Coordination and thermodynamic properties of aqueous protactinium(V) by first-principle calculations

Protactinium ($Z$ = 91) is a very rare actinide with peculiar physico-chemical properties. Indeed, although one may naively think that it behaves similarly to either thorium or uranium by its position in the periodic table, it may in fact follow its own rules. Because of the quite small energy gap between its valence shells (in particular the 5$f$ and 6$d$ ones) and also the strong influence of relativistic effects on its properties, it is actually a challenging element for theoretical chemists. In this article, we combine experimental information, chemical arguments and standard first-principle calculations, complemented by implicit and explicit solvation, to revisit the stepwise complexation of aqueous protactinium(V) with sulfate and oxalate dianionic ligands (SO$_4$$^{2-}$ and C$_2$O$_4$$^{2-}$, respectively). From a methodological viewpoint, we notably conclude that it is necessary to at least saturate the coordination sphere of protactinium(V) to reach converged equilibrium constant values. Furthermore, in the case of single complexations (i.e. with one sulfate or oxalate ligand bound in the bidentate fashion), we show that it is necessary to maintain the coordination of one hydroxyl group, present in the supposed [PaO(OH)]$^{2+}$ precursor, to obtain coherent complexation constants. Therefore, we predict that this hydroxyl group is maintained in the formation of 1:1 complexes while we confirm that it is withdrawn when coordinating three sulfate or oxalate ligands. Finally, we stress that this work is a first step toward the future use of theoretical predictions to elucidate the enigmatic chemistry of protactinium in solution.