Determining the kinetics of discrete aqueous redox reaction sub-steps using computational methods: Application to reactions of plutonyl (PuO₂^+/2+) with Fe²⁺, Fe³⁺, and hydroxyl radical (•OH)

Abstract

The solubility and mobility of actinides, such as plutonium, are highly-dependent on their oxidation state, with the penta- and hexavalent species forming soluble actinyl ions (for example, PuO₂^+/2+). While significant data exist on the equilibrium thermodynamics of these species, the kinetic datasets for actinide reactions are less robust. To understand these reactions in greater detail, this study assesses the degree to which different sub-steps affect the overall rate of an aqueous reaction. In this approach, reactions are broken into three steps: (1) the diffusion of reactants toward each other in solution to form an outer-sphere complex, (2) the transition from outer- to inner-sphere complex, and (3) the transfer of an electron. We address encounter frequency using collision theory and the last two steps using quantum-mechanical modeling to analyze the energy, as well as atomic charges and spins, as a function of distance between the two reactants.

This approach is applied to the reactions of PuO₂²⁺ and PuO₂⁺ hydrolysis species with Fe²⁺, Fe³⁺, and hydroxyl radical (•OH) at high pH. Regardless of the hydration treatment scheme or spin configuration (explicit vs. explicit with an implicit continuum model; ferromagnetic vs. antiferromagnetic), once species are within distances of 7.3 to 11.0 Å, the formation of an outer-sphere complex is found to be energetically favorable. This process proceeds rapidly even at low, environmentally-relevant plutonyl concentrations. The half-life of plutonyl in the bulk solution (that is, that which has not yet formed an outer-sphere complex) is found to be <2 min even with initial concentrations as low as the pM range, increasing rapidly if concentrations are more elevated. A program was developed in this study to determine the concentrations of different species over time based on the activation energies and rate constants derived from quantum-mechanical energy curves. Results from this program indicate that the outer-sphere configuration(s) are consumed over similar time scales as those of outer-sphere complex formation due to collision and then convert quickly to thermodynamically-favorable inner-sphere complexes.

From the quantum-mechanical calculations, changes in system energy versus reactant distance reveal the transition from outer- to inner-sphere complex, along with specific changes to the physical and electronic structure. The energy gain associated with hydrogen bonding between the first hydration spheres drives the reaction to form progressively interconnected complexes. In the models with Fe²⁺, charge and spin analysis confirms the formation of the inner-sphere complex is coincident with the reduction of Pu⁵⁺ and Pu⁶⁺. Since there is no change in angular (spin) momentum of the overall system when the spins of Fe and plutonyl assume opposite directions (antiferromagnetic case) during this redox process, such a spin configuration is more likely to further electron transfer. Overall, the derived kinetics of the conversion between different complex configurations indicate that collision and outer-to-inner sphere conversion of these reactions proceed quickly and are likely not rate-limiting for these systems.

This methodology can provide insight into rate-limiting sub-processes and allow us to explore the redox behavior of Pu and other metals in greater detail. The computational scheme can now be reasonably extended to determine the kinetics of complex formation at mineral-solution interfaces and also combined with Marcus theory calculations to determine explicit electron transfer rates for complex-dependent redox processes.