Geometries, interaction energies and bonding in [Po(H$_2$O)$_n$]$^{4+}$ and [PoCl$_n$]$^{4-n}$ complexes

Polonium (Z = 84) is one of the rarest elements on Earth. More than a century after its discovery, its chemistry remains poorly known and even basic questions are not yet satisfactorily addressed. In this work, we perform a systematic study of the geometries, interactions energies and bonding in basic polonium(IV) species, namely the hydrated [Po(H$_2$O)$_n$]$^{4+}$ and chlorinated [PoCl$_n$]$^{4-n}$ complexes by means of gas-phase electronic structure calculations. We show that while up to nine water molecules can fit in the first coordination sphere of the polonium(IV) ion, its coordination sphere can already be filled with eight chloride ligands. Capitalising on previous theoretical studies, a focused methodological study based on interaction energies and bond distances allows us to validate the MP2/def2- TZVP level of theory for future ground-state studies. After discussing similarities and differences between complexes with the same number of ligands, we perform topological analyses of the MP2 electron densities in the quantum theory of atoms in molecules (QTAIM) fashion. While the water complexes display typical signatures of closed-shell interactions, we reveal large Po-Cl delocalisation indices, especially in the hypothetical [PoCl]$^{3+}$ complex. This "enhanced" covalency opens the way for a significant spin-orbit coupling (SOC) effect on the corresponding bond distance, which has been studied by two independent approaches (i.e. one a priori and one a posteriori). We finally conclude by stressing that while the SOC may not affect much the geometries of high-coordinated polonium(IV) complexes, it should definitely not be neglected in the case of low-coordinated ones.