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The nuclear waste problem is one of the main interests of the rare earth andactinide elements chemistry. Studies of Actinide-containing compounds are atthe frontier of the applications of current theoretical methods due to the needto consider relativistic effects and approximations to the Dirac equation inthem. Here, we employ four-component relativistic quantum calculations andscalar approximations to understand the contribution of f-type atomic orbitalsin the chemical bonding of actinides (Ac) to organic ligands. We studied therelativistic quantum structure of an isostructural family made of Plutonium(Pu), Americium (Am), Californium (Cf), and Berkelium (Bk) atoms with theredox-active model ligand; DOPO(2,4,6,8-tetra-tert-butyl-1-oxo-1H-phenoxazin-9-olate). Crystallographicstructures were available to validate our calculations for all mentionedelements except for Cf. In short, state-of-the-art relativistic calculationswere performed at different levels of theory to investigate the relativisticeffects and electron correlations on geometrical structures and bondingenergies of $Ac$-DOPO$_3$ complexes ($Ac$=Pu, Am, Cf, Bk) : 1) the scalarrelativistic zeroth order regular approximation (ZORA) within the hybriddensity functional theory (DFT) and 2) the four-component Dirac equation withthe Dirac-Hartree-Fock (4c-DHF) and L\'evy-Leblond (LL) Hamiltonians. We showthat scalar DFT-ZORA could be used as an efficient theoretical approximation tofirst approximate the geometry and electronic properties of actinides which aredifficult to synthesize or characterize; but knowing that the higher levels oftheory, like the 4c-DHF, gives closer results to experiments than the scalarDFT-ZORA. We also performed spin-free calculations of geometric parameters forthe Americium and Berkelium compounds.

Relativistic Quantum Calculations to Understand the Contribution of f-Orbitals and Chemical Bonding of Actinides with Organic Ligands