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.