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.

中文翻译：

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使用计算方法确定离散水性氧化还原反应子步骤的动力学：应用于钚基 (PuO2+/2+) 与 Fe2+、Fe3+ 和羟基自由基 (•OH) 的反应

钚等锕系元素的溶解度和迁移率高度依赖于它们的氧化态，五价和六价物质形成可溶性锕基离子（例如，PuO2+/2+）。虽然存在关于这些物种的平衡热力学的重要数据，但锕系反应的动力学数据集不太可靠。为了更详细地了解这些反应，本研究评估了不同子步骤对水性反应总体速率的影响程度。在这种方法中，反应分为三个步骤：（1）反应物在溶液中相互扩散以形成外球复合物，（2）从外球复合物到内球复合物的转变，以及（3）一个电子的转移。我们使用碰撞理论解决相遇频率，最后两个步骤使用量子力学建模来分析能量以及原子电荷和自旋，作为两种反应物之间距离的函数。这种方法适用于 PuO22+ 和 PuO2+ 水解物质与 Fe2+、Fe3+ 和羟基自由基 (•OH) 在高 pH 值下的反应。无论水化处理方案或自旋配置（显式与显式与隐式连续模型；铁磁与反铁磁），一旦物种在 7.3 到 11.0 Å 的距离内，就会发现外球复合体的形成是能量的有利。即使在与环境相关的钚酰基浓度较低的情况下，该过程也能快速进行。plutonyl 在本体溶液中的半衰期（即，即使初始浓度低至 pM 范围，尚未形成外球复合体的浓度小于 2 分钟，如果浓度更高，则迅速增加。本研究开发了一个程序，根据从量子力学能量曲线得出的活化能和速率常数，确定不同物种随时间的浓度。该程序的结果表明，由于碰撞，外球结构在与外球复合体形成相似的时间尺度内被消耗，然后迅速转化为热力学有利的内球复合体。从量子力学计算，系统能量与反应物距离的变化揭示了从外球到内球复合体的转变，随着物理和电子结构的具体变化。与第一个水合球之间的氢键相关的能量增益驱动反应形成逐渐互连的复合物。在含有 Fe2+ 的模型中，电荷和自旋分析证实内球复合体的形成与 Pu5+ 和 Pu6+ 的还原一致。由于在此氧化还原过程中，当 Fe 和钚基的自旋方向相反（反铁磁情况）时，整个系统的角（自旋）动量没有变化，因此这种自旋配置更有可能进一步进行电子转移。全面的，不同复杂构型之间转化的衍生动力学表明，这些反应的碰撞和从外球到内球的转化进行得很快，并且可能不会限制这些系统的速率。这种方法可以深入了解限速子过程，并使我们能够更详细地探索 Pu 和其他金属的氧化还原行为。现在可以合理地扩展计算方案来确定矿物-溶液界面上复合物形成的动力学，并结合 Marcus 理论计算来确定依赖于复合物的氧化还原过程的显式电子转移速率。