Segmented Contracted Error-Consistent Basis Sets of Quadruple‑ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations

Segmented contracted basis sets of quadruple-ζ quality for exact two-component (X2C) calculations are presented for the elements H–Rn. These sets are the all-electron relativistic counterparts of the Karlsruhe “def2” and “dhf” systems of bases, which were designed for Hartree–Fock and density functional treatments andwith a somewhat extended setalso for correlated treatments. The bases were optimized with analytical basis set gradients and the finite nucleus model based on a Gaussian charge distribution at the scalar-relativistic X2C level. Extensions are provided for self-consistent two-component treatments to describe spin–orbit coupling, polarization effects, and nuclear magnetic resonance (NMR) shielding constants. The basis sets were designed to yield comparable errors in atomization energies, orbital energies, dipole moments, and NMR shielding constants all across the periodic table of elements. A test set of more than 360 molecules representing (nearly) all elements in their common oxidation states was utilized for the valence properties, and a test set of more than 250 closed-shell molecules was employed for the NMR shielding constants. The quality of the developed basis sets is compared to other frequently used relativistic all-electron bases.