Surface diffusion can bring redox pairs closer together, which is necessary for electron transfer to happen, thereby strongly influencing the overall kinetics. However, little is known about the diffusion kinetics of redox-active species on pyrite and other sulfides, which aid in catalyzing many redox reactions. Here, we calculate the diffusion of oxidant (UO₂²⁺) and reductant (Fe²⁺, HS^–) species on pyrite {100} surfaces using quantum-mechanical calculations. Energy curves along different diffusion paths are derived for both inner- and outer-sphere complexes by moving the species in small increments (0.05–0.25 Å). The diffusion path along the molecular ridges formed by disulfide groups on the uppermost pyrite surface has the lowest energy barrier for the diffusion of all species tested. Single-particle diffusion coefficients along their optimal diffusion pathways are derived from diffusion energy barriers and attempt frequencies. Calculations are performed on flat defect-free pyrite surfaces, while on actual surfaces, diffusion is affected by defects, steps, and impurities. Calculated mobilities of the outer-sphere complexed uranyl and ferrous iron are about 4–5 times faster than their inner-sphere ones. Although the results here focus on single-particle diffusion, UO₂²⁺-HS^– was used as an example for interdependent multiple-particle diffusion on the pyrite surface. Interactions between diffusing species (uranyl vs HS^–), and to a limited degree jump correlations, were derived quantum-mechanically. Interactions are a combination of electronic interactions underneath the mineral surface and through the aqueous near-surface region; their interdependent diffusion can be approximated by apparent Coulomb interactions (with a dielectric constant of ∼7.7) for processing in subsequent Monte Carlo simulations.

中文翻译：

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黄铁矿表面吸附物质的扩散动力学

表面扩散可以使氧化还原对更靠近，这是发生电子转移所必需的，从而强烈影响整体动力学。然而，关于氧化还原活性物质在黄铁矿和其他硫化物上的扩散动力学知之甚少，这有助于催化许多氧化还原反应。在这里，我们计算氧化剂 (UO ₂ ²⁺ ) 和还原剂 (Fe ²⁺ , HS ^–) 使用量子力学计算在黄铁矿 {100} 表面上的物种。通过以小增量 (0.05–0.25 Å) 移动物质，可以推导出内球和外球复合物沿不同扩散路径的能量曲线。沿着由最上层黄铁矿表面上的二硫化物基团形成的分子脊的扩散路径对于所有被测物质的扩散具有最低的能量势垒。沿其最佳扩散路径的单粒子扩散系数来自扩散能垒和尝试频率。计算是在平坦的无缺陷黄铁矿表面上进行的，而在实际表面上，扩散受缺陷、台阶和杂质的影响。外球复合铀酰和亚铁的计算迁移率比内球快约 4-5 倍。₂ ²⁺ -HS ^–被用作黄铁矿表面上相互依赖的多粒子扩散的例子。扩散物质（铀与 HS ^-）之间的相互作用以及有限程度的跳跃相关性是通过量子力学推导出来的。相互作用是矿物表面下方和通过含水近地表区域的电子相互作用的组合；它们的相互依赖的扩散可以通过表观库仑相互作用（介电常数为~7.7）来近似，以便在随后的蒙特卡罗模拟中进行处理。