Relativistic quantum calculations to understand the contribution of f-type atomic orbitals and chemical bonding of actinides with organic ligands.

The nuclear waste problem is one of the main interests of rare earth and actinide element chemistry. Studies of actinide-containing compounds are at the frontier of the applications of current theoretical methods due to the need to consider relativistic effects and approximations to the Dirac equation in them. Here, we employ four-component relativistic quantum calculations and scalar approximations to understand the contribution of f-type atomic orbitals in the chemical bonding of actinides (Ac) to organic ligands. We studied the relativistic quantum structure of an isostructural family made of Plutonium (Pu), Americium (Am), Californium (Cf), and Berkelium (Bk) atoms with the redox-active model ligand DOPO (2,4,6,8-tetra--butyl-1-oxo-1-phenoxazin-9-olate). Crystallographic structures were available to validate our calculations for all mentioned elements except for Cf. In short, state-of-the-art relativistic calculations were performed at different levels of theory to investigate the influence of relativistic and electron correlation effects on geometrical structures and bonding energies of Ac-DOPO complexes (Ac = Pu, Am, Cf, and Bk): (1) the scalar (sc) and spin-orbit (so) relativistic zeroth order regular approximation (ZORA) within the hybrid density functional theory (DFT) and (2) the four-component Dirac equation with both the Dirac-Hartree-Fock (4c-DHF) and Lévy-Leblond (LL) Hamiltonians. We show that sr- and so-ZORA-DFT could be used as efficient theoretical models to first approximate the geometry and electronic properties of actinides which are difficult to synthesize or characterize, but knowing that the higher levels of theory, like the 4c-DHF, give closer results to experiments. We also performed spin-free 4c calculations of geometric parameters for the Americium and Berkelium compounds. To the best of our knowledge, this is the first time that these kinds of large actinide compounds (the largest contains 67 atoms and 421 electrons) have been studied with highly accurate four-component methods (all-electron calculations with 6131 basis functions for the largest compound). We show that relativistic effects play a key role in the contribution of f-type atomic orbitals to the frontier orbitals of -DOPO complexes. The analysis of the results obtained applying different theoretical schemes to calculate bonding energies is also given.