Automatic Generation of Density-Fitting Auxiliary Basis Sets for All-Electron Dirac–Kohn–Sham Calculations

In this study, we present a general workflow that enables the automatic generation of auxiliary density basis sets for all elements of the periodic table (from H to Og) to facilitate the general applicability of relativistic Dirac-Kohn-Sham calculations. It is an important tool for the accurate description of relativistic effects, including spin-orbit coupling, in molecules containing heavy elements. The latter are very important in various fields, ranging from catalysis to quantum technologies. The automatic generation algorithm is based on an even-tempered scheme inspired by a previous work by P. Calaminici et al. J. Chem. Phys. 2007, 126, 044108, in which the auxiliary basis sets were generated for nonrelativistic DFT calculations within the GGA approximation. Here, the algorithm uses basic information from the principal relativistic spinor basis set (exponents and angular momentum values) and includes a simple strategy to account for the high angular momentum of electrons in heavy and superheavy elements. The workflow developed here allows us to perform extensive automated tests aimed at verifying the accuracy of the auxiliary basis sets in a large molecular data set of about 300 molecules representing all groups and periods of the periodic table. The results show that our auxiliary basis sets achieve high accuracy, with errors in the Coulomb energies of a few mu-hartree, which are of the same order of magnitude as in the nonrelativistic density fitting. The automatic workflow developed here is general and will be applied in the future for the optimization of auxiliary basis sets to include exact exchange in relativistic approaches. The latter will be a crucial step for the accurate description of spectroscopic properties and spin dynamics in molecular systems containing heavy elements.