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.