ZORA Gaussian basis sets for Fr, Ra, and Ac

Segmented all-electron basis sets of double and triple zeta valence qualities plus polarization functions (DZP and TZP) for the elements Fr, Ra, and Ac to be used with the zeroth-order regular approximation (ZORA) were presented. These sets were constructed from the reoptimization of the contraction coefficients of the corresponding non-relativistic basis sets. In order to adequately describe electrons distant from the atomic nuclei, these sets were augmented with diffuse functions and were, respectively, designated as ADZP-ZORA and ATZP-ZORA. At the ZORA-B3LYP theory level, the relativistic sets were employed to calculate ionization energies of Fr, Ra, and Ac as well as bond lengths, dissociation energies, harmonic vibrational frequencies, and static mean dipole polarizabilities of some diatomics. Comparing with benchmark theoretical results and with experimental data available in the literature, it can be verified that our basis sets are able to produce reliable and accurate results. Evaluation of the performances of ZORA and second-order Douglas-Kroll-Hess Hamiltonians was performed.