An approach for modeling electron transfer in solids and at surfaces of iron-(oxyhydr)oxides and other redox active solids has been developed for electronic structure methods (i.e., plane-wave density functional theory) capable of performing calculations with periodic cells and large system sizes efficiently while at the same time being accurate enough to be used in the estimation of the electron-transfer coupling matrix element, V_AB, and the electron transfer transmission factor, κ_el. This method is an extension of the valence bond theory electron transfer method for molecules and clusters implemented by Dupuis and others and used extensively by Rosso and co-workers in which scaled corresponding orbitals derived from the Bloch states are used to calculate the off-diagonal matrix elements H_AB and S_AB. A key development of the present work is the formulation of algorithms to improve the accuracy of the integration of the exact exchange integral in periodic boundary conditions. This method is demonstrated on model systems for electron small polaron transfer in iron-(oxyhydr)oxides, including bare Fe²⁺–Fe³⁺ ions, and in [Fe³⁺(OH₂)₂ (OH^–)₂)]_nⁿ⁺ chains representing the common edge-sharing Fe octahedral motif in these materials.

中文翻译：

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过渡Bloch态衍生的相应轨道，用于过渡金属氧化物的电子转移计算

对于电子结构方法（即，平面波密度泛函理论），已经开发出一种模型化固体以及氧化铁（羟基氧化物）氧化物和其他氧化还原活性固体表面的电子转移的方法，该方法能够使用周期单元和大型系统进行计算尺寸有效，而在同一时间在电子转移耦合矩阵元件，的估计中使用是足够准确的V _AB，和电子传递透射系数，κ _EL。此方法是Dupuis等人实现的分子和簇的价键理论电子转移方法的扩展，并由Rosso和同事广泛使用，其中使用从Bloch态得出的比例化的对应轨道来计算非对角矩阵元素H _AB和S _AB。当前工作的关键发展是制定算法，以提高周期性边界条件下精确交换积分的积分精度。该方法已在用于电子小极化子转移的铁-（羟基氧化物）氧化物（包括裸Fe ²⁺ -Fe ³⁺离子）和[Fe ³⁺（OH ₂）的模型系统中得到了证明。₂（OH ^- ）₂）] _Ñ ^{Ñ +}代表链中的共同的边缘共享的Fe八面体基序中这些材料。