Approach

We investigate the basis set requirements for calculating properties corresponding to removing core electrons by the Δ self-consistent-field approach using Hartree–Fock and density functional theory. Standard contracted basis sets are shown to produce large errors and the improved performance of core-augmented basis sets is traced to the fact that the core-augmenting functions effectively create an auxiliary set of uncontracted functions in the core region. We propose two specific basis sets of double and triple-ζ quality based on exponent interpolation of the polarization consistent basis sets, denoted pcX-1 and pcX-2, that display significantly lower basis set errors compared to other alternatives. These are suitable for both nonrelativistic and relativistic calculations of the Douglas–Kroll–Hess type, with typical basis set errors of 0.1 and 0.01 eV, respectively, and they can be used in a mixed basis set approach with only a minor degradation in performance. The versions augmented with diffuse functions (aug-pcX-1 and aug-pcX-2) are shown to perform better than other alternatives for X-ray absorption spectroscopy. When used in connection with range-separated hybrid density functional methods and relativistic corrections, the pcX-n basis sets can in favorable cases reproduce experimental results to within a few tenths of an eV.