Development of all-electron scalar relativistic basic sets

Routine computational investigations of chemical systems containing elements beyond Kr are dominated by the use of effective core potentials (ECPs) because they reduce the size of the computational task while providing an easy, if approximate, way to account for the most important relativistic effects. However, they have their drawbacks and limitations, for example when there is a need to model a property that depends on the electron density near the nucleus or for topological analysis of electron densities. Therefore, either for validating the use of ECPs or for circumventing their inherent limitations, it is necessary to have all-electron basis sets that allow efficient calculations with the popular scalar relativistic Hamiltonians, such as the Zeroth Order Regular Approximation (ZORA), and the Douglas-Kroll-Hess (DKH) approach.
An answer to this need is the family of Segmented All-electron Relativistically Contracted (SARC) basis sets, constructed specifically for DFT treatments in conjunction with the DKH2 and ZORA Hamiltonians. The SARC basis sets are segmented CGTO sets of polarized triple-zeta quality. They present an efficient alternative to ECPs for routine DFT studies of large molecules and their performance has been benchmarked for both atomic and molecular properties.
Exponents are derived from relatively simple rules, using the radial expectation values from accurate atomic calculations as generator quantities. In contrast to non-relativistic basis sets, the SARC basis sets are flexible in the core region, with high exponents required by relativistic Hamiltonians. Polarization functions are added with the requirements of DFT in mind, building flexibility to the chemical valence space without introducing redundant angular momentum (correlation) functions.
Contraction coefficients are optimized separately for the DKH2 and ZORA Hamiltonians, because these two scalar relativistic approximations produce quite different shapes for the orbitals close to the nucleus. From the differences of DKH2 and ZORA radial distribution functions (figure shows differences for the Hg atom), it is readily seen that the ZORA potential is more attractive than DKH2. This issue is explicitly addressed with individually adapted contractions.

Typical applications of SARC basis sets include

• Benchmarking effective core potentials before employing them in extended projects.
• Molecular properties that depend on the density near the nucleus: NMR, Mössbauer, EPR, XAS, etc.
• Topological analysis of electron densities with AIM and ELF.
• Magnetic interactions in f-element-containing molecules, e.g. in 3d-4f single-molecule magnets.
• Processes in lanthanide and actinide chemistry that involve electrons in f-orbitals (e.g. luminescence).

SARC basis sets are available for the third-row transition metals (5d series, Hf-Hg), the 6p elements (Tl-Rn), the lanthanides (4f series, La-Lu), and the actinides (5f series, Ac-Lr). All SARC basis sets for Z > 54 (along with corresponding auxiliary basis sets) are included in the ORCA program package, which also contains scalar relativistic recontractions of the Karlsruhe basis sets up to Xe.